SHA544: Displacement and Negotiated Pricing

Transcription

1 SHA544: Displacement and Negotiated Pricing

2 MODULE OVERVIEW Module 1: Introduction to Displacement It's critical to create the right mix of negotiated group rate customers and transient customers. Generally, the posted prices offered to transient guests are higher than those offered to groups. Transient guest revenue, however, is not guaranteed. Knowing the occupancy rates for your facility, including the number of guests you turn away because no rooms are available, helps you determine what mix of negotiated and transient rooms will maximize revenue for your hotel. By the end of this module you will be able to: Determine the fraction of your business that should be allocated to group business Determine the break-even point for group requests of multiple-night stays with and without ancillary costs Determine the implications of multiple rate classes and multiple lengths of stay on group break-even prices

3 TOPIC OVERVIEW Topic 1.1: Strategic Segment Allocation Through a strategic approach to segment allocation, the hotel estimates what percentage of its inventory it should make available to groups and what percentage it should "protect" for transient sales. The hotel's decision regarding how many rooms to allocate to groups must consider the potential revenue lost from having those rooms unavailable to transient guests. This topic examines these issues. By the end of this topic, you will be able to: Determine the fraction of your business you should allocate to group business Apply a strategic approach to allocating rooms to group and transient segments

4 Segment Contracts Group business is the segment of hotel business that is transacted in a negotiated fashion. Types of group or negotiated business include: Associations (national, regional, governmental, educational, etc.) Corporate groups Local social organizations and clubs Work teams or crews (pilots and flight attendants) Wholesalers Other volume accounts By their negotiated nature, group bookings are different from transient bookings. For example, groups negotiate blocks of rooms at specified, discounted rates. Group rates are established well in advance of the stay date-often a year in advance or more. Group packages are for blocks of rooms (typically ten or more). Group contracts often stipulate a cut-off date, the last date at which the group can book rooms at their discounted rate. Beyond that date, rooms are booked at the standard transient rate. G roup rate offers may also involve fees for attrition, or wash-groumaterialize. The group contract may stipulate a penalty if the group books fewer rooms than the contracted reservations that are planned for but that do not block. Different group types may have different arrangements. Negotiated rates for corporations, governments, or crews, for example, are often not associated with specific dates the way conferences or wedding bookings would be. Often, corporate, government, and crew negotiated rates have other stipulations, such as blackout dates during which stays would be booked under the standard transient rate, not the contracted rate. Some contracts also have last room availability (LRA) clauses, under which the contracted rate is available as long as there are rooms of any type available. If a contracted rate does not have an LRA, the hotel may close out the rate class specified in the contract, making it unavailable to be booked. For all intents and purposes, the rooms associated with a group rate are considered unavailable for booking by nongroup members. This blocked nature of these rooms, in concert with potential attrition, indicates how important it is to manage group bookings with an effective revenue management strategy. In this course, you consider the booking challenges faced by fictional character Pascale Moreau, the rooms division manager at Hotel Ithaca, a fictional 210-room hotel. In this scenario, the hotel historically has allocated about 25% of its rooms to group business of all types, leaving just 75% for transient business. Pascale is trying to decide if she should increase her sales efforts to attract more group business. She knows that, in the past, the hotel has had to turn away higher-yielding guests because too many rooms were allocated to groups. Yet there were also periods with significant vacancies when Pascal would have welcomed group business. Let's take a closer look at this issue of group vs. transient business, to see if we can help Pascale in her analysis of Hotel Ithaca's segment mix.

5 The Segment Mix When analyzing a segment mix, consider the characteristics of the different segments that make inventory requests. Transient business, or guests who are not part of a group or contract sale, typically make requests closest to the arrival date, generally within 90 days before arrival. Among group contracts, negotiations for corporate and government contracts generally take place once a year, whereas negotiations for large group blocks for an association or conference often take place two years in advance. Timing affects rate negotiations, so the rates associated with these segments differ, too. Reservations made the furthest in advance receive the lowest rates or the greatest discounts, so association rates are typically the lowest, followed by government rates; there is an increase for corporate contracts, and finally transient rates are the highest. This rate mix presents a dilemma for revenue managers: how many group rooms should be sold in advance of the later-arriving, higher-yielding segments? You can strategically approach this allocation decision with a focus on marginal value. Once a room is booked as part of a group block, that room is unavailable to transient guests. If demand may be great enough that the room could be sold to a higher-paying, later-arriving transient guest, we may not want to use it for a group booking now. How should we decide? One way is to compare group revenue to the lost potential revenue from transient guests. Figure 1 above illustrates a segment mix in which only 20% of bookings are transients, the other 80% being group segments.

6 Allocating Rooms at Hotel Ithaca A video presentation appears below, along with a text transcript. Use these resources to learn about allocating rooms. Transcript: Allocating Rooms at Hotel Ithaca So, today our focus is going to be a long-term focus on groups, specifically on the segment mix. So when we focus on groups, we're really talking about non-yieldable business. So this is may be an association or a meeting. Maybe a local social event, airline crew, wholesalers, any sort of non-posted price transaction, where there has been some negotiation that's taking place in setting that rate and also the volume associated with that rate. So, when we look at this sort of mixed decision we're trying to really sort of strategically look at what proportion or what fraction of my property should be allocated to these distinct segments. So what fraction should be groups? What fraction should be sort of "groups and government" and then what fraction should be "groups, government and corporate"? Then lastly, what's my total mix? So what we're going to go through here is a set of steps on how to determine what this allocation should be, based on the rates these different segments yield. When we focus on the segment mix, one of the things that's important to realize is that typically these segments are going to arrive or make requests for inventory in increasing yield order. So groups are going to make their requests one to three years in advance and they're going to be at the deepest discounts. Typically maybe a government contract is negotiated once or twice a year or once a year, a little less frequently than a corporate contract and then lastly, transient business is arriving in the last 30, 60, 90 days before check-in. So this business is arriving in the same sort of order as they are yielding and so ultimately our focus is going to be on the marginal value of the rooms we allocate to each of these segments. So let's walk through an example so we see how the mechanics work here. So let's focus on Hotel Ithaca again. Remember, Hotel Ithaca has 210 rooms. For simplicity we're going to focus on just two segments, transients and groups, but the focus of what we talk about here can be extended to if we want to focus on not just transient groups, but also corporate and government. So our transient ADR is forecasted or budgeted for around 258 euros for two years from today. Right now group rates are coming in or group requests are coming in right around 169 euros. Historically our transient demand for this period has been around 150 rooms with the standard deviation of around 30. So, we know we're two years before that arrival date and we're trying to get a sense of what should be that group mix for that period given estimated prices, as well as estimated demand for that period.

7 So, given that our capacity is 210 and our typical demand is 150, obviously we have some surplus capacity, but how much-10, 20, 30 rooms? It's hard to say how many of those rooms we should allocate to groups. So let's focus on say the decision should we allocate 65 rooms to groups or should we allocate 64 rooms to groups? So if I allocate 65 rooms to groups, that means I'm reserving 145 rooms for these transients, whereas if I allocated 64 rooms to groups I would be allocating 146 rooms to transients. So really, what's the value of that 146th room? Is it better off being a transient room or should I accept this group request that's coming in? So now, that 146th room is a transient room, we only sell that if transient demand is greater than or equal to 146. So let's for simplicity assume that demand falls in normal distribution, so it's relatively symmetric around that mean of 150 and it has this standard deviation of 30. We can then estimate the probability that demand is going to be at least as big as 146. So if we're using Excel for that, we use the NORMDIST function in Excel. Remember that the NORMDIST function in Excel gives us the probability that demand is less than or equal to some point. We are focused on demand being greater than or equal to that point. So we're going to talk about one minus NORMDIST and again, we're focusing on this 146th room. So if we were to estimate the probability that demand is greater than or equal to 146, given that has a mean of 15, a standard deviation of 30, that results in a probability of.55. So there is a 55 percent chance we're going to sell that 146th room-.55 times 258 is right around 143 euros. So that tells us that 146th room, so what we're going to sell it for times the likelihood we're going to sell it is right around 143 euros, which is less than this group-this forecasted group rate of 169 euros. So therefore, this room is better off to be allocated to the group segment versus held back for the transient segment. We could extend this logic now and focus on well, what about the 145th room? What about the 144th room? So as I allocate less rooms to transients, i.e., more rooms to groups, so 66 rooms to groups, 67 rooms to groups, 68 rooms to groups, then the probability of selling those rooms increases. We want to keep allocating more rooms to groups, less rooms to transients, until this point such that the probability we sell that room at the transient rate times 258 is equal to 169. So this point and we're indifferent to keeping it as a group room versus a transient room. In Excel we can do this with the NORMInverse function and just like NORMDIST tells us the probability of being less than or equal to something, NORMInverse also talks about what number has this associated probability. We're going to focus on the right tail, so we're going to do NORMInverse of one minus 169 over 258, given we have a mean of 150 and a standard deviation of 30 and this critical point turns out to be 138 and change. So given that we can't allocate a partial room, we're going to round that down to 138. So basically keep 138 rooms for transients, therefore our group mix here is going to be 210 minus 138 or 72. So we can allocate segments similar to how we had been allocating rate classes in the past. It's the same sort of logic based upon when they arrive and what their resulting revenue streams are.

8 A Guide to Room Allocation The revenue manager's goal is to determine the fraction of the property to set aside or protect for each segment: transient, corporate, government, etc. As discussed in the video on the previous course page, you can perform a segment evaluation to determine the optimum segment mix for your hotel. This is a step-by-step guide to a segment mix calculation evaluating transients vs. group. Step-by-Step Guide to Calculating the Value of the "Last Room" and Using It for Room Allocation 1. Get historical data for your hotel: ADR and demand (occupancy) data sorted by segment. 2. Calculate the average ADR for transients and for groups. 3. Calculate the average and the standard deviation for demand for each segment. 4. Use probability to determine whether the last room is more valuable as a transient room or as a group room. a. Using the Excel function NORMDIST, get the probability that the demand is less than or equal to the number of rooms you allocated for transients. The values to enter for this function are: the number of rooms, the average demand, the standard deviation of demand, and 1. (By entering "1" you indicate that you want the probability that demand is less than or equal to a particular value-cumulative; an entry of "0" results in the probability that demand is that value.) b. Subtract your answer in part (a) from 1 to get the probability that the demand is at least as big as your allocation: 1 NORMDIST(x). This value is the probability of selling the last room to a transient guest. 5. Find the value of that last room as a transient room using the equation Room Value = (Segment ADR) * (1 NORMDIST(x)). If the value of the room as a transient room is LESS THAN the group ADR, you should allocate this room to GROUP. If the transient value is greater than the group value, then keep this room for the higher-yielding, later-arriving segment (i.e., the transient rate in our two-segment example). 6. Use steps 4 and 5 to determine the number of rooms to allocate to groups. At some maximum number of transient rooms, the average transient rate will be equal to the average group-segment ADR. That "last room" could be either a group room or a transient room. Example: Allocating Rooms at the Rest-a-While At the 100-room Rest-a-While Hotel, for the fall travel season, group ADRs in the past year have been around 179, whereas transient ADRs are closer to 259. Occupancy (demand) data shows that at times the hotel was well below 100%, while at other times it was full and had to reject some high-yielding transient guests. It has had average transient room demand of 73 rooms per night, with a standard deviation of 10 rooms per night. (We assume that transient room demand follows a normal distribution.) The current transient-to-group mix is approximately 75:25. If the hotel raises its percentage of group business, maybe it could improve occupancy. On the other hand, if it allocates more rooms to group business, it might have to turn away more high-paying transient customers. Let's try to determine the optimum mix. First, let's answer the question, what is the value of the 75th room as a transient room? To answer this question, we need to know the probability that we will sell that room as a transient room. We need to estimate the probability that demand will be at least 75. Using the NORMDIST function in Excel, NORMDIST(75,73,10,1), we can determine the probability that the demand is at

9 most 75. We can then calculate 1 NORMDIST(75,73,10,1) to get the probability that the demand is at least 75. In this case, 1 NORMDIST(75,73,10,1) = This means that the 75th room only sells 42% of the time. In other words, 42% of the time, the 75th room generates 259 and 58% of the time it generates 0, if it is allocated as a transient room (not allowed to be booked as a group room). As a result the value of the 75th room as a transient room is 259 *.42 = We can use the following equation to determine how much the room is worth as a transient room: This equation tells us that, on average, the last transient room (the 75th room) is worth only 109. If we sell this room as a group room at an average ADR of 179 instead, we will be better off, on average. Apparently, the Rest-a-While Hotel should allocate a smaller number of rooms to transient business. But how many? If we do the same calculation for 74 rooms, 73 rooms, 72 rooms, and so on, we find that those numbers are also too high. It's not until the 68th room that we get an average of 179 in revenue, equal to the average group-segment ADR. So the hotel should not allocate any more than 68 rooms to transient business, and in fact that 68th room could be either a group room or a transient room. The optional video provided below is for learners who would like additional information on customer segmentation. Transcript: Customer Segmentation and Demand Controls Using customer segmentation and inventory controls to manage revenue is commonplace in many industries. But this wasn't always the case. The airline industry has a strong influence in their use. Today you find a lot of volatility in airfares, but this is a relatively new phenomenon.

10 In the early years of air travel U.S. airlines were subjected to government regulations that consistently kept fares high and made air travel a luxury item. But eventually the demand for more affordable air travel led to the passing of the Airline Deregulation Act in The result of this act was complete elimination of fare restrictions, leaving the airline industry in a free market. Almost immediately, a number of new airlines arose to compete with the existing carriers and the number of passengers dramatically increased. A new way of pricing was introduced as existing carriers (serving guests willing to pay higher prices) now also had to offer lower prices to compete with new entrant airlines. So how did they price? They began with segmenting customers. If we oversimplify we could assume there are only two types of customers seeking to travel-business customers travelling for work-related issues and leisure travelers. The typical business traveler is willing to pay a higher price in exchange for flexibility of being able to book a seat at the last minute (or cancel his ticket if his plan changes) while the vacation traveler is willing to give up some flexibility for the sake of a more inexpensive seat. The demand from the price-sensitive customer tends to come before the demand from business customer. But with multiple price points and demand for more expensive seats arriving after price-sensitive demand the airlines had to determine how many seats they should sell to the early price-sensitive customers and how many they should protect for late, full-fare customers. If too few seats are protected, the airline will lose the full-fare revenue. If too many are protected, flights will leave with empty seats. Littlewood (working for British Airways) proposed a way to make this determination. He proposed that discount-fare bookings should be accepted as long as their value exceeds that of anticipated full-fare bookings, assuming that customers can be segmented according to when they purchase their tickets. This simple, inventory control system was the beginning of what eventually lead to revenue management. Using Littlewood's approach we can designate two fare classes as having fares of R2 and R1, where R2 is greater than R1. The demand for class R1-the lower fare-comes before demand for class R2. The question now is how much demand for class R1 should be accepted so that the optimal mix of passengers is achieved and the highest revenue is obtained? Littlewood suggested closing down class R1 when the certain revenue from selling another low fare seat is less than the expected revenue of selling that same seat at the higher fare. In other words, as long as the probability of selling all remaining seats at the higher price is greater than the ratio of the lower price over the higher price, we are better off not selling at the low price and keeping it for the high price. This is our Target Probability. Let's look at an example. Grand Sky Airlines sells tickets on one of its 85-passenger planes for 150 (the discounted fare) and 250 (the full-fare). In general, their customers are aware of the pricing and those seeking discounts tend to book early. Sean, one of the managers at Grand Sky, knows that he can fill his entire plane at 50 per seat if he so desires, but at some point it is best to stop selling discounted seats and reserve some inventory for later arriving higher yielding ( 250) passengers. How does Sean calculate this target or the point at which to stop selling 150 seats and reserve the remaining seats for the 250 customers? Using Littlewood's rule (R1 divided by R2) we can calculate Sean's target probability. In this case it is.6 or 60%. As long as the probability of selling all remaining seats ("n" seats) at 250 is equal to or greater than 60% then Grand Sky is better off selling seats at 250. Now we need to calculate the probability of selling "n" or more seats. We use historical data to help calculate the probability of future events. The graph shows the number of 250 seats Grand Sky Airlines sold each day for the last 100 days.

11 For example, seats were sold on one of the days and seats were sold on 12 of the days. Now we can calculate the probability of selling at least a certain number of seats at 250 and compare that number to our target of 60%. To calculate this probability, divide the number of days we sold "n" or more seats by the total observations. We could start the calculations at any point (selling 24 or more seats, selling 25 or more seats, etc.). But we can use our graph to select a reasonable starting point. On the graph we see that the mid-point is around 34 seats. This will make a good starting point for our calculations. It may be easier to calculate these probabilities if we look at the data in a table format. This table displays the same data that we just saw in the form of a graph. We want to calculate the probability that there will be future demand for 34 or more seats. Start by finding the number of days 34 or more seats were sold in the past. To do this, add the frequencies when demand was 34 or more seats. We add the frequency of demand at 34, 35, etc. up to 41 together to arrive at 56 days when demand was 34 or more seats. Now divide 56 by the total observations (100). This gives us the probability that demand will be greater or equal to 34 seats at 250 as.56 or 56%. If we do the same calculation for the sale of 33 or more seats we arrive at a probability of 68%. Now we can compare these probabilities to our target probability. Remember, as long as the probability of selling all remaining seats at 250 is 60% then Grand Sky is better off selling seats at 250 rather than 150. The probability of selling the 33rd seat at 250 is 68% thus greater than 60% and the probability of selling the 34th seat at 250 is 56%, less than 60%. We can also look at this from a monetary viewpoint. The probability of selling 34 or more seats at 250 is 56%. To find the expected revenue of the last seat we sell multiple.56 by 250 which equals 140. Given the expected revenue of the 34th seat is 140, less than the 150 we obtain for certain if sold as a discounted seat, 34 seats is not our threshold. Let's look at selling 33 or more seats. This probability is 68%, giving us an expected revenue from selling the 33rd seat at 250 of 170. We can go back to our original question: What is the point at which to stop selling 150 seats and reserve the remaining seats for the 250 customers? Assume that on our 85 seat plane the 85th seat is sold first and the 1st seat is sold last. Thus the airline is better off selling up to 52 seats (85 total minus 33) at 150 and reserving the remaining 33 seats for the 250 paying customers. In essence we are calculating the expected marginal revenue of keeping a seat (or room) for later arriving higher yielding guests. We should continue to sell at lower discounted rates as long as these rates exceed the expected marginal revenue of selling at higher rates.

12 TOPIC OVERVIEW Topic 1.2: Tactical Segment Allocation So far our approach to group decisions has been very strategic. Essentially, we have asked, "What fraction of my property (or fleet) should be allocated to each segment?" Now let's consider a tactical approach to segment allocation. Here we evaluate each (group) request individually, to determine the revenue from the room bookings plus the potential ancillary revenue. In this topic, we tactically decide between individual group requests and demand, assessing the group booking's potential impact on transient room availability. By the end of this topic, you will be able to: Determine under what conditions a group room block request provides incremental revenue Decide whether to accept a large block of negotiated business at a discounted rate based on break-even information Determine displacement by rate class

13 Calculating the Group Break-even At the simplest level, the decision to book a group depends on whether the group contribution gained is likely to be greater than the transient contribution lost through displacement. That is, the hotel must decide if it is worth it to book the group and not have those rooms available for transients to book later. At the very least, the group contribution gained must be enough for the hotel to break even, or recover that lost contribution. You can calculate the group break-even rate by setting the group contribution equal to the displaced contribution and solving for the rate. If we assume that the group is only staying one night, the two contributions can be expressed very simply. The group contribution can be written as the number of rooms in the group block B multiplied by the group rate G minus variable cost VC: The number of rooms (likely to be) displaced is calculated as the number of rooms in the group plus forecasted demand minus capacity: Here the displacement results when rooms set aside for the group become unavailable (hence not reservable) by later-arriving forecasted demand. The contribution that might be lost due to displacement is simply the number of rooms displaced multiplied by their ADR (rate R) minus variable costs: When the group contribution is just enough to break even, it is equal to the lost transient contribution. We can write the relationship like this: Finally, we can solve this equation for G, the break-even rate: Professor Anderson presents this break-even calculation along with an example in the video on the next course page.

14 The Group Break-even at Hotel Ithaca A video presentation appears below, along with a text transcript. Use these resources to find out how ancillary contributions are included in calculating the break-even. Transcript: The Group Break-even at Hotel Ithaca So now our focus is going to be more tactical, sort of medium term in nature, and these are individual group requests. So these are typically six months to a year and a half before their check-in date and our focus is going to be on a size of a group request and the associated price with that group request. We're going to focus on the break-even price, i.e., the price at which we're indifferent to accepting the group versus selling to transients. So one of the things to keep in mind here is groups are coming in six months, a year and a half prior to check-in, and the transients are coming in 30, 60, 90 days. So if I accept this group request, that means I don't have those rooms available to sell to these later-arriving, higher-yielding transients. So our focus is going to be on here this group taking inventory away from transients. One of the keys here is that groups are usually incremental demand. This is new demand to your market. It's not included in part of your forecasted demand. So if you accept this group as this new demand, it's not going to be dilutive; these people wouldn't have been there otherwise. So here is our situation. We have forecasted transient demand for a particular stay date. Our request comes in for a block of rooms for a group, most likely at some deep discount. So we do accept that request, reject it, or more generally, under what conditions would we like to accept that request? Let's have a little nomenclature here. So, our hotel has capacity C rooms, which typically have a variable cost of VC. We have an ADR of R and the day in question has a forecasted demand of D. A group block has come in requesting B rooms for the same stay date. So, we have two potential situations here. So the group block plus our forecasted transient demand could be less than capacity or it could be more than capacity. If the group block plus the transient request is greater than capacity, given that the group request comes in first, that means we're going to have to reject some of these transients, because we no longer have the space available. We refer to these transients that we have to reject as a result of accepting the group block as "displacement" or "displaced transients." So now, we can focus on, when do I like this group? So I've got this group block B coming in, say with some group rate G minus their variable cost. So that's the contribution that this group brings in. So the group block times its contribution per

15 room. The flip side, if I accept this group, then I'm going to displace some of these transients potentially and so the transients that I displace are going to be my group block plus my forecasted demand for transients minus my capacity. So those are the transients that I otherwise would have accepted, but now I have to reject. Had I accepted those I would have made my regular rate minus variable costs and contribution. So that is what I lose if I accept the group versus I gained the actual group contribution. So we can simply set these two expressions equal to each other. So when is the group contribution equal to the displaced transient contribution? Then we can do a little bit of algebra and our goal here is to solve for this group rate. Solve for this break-even group price. So we're simply going to take the B over to the right-hand side of our expression, then we'll also move their variable cost over to the right-hand side and so now basically I have my group rate equals my variable cost plus my transient contribution times my displacement divided by my group block. So, B plus D minus C divided by B. That's what fraction of that group block is displaced. So now we can simply solve for G, knowing all our other inputs. So let's do an example. So we have a 210-room facility. Our forecasted regular rate for this particular stay date is 195 euros with 25 euros in variable costs. Our forecasted occupancy for this particular date is 70 percent or 147 rooms. A group request has come in for 110 rooms, so B is equal to 110. So, do we have any displacements? Yes, because 147 plus 110 is bigger than 210. At actually 110 plus 147 minus 210 equals 47. So if we accept this group request we displace 47 transients. So now we can calculate this group rate with our variable cost plus my transient contribution, which is 195 minus 25 times what fraction of this group request is displaced transients, i.e., times 47 over 110, and that equals 9,764. So if this group was to pay 98 euros, then I would be indifferent to the group and not having the group. So not that you're going to sort of quote them 98 euros, but now you have a point at which to start negotiations and obviously as you negotiate above 98 euros, this group is going to bring in incremental contribution. One of the things about groups is that they typically spend more time at your property than a regular transient guest. So they are typically doing some activity in or around your property versus just visiting the area. So as a result of that they tend to spend more money than a typical guest. So we should sort of factor that in when talking about the contribution of this group. So remember, before we had group contribution, group block times group rate minus variable contribution. On the other side we had transient contribution times displacement. Now, on the left-hand side, now we're going to have some additional contribution. We'll refer to that as ancillary contribution and so this is non-rooms contribution that the group brings in. So we can bring all our terms back to the right-hand side and so basically we end up with a similar expression, where we have my break-even group rate equals my variable costs minus this per-room incremental ancillary contribution, so that ancillary contribution divided by the group block. So that's the per-group-room ancillary contribution and then plus this fraction of lost transient contribution. So this logically you can see here is that this is the same expression as before, but now we have this minus ancillary contribution divided by B on the right-hand side and so that tells you now this break-even group rate is going to be lower, as the group brings in incremental ancillary.

16 Break-even with Multiple-night Stays As you now know, the group contribution and the lost contribution due to displacement are equal at the break-even point, and this relationship can be written very simply for the case that the group is staying only one night: In reality, though, most groups stay longer than one night. In fact, they have a higher average length of stay than transients. Fortunately, we can use the equation above as a starting point to consider multiple stay dates. Extending it to multiple stay dates for the group gives us the following equation: The sums from 1 to n represent the group stay dates. Note that the equation allows for a different number of requested group rooms (B i) and different demands on each day. We can augment it to include ancillary contribution (AC) for each of the group stay dates, too: We can rewrite the above equation and solve for G: This gives us the group break-even rate G for the case in which the group stays multiple dates.

17 Considering Multiple-night Stays at Hotel Ithaca Let's look at an example of a group room request spanning multiple days. Pascale Moreau, Hotel Ithaca's rooms manager, is evaluating a group request from ABC Corp. for stay dates Oct She has documented the forecasted demand for the block of dates in question. The capacity of Hotel Ithaca is 210 rooms with each room having variable costs of 25 and an average daily rate of 179. Once Pascale has all the forecast figures, she needs to determine transient displacement. She uses the following formula to calculate displacement: For example, for October 17, the group request is 25, the demand is 205, and the hotel capacity is 210. Pascale finds that displacement = = 20. That is, on October 17, 20 transients would be displaced. Pascale calculates displacement for each of the five stay dates. She gets the following: Now Pascale must determine the lost revenue from displaced transient guests. The total number of displaced guests from Oct is 133. (This is the sum of displaced transients across each of the group stay dates.) The contribution lost due to displacement is calculated as: She calculates the displaced contribution as 133 * (179 25) = 20,482.

18 Pascale now knows that to break even on the ABC Corp. rooms, she needs at least 20,482 in revenue for the negotiated group rate. She also knows that the total number of group rooms requested is 195 (the sum of group rooms across group stay dates). Now she can calculate the break-even rate with the following equation: Break-even Rate= ( 20,482 / 195) + 25 = (Pascale has decided to disregard ancillary contribution here.) So Pascale must charge ABC Corp. a group rate of at least to break even.

19 Evaluate Group Request: Review In the previous exercise, you evaluated a group request with ancillary costs. Here is a guide to how we calculated the answers to the questions. The values found are:

20

21 Displacement of Multiple Rate Classes A video presentation appears below, along with a text transcript. Use these resources to learn about allocation of multiple rate classes. Transcript: Displacement of Multiple Rate Classes So up until this point we focused on relatively simple group requests and at the same time we've looked at transients really from a very simple ADR standpoint. What we're going to focus on now is a little more realistic approach, where the group request is coming in for multiple days and we have the potential to displace transients across multiple rate classes on each of those multiple stay dates. Of course, we're going to have some ancillary contribution that the group brings in. So we can use our original framework of group contribution versus displaced transient contribution. We're just going to augment that across rate classes and across stay dates. So remember we had the group block B times the group contribution G minus variable costs. On the right-hand side we had our transient contribution, our transient rate minus variable costs times our displacement, where the displacement was the group demand plus regular demand minus capacity. If I have multiple stay dates, then I'm just going to sum up both sides, their left-hand side and their right-hand side across my N stay dates. So this group is going to stay potentially across N different dates. For each of those dates they might request different rooms. So I'm going to have a group block B that's going to be potentially different for each of those stay dates. On the right-hand side again, we're going to sum up across all N group stay dates, and just like we have different group requests on those individual stay dates, I may also have different forecasted demand on each of those stay dates and a result of that have different displacement on each of those stay dates. Keep in mind, on the group side we're also going to have some ancillary contribution and that ancillary contribution may be different for each of those stay dates. So one day they may have a banquet, the other day they may not, so they might have different ancillary contributions on different stay dates. We can simplify that expression by moving everything but the group rate to the right-hand side, so we're simply going to have our variable costs minus the sum of our ancillaries divided by the sum of the group block across the N stay dates. So that's the ancillaries per group night. Then we have the sum of the displaced transient contributions across each of those N stay dates. What we do now is we add further complexity, because the displaced transients can occur at multiple transient rates. So

22 we add a second summation, so now we're going to sum across potentially M rate classes. So each of these rate classes can have a different rate and a different contribution as a result of that different rate, and then we may have now different displacement for each rate class for each of those stay dates. So now we have multiple levels of displacement on a given stay day across or up to these M different rate classes. So we're going to have this double summation for this lost transient contribution. Now, this seems more complex if we've added multi stay dates, multi rates, and ancillaries, but one of the things that I want you to realize here, at no time have we talked about length of stay. In essence, we have assumed that the transients that are displaced were all only staying for one night. So obviously, that's going to increase my displacement as I start to displace some two-night stay versus one-night stay.

23 Displacing Multiple Rate Classes at Hotel Ithaca To better understand the value of multiple rate classes, let's look at an example at Hotel Ithaca. This hotel has 210 rooms. Its rates are 195 and 250, and it has 25 in variable costs. A certain group has made a request for two stay dates, for 110 rooms both nights. Now let's look at total displacement for each of these two days. On the first day, the group block of 110 rooms plus the forecasted transient demand of 147 is 257, whereas the hotel's capacity is only 210. The displacement for that day is 47. On the second day, 110 plus 126 transient is 236, so the displacement is 26. The equation for calculating the group break-even rate is: The group rate G is equal to the variable cost, minus some ancillary contribution term, plus a transient displacement term. m is the number of stay dates and n is the number of rate classes. Let's consider two cases for the break-even rate. In the first, the hotel has perfect segmentation; in the second, the hotel does not have perfect segmentation. We'll look at the perfect segmentation case first. If Hotel Ithaca has perfect segmentation, then all the displacement would occur at the 195 rate and there would be no displaced transients at the 250 rate. In this case, we only have to do a single summation, because we have no displacement across the 250 rate. So that simplifies things somewhat. We don't know what the ancillary contribution will be, but we can estimate it based on historical data for similar groups. If our data show that groups spend approximately 10,000 with a margin of 33%, we can estimate that this group's contribution will be 33% of 10,000, or 3,300. We would then divide this amount by 220 (total group rooms over the two days), resulting in 15 of ancillary contribution per room. Because this is added revenue for the hotel, this term reduces the break-even rate. What is the displacement that could result from this group booking? As summarized in the table, we have 73 displaced transient rooms-47 on the 18th and 26 on the 19th. On each of these two arrival days the demand at 195 is greater than the displacement (121>47 on the 18th and 89>26 on the 19th); as a

24 result we could assume that all displacement occurs at the 195 rate. Displacement is accounted for in the final term. R VC, the rate minus the variable cost, is 195 minus 25, or 170. This amount is multiplied by 73 displaced rooms and divided by the total 220 group rooms (over two days). The displacement term is equal to approximately 56. This results in a break-even group rate of , or 66. The Hotel Ithaca will not offer the 66 rate, but this rate provides a floor that the hotel will not go below. Now let's consider the case of imperfect segmentation. Instead of only having displacement at 195, here we end up displacing some 250 guests in addition to the 195 guests. If segmentation is 90% perfect, of those 73 rooms, 63 are displaced at 195 and 10 are displaced at 250. So here displacement results in two displacement terms: This results in a rate of about 59. With variable costs and ancillary contributions, the group rate is 69. This break-even group rate is higher because there is a higher cost associated with displacement. In this example, we have considered multiple stay dates, multiple rates, and ancillary contributions. However, we have not addressed length of stay as it relates to the displaced transients. We will do this in the next course topic.

25 TOPIC OVERVIEW Topic 1.3: Optimizing Segment Allocation In our calculations of group rate thus far, our assumption has been that every displaced guest would have stayed just one night. This, of course, is not always the case. Many displaced guests would have stayed more than one night. In this topic, we go back to the optimization framework to incorporate lengths of stay greater than one. We expect to see displacement increase as we start to displace some two-night stays versus one-night stays. As a result, t he break-even group rate should be higher. Having created a strategic and a tactical approach to segment allocation, we now optimize the allocation by taking into account the length of stay (LOS) of transient guests. By the end of this topic, you will be able to: Use a simultaneous decision-making framework to calculate the break-even price, including multiple rate classes and multiple LOS in the decision process

26 Directly Incorporating LOS Effects In our previous calculations, we assumed that all displaced transient guests are staying for one night only. As we calculate displacements on the group stay dates, we see that if the hotel had an average length of stay (LOS) that was greater than one, then displacement may also occur on shoulder days around the group stay. For example, a transient with a LOS of three days arriving on the last group stay date may get displaced and not book any of the three nights. Therefore, this guest represents three displaced room nights, not just one. As a result, LOS issues increase the break-even group price. In fact, as a rule, displacement increases as the average length of stay increases. Our goal is to minimize the cost of those displaced transients even though this is true. Therefore, we need to use a simultaneous decision-making framework to include length-of-stay impacts as we calculate the (increased) break-even price. We're going to focus on optimization of our simultaneous decision-making framework from earlier. Background information and historic data for Hotel Ithaca is provided. Click here to download. For learners who are interested in additional information on using Solver we include the following video.

27 Transcript: Using Solver We'll use the Hotel Ithaca spreadsheet and Solver to do allocations, generate shadow prices, and use the shadow prices to determine availability. The information on this tab is divided into five parts. Part 1 stores the decision variables. Part 2 stores the total number of rooms sold on each day. This includes both arrivals on that stay date as well as stay-overs-that is, guests who checked in yesterday or the day before and stayed two or three nights. Part 3 contains the rooms available-that is, hotel capacity minus any reservations (and stay-overs) already accepted for those dates. Part 4 stores the total revenue for all rooms and days listed. Part 5 displays the forecasted demand for the stay dates in question. We have already built the model. Now we need to run Solver. Our objective is to maximize revenue by determining the number of reservations we will accept for each day, rate class, and length of stay. We have two constraints. The first is that the number of reservations we are able to accept must be less than or equal to our forecasted demand. The second constraint is that the number of reservations we accept must be less than or equal to the rooms available. We also need to require that the result be non-negative and use "Simplex LP" for a solution method.

28 Considering Multiple LOS A video presentation appears below, along with a text transcript, a spreadsheet document, and an instructional document to assist you in using the Solver tool in Excel. Use these resources to learn about Multiple LOS. Solver instructions are provided. Click here to download. Use the provided spreadsheet to follow along with the video. Click here to download. Transcript: Considering Multiple LOS Our focus now is going to be directly including length-of-stay impacts in how we estimate this break-even group rate. On the assumption that your average length of stay is more than one, then that's going to increase your displacements given a group request. So we need to sort of incorporate that into our modeling framework. Let's focus on Hotel Ithaca again. Hotel Ithaca is selling at three rates and has three different lengths of stay, one, two, and three nights, and has forecasted demand across these rates and has a subset of available rooms for each of these stay dates as a function of current res on hand or prior group requests. So we're going to structure our optimization model or our linear program as before, such that we can maximize revenue. For the time being, let's ignore the group, so let's do this as before, let's help Hotel Ithaca maximize in this stage contribution by first ignoring the group and then we're going to add the group request in. Keep in mind that our rooms sold is the sum of our arrivals plus our stay-overs and our contribution here is going to be the sum of our revenues minus the sum of our rooms occupied minus their variable costs. Earlier, when we talked about maximizing revenue, we ignored our contribution impacts, but again, because we're focused on groups, groups bring in other revenue sources. We're going to focus on contribution. We're going to require Solver to help us optimize this model, so you're going to launch Solver. We're going to do that by making sure that the rooms sold are less than or equal to the rooms I have available and that the rooms that I accept are less than or equal to my forecasted demand. We're going to do this by changing those reservations that we accept. So which reservation should I accept to maximize my contribution, given that I can't accept more demand than I have and I can't occupy more rooms than I have? This results in a contribution-a maximal contribution of 213,490 euros. So that would be our maximized contribution. Now, let's assume a group request has come in for three nights arriving on October 24th. So they want 50 room nights on the 24th, 50 on the 25th, and 50 on the 26th. Our goal now is to find out this break-even group rate such that we're

29 indifferent between having the group and not having the group. All we simply do now is go back to our model. We insert this group request. So this is a new product we're selling now, which is demand of 50 across these three stay dates. If I accept these 50 room requests on each of these three days, that's capacity I no longer have to sell. So that becomes basically-so some group sold. My total rooms sold now is going to become my transient rooms sold plus my group rooms sold and that has to be less than my available rooms. I rerun my model and as a result of that my contribution is now 185,710 euros, a lot lower, but keep in mind all we did at this stage was allow the group access to rooms, but not bring in any revenue. Of course that's going to lower our contribution, but the question is by how much? So that's simply the 213,490 minus the 185,710. That's our difference in contribution as a result of accepting the group. Now it should be obvious that I simply take that difference, I divide that by the 150 room-nights that a group has requested. That's the group contribution I need from room revenue. Add back in my variable cost and that's my break-even group room rate. Similarly, I can look at displacements. I can look at what transient rooms I sold before and what transient rooms I sold now, as a result of accepting the group, and that helps you get a sense of where that displacement occurs. As you'll notice, there is some displacement that occurs on stay dates that the group is not staying at your property. Specifically, on some of the shoulder dates around the group you may or may not have displacement as a result of the group given length-of-stay impacts. So the interesting thing here is this goes right back to our earlier discussion, that by having length of stay greater than one, we're going to have displacement on-potentially on-non-group stay dates.

30 Allocate Multiple Rate Classes & Multiple LOS: Review In the previous exercise, you allocated multiple rate classes and multiple LOS. You may download this spreadsheet that displays how we calculated the answers to the questions. Answers 1. Set up and run Solver to calculate the transient revenue two ways. Click to download. 2. Calculate the difference in transient revenue due to the group request. The difference in transient revenue is 327, ,720 = 15, In addition to finding the two values for transient revenue, answer the following questions: a. How many transients would be displaced as a result of the group? Forty-eight transients are displaced. b. Are any transients displaced on dates before or after the group dates? Eight transients are displaced on 11/18. c. Given the two transient revenue totals you calculated, what is the minimum rate you must charge the group to break even? 15,000/40 = per room-night. d. If you assume this group will bring in an ancillary contribution of 1000 per day, what is the new break-even rate? ( 15,500 4,000)/40 = 275 per room-night.

31 Module 1 Wrap-up You should now understand how important it is to create a balance between negotiated group-rate customers and transient customers. We've discussed strategic and tactical segment allocation and using a simultaneous decision-making framework to calculate the break-even rate while taking into consideration multiple rate classes and multiple LOS. Having completed this module, you should be able to: Determine the fraction of your business that should be allocated to group business Determine the break-even point for group requests of multiple-night stays with and without ancillary costs Determine the implications of multiple rate classes and multiple lengths of stay on group break-even prices

32 MODULE OVERVIEW Module 2: Group Arrival Uncertainty Revenue managers cannot change the fact that there is uncertainty associated with every booking, both group and transient. However, they can work to understand the nature of booking uncertainty and to manage it. Though similar, uncertainty in group bookings differs from transient uncertainty in timing and magnitude. The two are different in terms of management, too. Group blocks reduce the hotel's available rooms, so group block arrival uncertainty is critical to revenue management of the rooms protected for transients. The question revenue managers must answer is, what fraction of the group block will the group actually utilize? In managing revenue, the hotel must be sure not to price transients too aggressively, or, on the other hand, to accept too many discounted transients. To make good decisions, the hotel must know how many rooms in the group block are likely to be booked. We considered long- and medium-term issues in Module 1. In this module we look at short-term issues of transient revenue management by considering forecasting, overbooking, and the uncertainty associated with demand. We see how an effective revenue management strategy deals with arrival uncertainty using forecasting and overbooking. By the end of the module, you will be able to: Evaluate group arrival uncertainty through group forecasting Create an effective overbooking strategy to protect revenue

33 TOPIC OVERVIEW Topic 2.1: Group Forecasting This topic approaches group arrival uncertainty through forecasting. By creating forecasts, the hotel uses booking data to estimate how many group block rooms will be booked, and when. Using an overbooking strategy, the hotel proactively takes into account group block rooms that won't be booked, working to reduce the number of empty rooms that would result. Both of these are necessary for effective revenue management. By the end of this topic, you will be able to: Evaluate historical data to estimate group bookings

34 Introduction to Group Forecasting A video presentation appears below, along with a text transcript. Use these resources to learn about group forecasting. Transcript: Introduction to Group Forecasting Now our focus is going to move to the short term and now we're sort of much closer to that cutoff date for that group, perhaps as tight as 30 or 60 days prior to that cutoff date. Here our goal is to focus on group arrival uncertainty. Right, so our focus is on group utilization, materialization, or sometimes referred to as wash, or what fraction of that group block is the group actually going to utilize? We're going to focus on this arrival uncertainty from two standpoints. One is forecasting, so given the information I have on hand, can I better estimate how many rooms that group block is going to need? And second, we're going to use overbooking to help us sort of manage that group block size given there's some arrival uncertainty associated with that group block. From a forecasting standpoint we really have, you know to start with, some historic data much like we would start with from a transient standpoint. So we would either have historical records for group behavior at our hotel-we may have relationships with other hotels that are sort of part of our same management company and there we would have information on similar groups from those hotels. And we can also get information, say, from local convention bureaus. So these are all good sources for group data given that every group tends to be different and unlike transients we don't have a lot of repeated data of this same sort of business. The data we have is similar to transient information, and basically we're looking at booking information or reservation build as a function of days before cutoff. Right, so typically this is not days before arrival but days before cutoff when we no longer accept that group rate. Unlike transients we would have a slightly longer booking window, as these group requests would come in 180 days or even longer prior to that cutoff date. One of the tricky parts with groups is that you know, most groups are of different size. Right, so we might have one group that's accepted 100 rooms, another group that was 75, etc., so every group block is going to have a different size. And so what we do with these group blocks of different sizes is we all standardize those to sort of one number. So basically we would divide all these reservations at different dates before arrival by the reservations we actually had at cutoff. So now we have basically a booking window from cutoff through to say 180 days before arrival and each one of these days before arrival we have a percent of total reservations on hand at that time. We would then average across a series of these different groups to in essence create a booking curve for group behavior. So this group booking curve would tell us what percent of this type of group is on the book at 90 days before arrival, what percent is on the books say at 30 days before arrival, or 14 days before arrival. And again I use arrival here but really what we're focusing on is cutoff.

35 Right so this is not the stay date, but this is the date at which we're no longer accepting that group rate. Right so I will use arrival and cutoff here interchangeably but really we're focused on this cutoff, which may be 30 or 60 days prior to that stay date. And so how do I use this sort of booking curve information to generate a forecast? Well typically we refer to this as a multiplicative forecast and we're simply using this historic behavior in a percent basis to scale up what we currently have. So for argument sake it's 90 days before the cutoff date for a specific event. Right now we have 10 reservations on hand for this particular group. We know that historically that at 90 days before arrival this type of group has 12 percent of its total bookings on hand at 90 days before arrival. And so now we can simply take the 10 reservations on hand that we have, knowing that that's sort of analogous to 12 percent of our total bookings, so 10 divided by.12 becomes 83. So our forecasted demand for this group as a function of having 10 reservations on hand at 90 days would be 83. Right, it's 10 divided by.12 is 83. So 10 is to 12 percent as 83 is to 100. And that would be our forecast or our multiplicative forecast based on this historic group behavior.

36 Evaluating Arrival Uncertainty at Hotel Ithaca Group forecasting, like transient forecasting, utilizes historical data on reservations on hand (ROH) to estimate how many group rooms will be booked by the group cutoff date. Forecasts are based on booking curves and the underlying data. D etailed information on a particular group's behavior is not usually available, but it's possible to create estimates using booking information from similar groups. Let's explore an example of group arrival uncertainty. Pascale Moreau, at the 210-room Hotel Ithaca, has recently accepted a group request from ABC Corp. for a block of 125 rooms. ABC Corp. is a large multinational firm, and she expects its booking behavior will resemble that of other firms of its size that have stayed at the hotel in the past. She has data on those other groups, shown in the tables below. Curre ntly it is 90 days before ABC's arrival date and the Hotel Ithaca has only seven ROH for the group. Should Pascale be concerned? She can forecast expected arrivals using the percentage data in the tables above. The tables show that, if this group is typical, she should have 12% of the bookings on hand at 90 DBA. That is, if the group is typical, then the 7 ROH represents 12% of the final booking. Pascal uses this data to assess her ROH. ROH = 7. 7 divided by 0.12 = 58. So, this group may utilize only 58 rooms. It looks like they may book substantively below their contracted 125 rooms! Pascal decides that she needs to revisit the hotel's transient room management strategy. She has been managing transient demand under the assumption that she had an effective capacity of 85 rooms (210 total rooms 125 group rooms). But it appears that the hotel's effective capacity is closer to 152 (210 total rooms 58 group rooms). She has many more available rooms than she thought.

37 Group Forecasting Implications What are the implications of the group forecast, and why is the forecast significant to revenue management? We'll look at these questions next. One element to keep in mind regarding group forecasting is timing. When the hotel forecasts group demand, it's with respect to the cutoff date, which may be 30 days prior to the stay date. So from a transient standpoint, there is still time to adjust if the forecast turns out to have been poor. Let's look at two possible results of a poor forecast and the implications of each. If the hotel overestimates group demand (fewer bookings materialize than planned), the hotel will have more transient rooms than planned. Because the hotel planned to have fewer rooms, it may have closed its discounted rates earlier than it should have, which could result in some empty rooms as the arrival date approaches. If the hotel overestimates group demand, it will have more rooms available for later-arriving transients than it anticipated. This may cause it to use overly strict rate and availability restrictions, which may result in rejection of some transient demand that, once true group demand is realized, it will wish it had accepted. If, on the other hand, the hotel underestimates group demand, the hotel will have fewer transient rooms than planned. A forecast that is too low exposes the hotel to the risks of overselling and rate dilution. Again, the hotel runs the risk of alienating transient guests. If the hotel had a more accurate forecast, it could have sold to higher-yielding transients rather than offering so many discounted rooms early on. It is important to realize that the purpose of a group forecast is to estimate the number of available transient rooms. Because the group forecast in a sense determines the hotel's capacity, errors in the group forecast have significant implications beyond the group. Over- and underforecasting are addressed in the topic on overbooking.

38 TOPIC OVERVIEW Topic 2.2: Overbooking The second strategy in dealing with group arrival uncertainty is overbooking. Overbooking is designed to proactively take into account no-shows (also referred to as wash). It is prevalent in many service industries, including rental cars, hotels, and airlines. If a hotel, for example, finds that it does not have an available room for a booked guest due to overbooking, it must "walk" that guest-that is, re-accommodate him or her at a nearby hotel. The cost of walking a guest is difficult to measure, primarily because it is difficult to estimate the cost of ill will. However, the "walk cost" is usually estimated to be higher than the room rate. For this reason, revenue managers must pay special attention to the hotel's overbooking strategy, to be sure it is not too aggressive. By the end of this topic, you will be able to: Develop an effective overbooking strategy to mitigate wash Evaluate risks to determine overbooking levels

39 Traditional Overbooking Before we examine group overbooking, here is a quick review of traditional overbooking. Overbooking is the earliest form of revenue management, dating back to the 1950s when air travel in the United States was regulated. Due to regulation, airlines operated under very strict guidelines, and conversely, passengers had a lot of flexibility. This passenger flexibility resulted in very high no-show rates. That is, large numbers of passengers with reservations did not arrive, cancel, or rebook; they simply did not show up. To guard against ending up with many empty seats, airlines overbooked their flights, accepting more reservations than they had seats. If more passengers arrived than the plane had seats, the airlines had to pay very structured penalties in passenger compensations such as food, lodging, partial refunds, and accommodations on the next available flight. An airline with an oversold flight often makes compensation available to travelers who are willing to rebook, motivating them to do so by choice. Most of us, as we wait at the gate to board our plane, have heard an announcement that the airline is looking for volunteers to take a later flight in exchange for a travel voucher. The airline may increase the compensation offered until it has enough travelers volunteering to move to later flights; this is called a reverse auction. Interestingly, this turns out to be a win-win for the airline and travelers, because the airline flies full, probably selling a few extra full-fare seats, and the passengers who volunteered to fly later are quite happy to do so for a few extra euros, plus a free flight, travel voucher, food, accommodations, and possibly more. Overbooking is prevalent in many service industries, including rental cars, hotels, and airlines. Unlike airline passengers, and unfortunately for hotels, all hotel guests don't arrive at the same time. Instead, hotel guests arrive throughout the day. The gradual arrival of guests means the hotel cannot hold the reverse auction. Instead, if it finds itself in the position of having more guests than rooms, it must "walk" a guest, reaccommodating the guest at a nearby hotel. The nearby hotel may be in the same chain, or it may be a competing hotel. This forced walk versus a volunteered walk results in costs ("walk costs"), which are often higher than the room rate at the hotel. For this reason, revenue managers must consider their overbooking policies carefully. Traditional overbooking is an attempt to manage walk costs. A good overbooking strategy uses an overbooking level that maximizes expected revenue. Let's look at revenue as a function of booked rooms. As you can see in the figure below, as a hotel accepts more reservations, the revenue increases. At a certain point, however, the hotel is accepting reservations beyond its capacity, and it begins to incur walk costs. At that point, net revenue starts to decrease. The peak of the net revenue curve in the figure below represents the booking level at which walk costs equal the revenue the hotel stands to gain by not allowing the rooms to remain empty.

40 Economic-Based Approach to Overbooking As you can see, there is a trade-off involved in overbooking. If we allow a room to be empty, we forgo revenue. If we overbook, we incur a walk cost (the cost of reaccommodation and possibly more). Managing the trade-off between revenue and cost entails an economic-based approach to overbooking. The marginal analysis of this problem assumes revenue R from a reservation, a cost D for denied service (the walk cost), and some probability P of a walk given that the hotel has accepted reservations beyond capacity. Let's use these parameters to write the two possible outcomes in overbooking: a walk cost or a room revenue. The hotel walks a guest with probability P and incurs the denied-service cost D. The hotel doesn't walk a guest with probability 1 P and receives revenue R. At some probability of a walk, the cost of a walk and the revenue of a not-walk are equal. We set these two equal to each other: We can solve for P simply by expanding both sides. When the probability of walking someone equals the ratio of room revenue divided by room revenue plus walk cost, room revenue and walk cost are equal. That is, the hotel can be indifferent regarding whether the guest is walked or not. This probability P is a break-even from an overbooking standpoint.

41 Traditional Overbooking at Rest-a-While A video presentation appears below, along with a text transcript. Use these resources to learn about traditional overbooking. Transcript: Traditional Overbooking at Rest-a-While Right, so let's do a little example here of our Rest-a-While hotel. All right, so Rest-a-While basically sells rooms say on average for 100 euros. If they walk a guest and they have to then reaccommodate them elsewhere, they estimate that that costs them 200 euros. So they've been keeping track of Thursday no-shows for the past six months and have found the following distribution or relative frequencies of the number of no-shows. So basically over the last six months on Thursdays, they've had between zero and 5 no-shows. Ten percent of the time they had zero no-shows; 25% of the time they had 2 no-shows; 5% of the time they had 5 no-shows. So this would be our no-show distribution. All right, so given that I have a distribution of no-shows, now I can estimate the probability I walk a guest given I overbook by a certain number. So if I overbook by zero, obviously there's no chance that I can walk anybody because I've accepted no reservations beyond my capacity. So the probability I walk somebody if I overbook by zero is simply zero. Now if I overbook by 1, I'm going to walk somebody if I have less than 1 no-show, basically if I have zero no-shows, which occurs 10% of the time. So the probability I walk somebody if I overbook by 1 is 0.1. If I overbook by 2, now I'm going to walk somebody if I have zero or 1 no-shows, which occurs 0.1 plus 0.15 or 0.25 or 25% of the time. If I overbook by 3, now I'm going to walk somebody if I have less than 3 no-shows, so either zero, 1, or 2, right, which is going to be 0.1 plus 0.15 plus 0.25 or 0.5 or 50% of the time. We could go on and estimate this for 4 at 0.8 and at 5 at 0.95.

42 Now the question is, so now I have the probability I walk given a certain overbooking level, what is the appropriate overbooking level to sort of minimize this cost of overbooking? So remember that our critical P was R over R plus D, which was 100 euros over 100 plus 200 euros, or 1 over 3 or simply a third. And so as we go down our probability of walks here-zero, 0.1, 0.25, and 0.5-we look at if I overbook by 2, the probability I walk somebody is So remembering back to our equations, on the one side we had P times D, so 0.25 times 200, that's actually less than 1 minus 0.25 times my 100 euros, so therefore I'm better off overbooking by 2. As I move to overbooking by 3, now the probability I walk somebody is times 200, from the walk side, is actually more than 1 minus 0.5 or 0.5 again times the 100 euros, right? So now we see that because 0.5 is bigger than a third, that my costs of denied service exceed my costs of an empty room and so therefore I should overbook by 2 but not overbook by 3. So we would use this approach to sort of determine what is the appropriate overbooking level given I've quantified this cost of denied service and this cost of an empty room.

43 Essential Reading: Overbooking at Wynn The following article from the Las Vegas Sun illustrates some of the implications associated with guest arrival uncertainty. Wynn Las Vegas has 2,716 rooms and does a large volume of business. Because of the large number of rooms booked, the hotel needs to actively manage room reservations. The article summarizes the implications of having booked more rooms than anticipated, and as a result needing to accommodate some transients who booked, but for whom they no longer had rooms. The article also illustrates that while overbooking can create problems, the hotel can adjust to unforeseen circumstances and create a positive experience for an otherwise potentially annoyed walked guest. Read about this situation in "Wynn Las Vegas apologizes for overbooking hotel," by Richard N. Velotta. View the article. Note: you will need Adobe Reader to be able to view the article. If it is not already installed on your computer, you can download it (free) from the Adobe website.

44 Estimating the Probability of a Group "Walk" Let's look at how we estimate and value a group "walk." In the context of a group booking, the probability that a guest is walked is a function of the group block size relative to the group request that was negotiated. We assume that the probability that any individual in the group won't show up is unaffected by the behaviors of the others in the group; that is, each group attendee is independent of the other group attendees, which is likely when people are coming from different places. We'll use utilization rate and details about the group block to create the estimate. Let's say that a particular group is requesting three room-nights. Let's also say that we have data on similar groups showing a 90% utilization rate. Another way of looking at that is to say that each potential guest in that group has a 90% chance of making and keeping his or her reservation. Let's say we have three potential reservations and each individual has a 90% chance of showing. What is the chance that this group will actually use all three of its allotted rooms? The probability is 90% for the first individual, 90% for the second individual, and 90% for the third individual. The product of the three is 0.9 to the third power (0.9 x 0.9 x 0.9), or Given that this group request is for three rooms, the probability that all three rooms will be utilized is simply The probability that two rooms will be used (that is, one guest does not show) is 0.9 multiplied by 0.9 multiplied by 0.1. However, note that there are several ways that one no-show could occur: it could be the first guest, the second guest, or the third guest. So there are three possible combinations, which we take into account by multiplying the product of the individual probabilities by three. Three times 0.9 times 0.9 times 0.1 is Now let's look at the probability of two no-shows. This is 0.9 times 0.1 times 0.1 times three, which is Finally, the probability of three no-shows is 0.1 times 0.1 times 0.1, or The probabilities of all the possible no-show cases for this three-room group are summarized in the table below. This simple example of a group requesting three room-nights should provide insight into the process of estimating group walks. Let's now consider how we can use Excel tools to simplify the probability calculations for larger groups. Using BINOMDIST to Estimate Probability We can calculate the probability that a group uses some number of rooms x given a group request of N rooms and given a particular utilization rate P using the properties of the binomial distribution. The Excel function BINOMDIST greatly simplifies this calculation. To use the BINOMDIST function, you need the following inputs: the number of successes (x), which in this case is the number of rooms booked; the total number of trials (N), which is the group size; and the probability P of a success (the utilization rate). You'll also need to know if you are finding the "cumulative" probability; the cumulative term for BINOMDIST is either 0 or 1 (enter 1 for a cumulative distribution). If you want to know the probability of receiving exactly 40 bookings for a 50-room group request when the utilization rate is 75%, your entry would look like this: Estimating the Probability of a Group Walk at Rest-a-While The Rest-a-While hotel has received a group request for 100 rooms. Based on data the hotel has on hand, it assigns a utilization rate to this group of 90%. It asks, what is the probability that this group is going to need more than 90 rooms given that there will be some wash? In this case, the number of successes is 90, the number of trials is 100 (possible requests), and the probability of success of each trial is 90% or 0.9. Rest-a-While wants to find the probability of having 90 or more requests, so cumulative = 1. Using the BINOMDIST function, the hotel finds that the probability of having 90 or fewer requests is 0.55.

45 This means that the probability of more than 90 requests is simply , or So if Rest-a-While only blocks 90 rooms for the group requesting 100 rooms, there's a 45% chance that the group would end up making more reservations than the hotel blocked for it. This is the probability of a group "walk." Next, we will use this logic to determine group overbooking levels.

46 Transient Cancellations and Overbooking with Groups Managing no-shows in the context of group reservations is very similar to managing no-shows for regular transient bookings. No-shows, as we have established, are simply transient guests who do not use their reservations and do not inform the hotel of their changes in plans. No-shows are different from cancellations, which occur when transient guests alert the property in advance that their travel plans have changed and they no longer need their reservations. Cancellations far outnumber no-shows. Some strategies suggest overbooking only to account for no-shows, not cancellations. As the figure illustrates, the overbooking pad incorporating cancellations is much larger than the no-show pad. If we had overbooked only considering no-shows, then the hotel would have rejected a considerable number of early bookings. Once cancellations are made we may reopen discounted classes, but the demand that we rejected early has probably already booked at other hotels. Because the timing of group overbooking is somewhat different than that of regular overbooking, we don't risk needing to walk a group guest to a competing hotel. Instead, overbooking means that we can't accept as many late-arriving, high-yielding transients as we might have. For groups, the costs of overbooking are: 1. Missing early demand at the discounted rates if we don't overbook enough 2. Missing higher-yielding, late bookings if we overbook too much Because groups quite often overestimate the number of rooms needed, hotels must overbook to accommodate this group behavior in addition to overbooking to address transient cancellations and no-shows. Let's look at two ways to determine the group overbooking level: the heuristic approach and the economic or risk-based approach. Heuristic Approach to Group Overbooking

47 Let's use the heuristic approach to find a group overbooking level. In this example, a group has requested 300 rooms in a 750-room hotel. If the group has overestimated the block size, it may not need all 300 rooms. If we don't overbook, then we will be faced with the same situation we faced when managing for transient cancellations: by the time we realize we have rooms available, guests have booked with competing properties. We need to proactively adjust our pricing by adjusting the group block size to make sure that we don't have empty rooms when we would have otherwise had higher demand. We can do this by applying a variant of the deterministic heuristic. First, let's assume that the 300-room group block behaves like other such blocks and had a typical utilization rate of 80%. If we adjust the 300-room block to reflect this utilization rate of 80%, we could simply block 240 rooms (80% of 300) and actively revenue-manage the remaining rooms. This approach to overbooking does not consider group or transient rates. Economic-Based Approach to Group Overbooking As shown earlier in the course, the economic- or risk-based approach to traditional overbooking uses the following equation to determine probability: For group overbooking, R=lowest rate, D=highest rate, and P is the probability that the group books a number of rooms exceeding our effective allotment ( instead of P being the probability of walking). In this example, the group block is 300 rooms with an 80% utilization rate, the lowest rate is $99, and the highest rate is $289. Given these values, the critical (break-even) probability is 99/(99+289) or We can then use that ratio to determine the best allotment. To do this, we first find use BINOMDIST to find the probability of a walk for each in a set of possible room allotments and then compare those probabilities to the break-even probability we calculated above. Similar to what we saw in the review of general overbooking, this approach assumes that at the break-even point, the hotel is indifferent to booking the room as group versus transient- in essence, they are the same.

48 As you can see from the table above, the probability of a walk that is closest to (but not more than) the break-even probability of occurs at 245 rooms. This method recommends 245 rooms for the group. Note that when we used the deterministic heuristic, we calculated a group allotment of 240 rooms. The risk-based approach resulted in a recommendation of 245 rooms. The difference is due to the fact that the risk-based approach considers two different rates (a high rate and a low rate), but the heuristic model considers only one. If we made the rates the same in the risk-based model, it would also advise a 240-room allotment.

49 Group Overbooking at Hotel Ithaca A video presentation appears below, along with a text transcript. Use these resources to learn about group overbooking. Transcript: Group Overbooking at Hotel Ithaca All right, now we're going to put all this content together and do a little example that hopefully cements this idea of group overbooking. Let's go back to Hotel Ithaca. If you recall, Hotel Ithaca had three rates- 195, 250, and 350. Hotel Ithaca has 210 rooms. Again, it's a short-term decision, so let's assume that Hotel Ithaca has already accepted a group request for 100 rooms at 169, and now they're trying to decide how many rooms they should actually allocate to this group block. So they've requested 100 rooms, but given we know there's some arrival uncertainty associated with group behavior, we're not necessarily going to allocate them all 100 rooms. Similar groups at Hotel Ithaca have had an 80% utilization rate, so this might be a conference or something of that nature. Similar types of groups have utilized 80% of the group request, so now our decision is how many rooms of this 100 requests to allocate, or said differently, how many rooms should we not allocate to the group and potentially use for transients and transient RM on the other side? Using our heuristic approach, given that it's a block of 100 with an 80% utilization rate, we would just allocate 80 rooms, or the utilization rate times the group request for a block of 80. What are the implications of this 80-room assignment? Well, if the group actually makes reservations beyond 80-remember, they have up to 100-if they make reservations beyond 80 and we allocated 80, and then keep in mind when I allocate 80, that really means I'm revenue-managing the remaining 130, now Hotel Ithaca thinks it has a 130-room hotel that it's actively revenue-managing. Given that they've requested more than 80 reservations, I'd probably regret accepting some of those early discounts at 195 because the group has now requested more than 80. As a result, I'm probably going to have a higher occupancy and have to reject some late-arriving 350s because I accepted too many of the early-arriving 195 transients. Keep in mind we have to honor this 100-room block at 169. Flip side-if they request less than 80 reservations, then, well, I'd probably wish I'd accepted more of the 195 discounted transients early on, because I probably rejected some of those, they went to competing hotels, now those people are out of the market, and my hotel is going to have a few empty rooms. Here's the trade-off if the group is on either side of my allocated block. If we focus on our economic approach now, we're really going to manage this trade-off between these two scenarios and those really had costs, of either 195 if they were under my block or 350 if they were over my block. Keep in mind that a heuristic approach really assumes that 195 equals 350, and most of us know that 195 does not equal 350. What's the probability that the group requests more than our block? Again, if we blocked 80, we can estimate the probability that group reservations exceed 80, which is 1 minus the probability that group reservations are less than or

50 equal to 80. Now we can use our BINOMDIST function, so 1 minus BINOMDIST of 80, 100, 0.8, 1-so remember that BINOMDIST of 80, 100, 0.8, 1 is the probability that I had 80 or less successes given each had a probability of 0.1, it's 80 or less because I used the 1 in the end for the cumulative. So 1 minus that equals So that means I have a 46% chance of incurring this 350 cost given that the group has requested more than my block, so 0.46 times 350 equals 161. Remember the flip side of this, 1 minus 0.46 is 0.54, so 0.54 times 195 equals 105. So here, because 161 is bigger than 105, then that means my cost of the group requesting more than my block exceeds my cost of the group accepting less than my block, so therefore my block is not big enough, so now I want to potentially allocate 81 rooms to the group versus 80. So now we can just simply repeat this for a block of 81 rooms, so the probability that the group requests more than my block of 81 is the probability that reservations are greater than 81, which is 1 minus the probability that reservations are less than or equal to 81, which is 1 minus the BINOMDIST of 81, 100, 0.8, 1, which equals times 350 equals minus or.638 times 195 equals 124, so now my cost of being over 127 is still greater than being under at 124, so again we could still say that my block is too small because my overage cost is less than being under; and so we could do this again for the probability that the group requests are more than 82 rooms, which turns out to be So now 1 minus is times 350 equals 95, which is actually now less than times 195 equals 142. Now we've switched from the cost of the group being larger than my block, being bigger and being under, to the reverse. Now the cost of the group being under my allocated block is larger than the cost of my group being over the block, and that tells me that a group block of 82-this is the first group block or the smallest group block such that my costs of the group being over are smaller than the group being under, so therefore I should block 82 rooms for this group request. We could see this differently knowing that, remember our critical probability was R over R plus D, which was 195 over 195 plus 350, which equals For 81, remember that that critical probability was 0.362, which was bigger than 0.358, but for 82, was smaller than So 82 was the largest number such that that probability was still less than 0.358, so therefore we should allocate 82 rooms to this group request of 100. Alright, so we can put our heuristic approach in terms of our economic model. Remember that for the heuristic approach, in essence we assume that R equals D, given that P is R over R plus D, so P is simply equal to a half. And if we remember back to our equations, the probability that reservations are greater than 80 equals 1 minus the probability that reservations are less than or equal to 80, which was 1 minus our BINOMDIST of 80, 100, 0.8, and 1, which was We see now that our heuristic approach is really the same as our economic approach but we've simply set R equal to D or P equal to a half. So these are two different methods, just with the same sort of framework but different assumptions associated with the costs.

51 Overbook with a Group: Review The group block requested is 45 rooms. The utilization rate is 75% based on historical data. So it is likely that the group will use only rooms. How many rooms should the hotel allocate to the group, 34? Some other number? Let's consider the room rates involved. The highest rate available is 350 and the lowest is 195. Use these rates to calculate the break-even probability (at which the hotel is indifferent to a walk versus a show). This probability is given by P = lowest rate/(lowest rate + highest rate) = Now use BINOMDIST to find the probability of a walk for the various group block sizes. Then look up the walk probability that is closest to but not greater than the break-even probability: That corresponds to 35 rooms.

52 The solution spreadsheet is provided. Download it here.

53 Module 2 Wrap-up You should now understand how to manage for group arrival uncertainty through forecasting and overbooking. In this module, we explored transient revenue management, forecasting, overbooking, and the uncertainty associated with demand. Having completed this module, you should be able to: Evaluate group arrival uncertainty through group forecasting Create an effective overbooking strategy to protect revenue

54 MODULE OVERVIEW Module 3: Optimal Group Pricing Our group pricing analysis so far has focused on determining how many displaced transients are likely to result from a group booking, calculating the resulting lost contribution, and then determining break-even group prices. Of course, hotels do not set group prices at the break-even level. Instead, they try to determine the group rates that will allow them to maximize revenue. In this module, we look at how to do this using methods for more focused pricing. Whereas Modules 1 and 2 presented detailed sets of instructions for performing calculations, this module is designed to provide an overview. The material shown here is complex, but by studying it, you will gain enough familiarity with the methods to see potential opportunities. You may decide to invest further resources to develop your ability to perform similar calculations. By the end of this module, you will be able to: Explain the importance of the price-acceptance relationship to determining optimal price Define "win rate" Define logistic and multinomial logistic regression Explain how regression is used to evaluate win rates

55 TOPIC OVERVIEW Topic 3.1: Modeling Win Rates The first step in determining the optimal price for a group booking is to look at the "win" rate, the rate at which offers are accepted, for previous bookings. This historical data will help you understand the acceptance level for group bids for each segment of group business. By the end of this topic, you will be able to: Explain the importance of the price-acceptance relationship to determining optimal price Define "win rate"

56 Price Versus Acceptance To maximize revenue, the hotel may be tempted to charge the highest rates possible. But it must be careful to consider the price its target market is willing to pay. So the process of arriving at an optimum price requires that the hotel maximize two things simultaneously: price and acceptance. The following figure illustrates this tradeoff. As the figure shows, the probability of acceptance is highest when the price is low, and it approaches zero as prices increase. The green line is the contribution margin multiplied by the probability that the client accepts the quoted price. The expected contribution is highest at a price of around 115, the price that would generate a contribution of around 100. One of our goals here is to understand how to maximize profit given the relationship between price and acceptance.

57 Win Rates Now that we've seen why acceptance is critical to the pricing decision, we need to find out how to determine the probability that a potential guest will accept an offer. As with other estimates, we look at historical data to estimate the probability of acceptance. The table below contains historical data showing group rates the hotel quoted to clients at different numbers of days prior to the group event, sorted by group types (private, business or corporate, and weddings). Each record includes whether or not it was a "win" (whether the client accepted the offer). The table indicates wins with a 1 and losses with a 0. Let's look just at the winning offers. The table below shows how they break down across segments. We can use this data to model the impact of price and days before arrival (DBA) upon "winning." Logically, we expect that as quoted prices get higher and higher, the chances of winning decrease. Time before the event is also influential: a client who needs the group rooms in 50 days is more likely to accept the offer than one who needs them in 200 days. In the next topic, we discuss using logistic regression to model win rates.

58 TOPIC OVERVIEW Topic 3.2: Evaluating Win Rates Using Regression The next step in determining the optimal rate is to evaluate win rates. This evaluation will further reveal the relationship between pricing and acceptance for different group segments and different booking timings. By the end of this topic, you will be able to: Define logistic and multinomial logistic regression Explain how regression is used to evaluate win rates

59 Logistic versus Linear Regression Regression is a way to describe the relationship between two variables. Up to this point in the series, we have used linear regression to describe various relationships. We have referred to the equation of a straight line, y = mx + b, as a linear regression model; it shows how y changes as a function of x according to the slope m and given the y-intercept b. An example of a line y = mx + b is shown in the figure below. Using linear regression, we can describe relationships such as the one between demand and price. Price is the independent variable in this case and demand is the dependent variable. Demand varies continuously ; it may, for example, take any value between 10 and 1,000. What if we had a dependent variable that was not continuous? Some are limited to just two values or a small set of values. For example, imagine a situation in which a researcher is investigating the flight options consumers tend to select. He might ask the question "Does the consumer select Flight 1?" Here the independent variable is the airfare associated with Flight 1. The dependent variable, the response to the question, might have just two possible values: "yes" and "no." The responses to the question "Does the consumer select Flight 1?" are plotted in the graph below, where "0" is "no" and "1" is "yes": The data shown here cannot be "fit" to a straight line using linear regression; the data points line up along 0 and also along 1, with no points occurring in between. Instead, these points are fit to what is known as an "s-curve" using logistic regression.

60 Modelling Wins Rates Using Logistic Regression Let's look at hotel group business pricing decisions as an example of how to use logistic regression. A hotel that typically handles group business often has a database of group request data containing the date that each request was made, how many days before arrival the request came in, the price quoted, the type of request (private group, business, or wedding), and whether the hotel succeeded in winning the group business. This historic data can help the hotel decide how it should quote future offerings. The hotel can categorize the historic data into wins and losses and look at how those wins and losses varied across attributes such as price. Let's look at wins by DBA in the following graph. As you can see in this graph, there are many wins when price is low. So price is one piece of the puzzle. DBA is another piece of that puzzle. As we can see from the losses graph, there is a big cluster of data points at high prices where DBA is large. This indicates that when there are many days before arrival and the price is high, consumers don't often buy the product. In the wins graph, there is a cluster of data closer to arrival, at lower prices. This shows that the closer the bid is to arrival, the more likely the hotel is to win it. Can we model this relationship? The only possible outcomes are "win" and "loss"-a binary outcome-so we need to use logistic regression. Typically the fit is to an S-shaped curve that asymptotically approaches zero at one end. The most common S-curve used is referred to as a logistic function. We can fit the data to this curve and see the relationship between win and price.

61 Here we use logistic regression to model how price dictates whether an offer is won or not. However, we need to look at the interplay between price and DBA and not just categorize them separately. A hotel that has access to its historic data can calculate the relative "utility" (the importance) of price, DBA, and other attributes that are part of the consumer decision. That hotel could then create a model that would describe the utility of any one offering as a function of those attributes. The expression for utility takes the form Hotels use the utility of the attributes to find the probability that a particular offering i will be selected. This probability is written In the next video, Professor Anderson provides an example.

62 Using Logistic Regression for Hotel Rate Quotes A video presentation appears below, along with a text transcript. Use these resources to learn about using logistic regression to determine win rates. Transcript: Using Logistic Regression for Hotel Rates All right, so our data give us a pretty good picture of the impact of one or two variables at a time, but really what we need is a model to help us look at all those variables at once. So keep in mind our outcome here is whether or not we win or we lose the quoted business, and we have a series of potential attributes, the attributes we've talked about so far: the type of group, private versus wedding, when did they need this space, how many days before the event is this request coming in, and obviously price. And then going forward you might collect other attributes that you thought were important. So what we do now is we fit this data to our logistic regression model. Remember that the underlying basis of our model is the relative utility of an offer. And here what we're comparing is whether or not this offer is accepted or rejected. So we say in logistic regression that the utility of an offer that's rejected is zero, so when we compare our utility of the zero option, keep in mind that that would be e to 0 and e to 0 is 1. So what we have is the probability that we accept this offer is e to its utility divided by 1 plus e to its utility, where 1 is the utility of the no-purchase option, right? So basically the no-purchase option has no utility. And so we use a statistical package, something like SPS, SAS, or R, to fit this model, and a sample outcome might look something like this, where we have a constant, right? That's the value that's independent of the attributes. And then we have a series of other attributes that we have estimated-in this case days before arrival, our price, and whether or not it was a private function. The coefficients for these attributes are all negative. That means we have less utility the further out this quote is made. We have negative utility for price: obviously the higher the price the less valuable to the consumer. And then if it's a private function, say versus a wedding, utility is also lower. So let's look at how we use those coefficients. So if we looked at a potential quote of 150 euros at 90 days before the event-here we would have the probability that someone would accept this offer is e to its utility divided by 1 plus e to its utility. If it was a private function that event would have a 0.34 chance of being accepted. If it was not a private function, say a wedding, then that would have a little bit higher probability of being accepted at 37.7 or almost 38, or basically 4 percent more likely to be accepted versus that private function. If we look at the impact of price, say instead of keeping price at 150-so still focused on 90 days before arrival but priced

63 over a range-what we'll see here is that for lower prices the probability of being accepted is quite high, and then as price increases that probability of the offer being accepted decreases. If we look at the product of the probability it's accepted and the price, that's really our expected revenue. So that's our revenue times the probability that we receive it or our expected revenue, and that expected revenue increases and then decreases. It's low initially because the price is low. It's low later because the probability we would win is so low. And so it reaches this peak and then starts to decay. If we look at how far in advance this offer is-if this offer is made close to the event really now the consumer doesn't have a lot of options, and so the probability of them accepting our quote is relatively high and therefore the expected revenue is quite high. But as we get further out from the event the consumer has more options, other hotels to look at, and as a result of that the probability of them accepting our 150 offer is lower. And so our expected revenue is lower. And so now we can look at, "Well what price should I quote, given I have this model?" So say for argument's sake I was going to quote them a price of 100 euros. Under that circumstance the probability they would accept my offer is So if I was to offer them a price of 100 on average I would make 82.80, given that 82 percent of the time I win; the other 18 percent of the time I lose. So for an average revenue of 82 or Now if I look at a whole series of prices, my goal is to find that price that maximizes that average revenue. And if we look at our graph here we'll see that again, the prospective revenue is increasing, then decreasing. If we look at what price it reaches the maximum that price is somewhere around 115. So therefore if we were to quote a single price the price which would maximize our return by managing this tradeoff between revenue and success is around 115. And so we can put this together now with our earlier discussions on groups, specifically our displacement calculator break-even price. And say for this example it might be 65. And so now we have this lower level of 65, we have this expected revenue-maximizing price of 115. And so now our sales agent could have a more intelligent negotiation with this meeting planner. They may start out at quoting 125 and then realizing that they may negotiate down to 115 as this profit-maximizing quote. And we get a sense for how well of a negotiator they are because we have this difference between the break-even price and this quoted price as the profit that our sales agent has negotiated on our behalf. So as you can see our modeling approach here sort of augments our earlier displacement approaches. Here we're looking at the exact profit-maximizing price to quote versus simply this price that's our break-even price. So we can use our modeling approach here to have more targeted prices, a little more insight into what's driving our success rate.

64 Using Multinomial Logistic Regression to Determine Ticket Prices If we have a set of outcomes beyond two, we use what is referred to as multinomial logistic regression as opposed to logistic regression. So let's consider a case in which we have a series of outcomes, as is the case when an air travel consumer must choose one flight from an array of flights. The following video presentation explores this. A text transcript is available below. Use these resources to learn about how to apply multinomial logistic regression to ticket prices and other attributes. Transcript: Using Multinomial Logistic Regression to Determine Ticket Prices If we have a set of outcomes beyond two, we quite often refer to this as multinomial logit versus just logistical regression. And so here we have a series of outcomes. Let's look at a simple airline example to put this in context. Typically if I'm looking at purchasing an airline ticket under most circumstances most consumers pick the most inexpensive option. So here we see that just under 70 percent of people pick the lowest available product. But then if we look at what fraction of people purchase products that are slightly more expensive, we see that roughly 20 percent are purchasing products with at least a $10 price premium. So this would tell us that price is king but perhaps there are other attributes which are driving this airline or flight choice. So how do we model these other attributes? Some of these attributes might be the brand of the carrier; the number of stops-is it a direct flight or does it have a layover; the total flight time-what's the total time for the layover? And then specifically something like schedule: if you wanted a 1:00 p.m. departure versus a 2:00 p.m. or 3:00 p.m. departure. And then we have some attributes associated with the consumer, such as how far in advance did they purchase this? What day of the week did they shop for this product? Ultimately how these offers are laid out on the screen also may dictate which flight a consumer chooses when they see these available options. So let's look at a sample display of potential flights. So we see here a consumer has searched for a flight from Dallas to Atlanta. They have indicated they want no more than one connection and they prefer to depart around 1:00 p.m. And here we have a series of potential flights that we have shown the consumer. But it's not clear which of these is the best in the eyes of the consumer. So we have our fastest flight. The problem with our fastest flight, just under two hours, departs considerably later in the day. Our cheapest flight has a stop and takes twice as long as our fastest flight. The flight that is close to our desired departure time then is considerably more expensive than our lowest-priced product. So which of these is most desirable to the consumer? And then, given we have different consumers, there's going to be a distribution of how desirable the consumers find these products. So how do we estimate this? We could look at using data from a series of choices that consumers have made. In this example here consumers saw these offers and the consumer chose the last one. And thenwe can fit one of our logistic

65 models to this data. And basically what we're doing is we're describing the utility of each of these offerings. The utility is some weighted factor of these attributes. So how important is price, how important is duration, how important is layover, that sort of thing. And then basically what we get at is that the weighted utilities-the utility of offer A versus the sum of the utilities of the other offerings-is the likelihood that a consumer would pick that choice. So the relative utilities dictate the likely outcome of a choice decision. So our goal now is to sort of fit a model to this data and then use this model to help us predict future outcomes. We have this equation that utility is some constant plus some parameter times a series of attributes, so that might be price, connections, carrier type, that sort of thing. And then we take these utilities and we put that to the power of E. Remember that E is this weird thing: , and so E to these utilities we refer to this as sort of exponential utility. So then what I can do is I can estimate this model that best fits that data and then the sum of these relative utilities tells me the probability that a consumer would choose one option over the other. And ideally we want these relative utilities to match this sample of historical data. Once we have these relative utilities, then we can sort of now look at a set of potential choices. So now we go back to our original display of options, we calculate these relative utilities. Again, these relative utilities are the likelihood that a consumer would purchase one product over the other. And then based upon these probabilities we can calculate the revenue from a series of offerings where here we calculate the expected revenue, which is the probability I would purchase this offering times its price. And so here now we have a way to quantify the value of these products, and given we have a value of these products we can quantify the potential revenue of these-the revenue here is the price times the likelihood that someone's going to purchase that. And then how would I use that? Well say he's an individual supplier, say an airline; well then I can take this model and use that to determine, "Well, how should I price my direct flight versus my flight with a layover? How should I price my 8:00 a.m. departure versus my 1:00 p.m. departure?" As an online travel agent here I look at a whole myriad of offerings from several carriers and I have to decide, "Well, how should I display those on my screen? Obviously if I put this offer on page 10, odds are the consumer's not going to see it. If I put this offer on the top of page 1 they're more likely to see it, therefore more likely to purchase it. So as the online travel agent I basically want to put the best offers up front. So we can use these sort of weighted utilities and probabilities as a way to sort from high value to low value. And so these choice models provide us a way to look at the utility of a set of potential alternatives given we have some historical data on what the consumers purchased.

66 Module 3 Wrap-up Having completed Module 3, you are aware of some of the tools that exist for developing targeted and optimal prices for groups and other types of business. You have opened the door to an interesting new way of thinking about pricing. Modules 1 and 2 focused on estimating how many displaced transients are likely to result from a group booking and asked, considering these displaced transients, what the lowest acceptable (or break-even) group rate would be. Module 3 illustrated that we need more than just an estimate the lowest rate; we need insight into the optimal rate. Armed with the necessary frameworks for good group-business decisions provided in Modules 1 and 2, you found in Module 3 that there are tools to help you not just minimize rate setting mistakes but capitalize on group business opportunities. Having completed this module, you should be able to: Explain the importance of the price-acceptance relationship to determining optimal price Define "win rate" Define logistic and multinomial logistic regression Explain how regression is used to evaluate win rates

67 Course Wrap-up If you have completed all of the modules in the course-congratulations! Having completed this course, you should be able to: Distinguish between transient revenue management and negotiated selling Calculate the implications of market mix Determine the optimal mix of negotiated versus transient business Evaluate requests for group and negotiated business

68 Thank You and Farewell Congratulations on completing the Displacement and Negotiated Pricing course. The course examined strategic- and tactical-level group booking decisions over the long, medium, and short terms, focusing on how an effective revenue management strategy can deal with arrival uncertainty using forecasting and overbooking. I hope to see everyone in the remaining courses in the series. Thanks, this is Chris Anderson.

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70 Customer Segmentation and Demand Controls Transcript: Customer Segmentation and Demand Controls Using customer segmentation and inventory controls to manage revenue is commonplace in many industries. But this wasn't always the case. The airline industry has a strong influence in their use. Today you find a lot of volatility in airfares, but this is a relatively new phenomenon. In the early years of air travel U.S. airlines were subjected to government regulations that consistently kept fares high and made air travel a luxury item. But eventually the demand for more affordable air travel led to the passing of the Airline Deregulation Act in The result of this act was complete elimination of fare restrictions, leaving the airline industry in a free market. Almost immediately, a number of new airlines arose to compete with the existing carriers and the number of passengers dramatically increased. A new way of pricing was introduced as existing carriers (serving guests willing to pay higher prices) now also had to offer lower prices to compete with new entrant airlines. So how did they price? They began with segmenting customers. If we oversimplify we could assume there are only two types of customers seeking to travel-business customers travelling for work-related issues and leisure travelers. The typical business traveler is willing to pay a higher price in exchange for flexibility of being able to book a seat at the last minute (or cancel his ticket if his plan changes) while the vacation traveler is willing to give up some flexibility for the sake of a more inexpensive seat. The demand from the price-sensitive customer tends to come before the demand from business customer. But with multiple price points and demand for more expensive seats arriving after price-sensitive demand the airlines had to determine how many seats they should sell to the early price-sensitive customers and how many they should protect for late, full-fare customers. If too few seats are protected, the airline will lose the full-fare revenue. If too many are protected, flights will leave with empty seats. Littlewood (working for British Airways) proposed a way to make this determination. He proposed that discount-fare bookings should be accepted as long as their value exceeds that of anticipated full-fare bookings, assuming that

71 customers can be segmented according to when they purchase their tickets. This simple, inventory control system was the beginning of what eventually lead to revenue management. Using Littlewood's approach we can designate two fare classes as having fares of R2 and R1, where R2 is greater than R1. The demand for class R1-the lower fare-comes before demand for class R2. The question now is how much demand for class R1 should be accepted so that the optimal mix of passengers is achieved and the highest revenue is obtained? Littlewood suggested closing down class R1 when the certain revenue from selling another low fare seat is less than the expected revenue of selling that same seat at the higher fare. In other words, as long as the probability of selling all remaining seats at the higher price is greater than the ratio of the lower price over the higher price, we are better off not selling at the low price and keeping it for the high price. This is our Target Probability. Let's look at an example. Grand Sky Airlines sells tickets on one of its 85-passenger planes for 150 (the discounted fare) and 250 (the full-fare). In general, their customers are aware of the pricing and those seeking discounts tend to book early. Sean, one of the managers at Grand Sky, knows that he can fill his entire plane at 50 per seat if he so desires, but at some point it is best to stop selling discounted seats and reserve some inventory for later arriving higher yielding ( 250) passengers. How does Sean calculate this target or the point at which to stop selling 150 seats and reserve the remaining seats for the 250 customers? Using Littlewood's rule (R1 divided by R2) we can calculate Sean's target probability. In this case it is.6 or 60%. As long as the probability of selling all remaining seats ("n" seats) at 250 is equal to or greater than 60% then Grand Sky is better off selling seats at 250. Now we need to calculate the probability of selling "n" or more seats. We use historical data to help calculate the probability of future events. The graph shows the number of 250 seats Grand Sky Airlines sold each day for the last 100 days. For example, seats were sold on one of the days and seats were sold on 12 of the days. Now we can calculate the probability of selling at least a certain number of seats at 250 and compare that number to our target of 60%. To calculate this probability, divide the number of days we sold "n" or more seats by the total observations. We could start the calculations at any point (selling 24 or more seats, selling 25 or more seats, etc.). But we can use our graph to select a reasonable starting point.