SHA541 Transcripts Transcript: Course Introduction Welcome to Price and Inventory Control. I am Chris Anderson, I'm the author of this course and a professor at Cornell University School of Hotel Administration. My teaching and research focus is largely on revenue management and pricing with an app, application specifically in service industries. This course focuses on one of the core concepts of revenue management. That being marginal analysis. We're gonna look at how firms can estimate the marginal value of the last room they sell, the seat on the plane. Or the last rental car in the parking lot. And then they use this marginal value then to control inventory,. Or to set prices going forward. This course serves as a solid foundation in revenue management for those of you who are relatively new to the area and as more of a reinforcement of the core concepts for those of you with prior RM experience. Thanks, and welcome and I hope you find the course impactful. 1
Transcript: Price and Duration Controls Successful revenue management has effective control of price and duration of stay the two strategic revenue management levers. Consider this matrix that plots firms along the dual axes of duration and price, where duration is controlled or uncontrolled and price is relatively fixed or variable. This chart provides an introduction to the revenue management perspective. Firms in industries traditionally associated with revenue management (hotels, airlines, rental car firms, and casinos) are able to apply variable pricing for a service that has a specified or predictable duration. These firms are in quadrant 2. To obtain the benefits associated with revenue management, industries should attempt to move to quadrant 2 by implementing the appropriate strategic levers. Most hospitality firms find that the more their firm operates in quadrant 2, the higher their revenue per available time- based unit. Not all firms within quadrant 2 industries practice revenue management or practice revenue management well. For example, a luxury hotel that is not implementing strict length- of- stay controls across its limited set of prices effectively operates in quadrant 3 due to the type of guests to whom it caters. 2
Assume you want to move your firm to quadrant 2; what are some of the things you should consider? If you have one price, you can institute multiple prices. A variable- price approach moves the firm from quadrant 3 (with few prices) to quadrant 4 (with many prices). In quadrant 4, you have several prices but uncontrolled duration. To add duration controls, you may use advance reservations to forecast demand, preferably by rate class and by length of stay. Now if you are able to incorporate length- of- stay controls as well as multiple prices, the firm is better positioned to move to quadrant 2. 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 1979. 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. 3
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. 4
For example, 24 250 seats were sold on one of the days and 33 250 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%. 5
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. Littlewood, K. (1972). Forecasting and control of passenger bookings. Proceedings from the Twelfth Annual AGIFORS Symposium, Nathanya, Israel. Transcript: Class Protection We re going to continue our discussion on using Littlewood s rule. Now our focus is going to change from controlling rates to actually controlling segments. We ll have a quick recap of Littlewood s rule and then we will move to how we use that technique to control segments. Remember, Littlewood s rule is about allocating inventory to certain price classes. Now we re going to think about allocating inventory to certain types of business, whether that s a transient late- arriving customer or a group traveler who's making that request one or two years in advance of check- in. As a quick sort of review, suppose we have two prices, 200 and 250. And just for argument's sake let s say today is Wednesday the 20th and we re looking at controlling inventory for next Wednesday. As of today we have 15 rooms available for next Wednesday. The decisions we need to make today are about those 15 rooms: Should we continue to sell some of those at 200 or should we keep them all for 250- paying customers? Euro paying customers. Right, so what stage is a function, of how many rooms we have left as well as days before arrival. When do we want to stop selling at 200? 6
We ve collected some data to help us assess those potential outcomes. Basically, this data would be the number of requests for 250- paying customers in this last week prior to arrival. We re focused on demand for the higher- yielding class versus demand for the lower- yielding class. Let s assume we ve collected data for over say the last 100 Wednesdays and during those 100 Wednesdays, in that last week before arrival, the average demand is 15. That demand has a standard deviation of 5 to represent its uncertainty. Remembering back to Littlewood s rule, we want to keep selling at 200 as long as that 200 exceeds the potential revenue from selling at 250. And the potential revenue from selling at 250 is the probability that we would sell all those remaining rooms at 250 times 250. So given that demand has a mean of 15 and a standard deviation of 5, let s assume some distributional form for that demand. For ease, let s assume that it follows a normal distribution, so a nice sort of symmetric- about- the- mean, sort of bell- shaped distribution. We can use some built- in functionality in Excel to help us estimate how many rooms to keep for the 250- paying customers. Excel always calculates probabilities from the left hand side. Basically the probability that demand is less than or equal to some critical level, we want probability the demand is greater than or equal to our critical level being 200 over 250. 7
Excel has a function called NormInv and what NormInv does, or Norm Inverse for the full version of that formula- - we provide a probability and some description of that demand, in our case the mean of 15 and the standard deviation of 5, and it tells us the number that corresponds to that probability. So in Excel we would simply use Norm Inverse of 1 minus 200 over 250, 15, and 5, and that would return to us 10.8. That basically means that the probability of us selling 10.8 or more rooms is 200 over 250. So if we kept exactly 10.8 rooms for the 250- paying customers, we would be indifferent between that 10.8th room as a 250 room versus it as a 200 room. 8
Given we can t sell partial rooms, and then we re going to keep 10 rooms. So basically the probability of selling 10 rooms is a little more than 200 over 250, but keep in mind that if we were to keep 11, the probability would be less than 200 over 250. So our logic here is to keep 10 rooms and allow us to keep selling up to 5 more rooms at 200. Now that we can have a solid idea of how we might use Littlewood s rule to calculate how many rooms to keep, we can extend that now to segments. Keep in mind that group requests typically are made one, two, even three years prior to check- in. These are large conferences looking for large blocks of rooms, typically at very big discounts. And so one of the questions that you have to face is what part of my hotel or what segment of my rooms do I want to keep for these low- yielding, early- arriving customers. Obviously, they re very valuable customers, but you don t want to sell all your rooms to these customers because you have later- arriving, higher- yielding customers. Right, so we could use the same Littlewood logic to look at this. I'm going to sell X rooms to groups, given the probability of selling capacity minus X to higher- yielding people as the same rate as that group class. Obviously, we d like to keep all our rooms for these people if we could stock out. We estimate that probability of stock out using our Norm Inverse function, given the ADR for the transients 9
versus the ADR for the corporate and government versus the ADR for the group. This way we re calculating those allocations across those segments, and in essence determining what our mix is for our property Transcript: Ideal Car Rental Types of Cars Peter Carter, at Ideal Car, has 100 days of data showing daily rentals. We can use this information to help Peter determine how many cars he should stock, striking a reasonable balance between utilization rates and the possibility of running out of cars with the subsequent loss of revenue. The chart shows the monthly revenue and costs for the three types of cars in Ideal s fleet. The first step in solving our problem is to find how many times a car must rent to cover its fixed costs. We ll demonstrate with the economy class car. The economy cars have monthly fixed costs of 336 ( 256 in lease plus 80 in insurance). Given that each economy car nets 24 per rental ( 26 rental rate minus 2 in variable cleaning costs) that means a car needs to rent at least 14 times per month to cover its fixed costs (i.e. needs to rent 14 times to break even) as 336 divided by 24 equals 14. We ll assume that each month has 30 days. That means on any given day for a car to be profitable it needs to have a probability of renting of 14/30 or 46%. Now instead of 30 days, let s look at 100 days of data for economy cars. The chart shows the frequency of the number of cars rented during the last 100 days. On 2 of the 100 days only 10 economy cars were rented. There is also two days when 11 cars were rented. On 7 days 12 cars were rented and so on. If Ideal had stocked 10 cars then they would have rented all 10 cars on 10
all 100 days (because demand is never less than 10). Each of these 10 cars is very profitable. If they stocked 11 cars then the 11th car would have rented on all days except the two days where demand was only 10. The probability of demand for the 11th car is 98/100 or 98% Remember, for a car to be profitable it needs to have a probability of renting of 46%. After calculating all the probabilities we see that 19th car rents enough to cover fixed costs and generates a little profit. Whereas if we stocked 20 cars the 20th car would not rent often enough to cover its fixed costs. In the 100- day period we rent 20 or more cars only 43 times, thus the probability of renting the 20th car is 43%, less than the 46% we need. Another way to look at this is by the number of times the car rents. Remember, in any given month a car must rent at least 14 times to generate enough contribution to cover fixed costs. Because we are now considering a little more than 3 months worth of data a car must rent 100/30 X 14 or 46 times to be profitable more than the 20th car but less the 19th car. 11
Transcript: Ask The Expert: Upgrading/Upselling Opportunities When are upgrades and upsells useful? Upgrades are especially useful when there is a mismatch between supply and demand. There are several reasons why capacity mismatches may occur in practice, including forecast errors and strategic supply limits that aim to skim revenues from customers with high willingness to pay. Upgrades become a key managerial lever in the case of travel and service industries in general when capacity is relatively fixed and difficult to change in the short run as demand fluctuates over time. How are upgrades useful? Upgrades help balance demand and supply by shifting excess capacity of high- grade products to low- grade products with excess demand. Upgrading allows firms to get consumers to commit to purchases at lower prices and then extract additional revenues with the upgrade/upsell. What are some of the main concerns with upgrading? In addition to potentially not having enough high- valued inventories available, upgrading can create strategic consumer issues especially for those receiving free upgrades. Consumers tend to expect upgrades and may become dissatisfied if usual upgrades become unavailable. What type of data do you need to determine if and when you should upgrade? The key to proper management of upgrades is a solid understanding of total demand for higher- valued inventory and when this demand materializes. Essentially you must be able to estimate the likelihood that you won't need that high- valued room once you've upgraded it and made it available to a lower- valued customer. Transcript: Simultaneous Decision Making Up until this stage, we ve been focusing on a single constraining resource. Right, how many rooms should I allocate to which different prices, how should I manage the seats on my particular flight? Going forward, going to add some complexity basically, so we re going to focus on not just one resource but multiple resources, so you can think of this as guests staying multiple nights at your property or individuals flying with your airline but stopping at interconnected cities and moving on to subsequent cities. Under this context of guests staying 12
more than one night or flyers having interconnecting traffic, it results in consumers purchasing different products using the same resource. So I might have a guest who checks in today for a one- night stay. I might have another guest who checks in today for a two- night stay. Both of those guests are staying tonight, but they each bought a different product. One bought a one- night stay, one bought a two- night stay, but they re both using rooms tonight. So when I decide how many rooms to allocate to each of those two different product classes, I need to realize that they re both using inventory tonight. So going forward, we re going to think about how to incorporate that complexity in my allocation decisions. This might be clarified with a simple example. So let s look at our property for the upcoming week. We have a very simple structure here. We have two prices, 150 and 200 Euros, and guests stay one or two nights. 13
In this particular example, we forecasted demand for the upcoming week, and it turns out that only Wednesday is booming with us and on Wednesday we have demand in excess of capacity. So managing inventory on Wednesday is relatively straightforward. We want to make sure we accept requests that bring in as much revenue as possible and reject those requests that bring in less revenue. So in this context we d accept two- night stays at 200, we d accept two- night stays at 150, but we may reject some one- night stays at 150 given their lower revenue. Now we extend this example to not just Wednesday having demand in excess of capacity but also Thursday. So now we have two constraining resources and while it seems still straightforward, if we were to maximize revenue on Wednesday by accepting two- night stays and rejecting some one- night stays, and then move on to Thursday and maximize revenue on Thursday by accepting some two- night stays and rejecting some one- night stays, we quickly realize that the decisions I made on Wednesday, i.e. the two- night stays I accepted on Wednesday, well, those people are now staying on my property on Thursday, and those 14
decisions I made on Wednesday impact the decisions I can make on Thursday. So I can t just make my Wednesday decisions first and then my Thursday decisions, I really need to make my Wednesday and Thursday decision simultaneously and not just Wednesday and Thursday, but because the guests who stayed two nights on Tuesday are going to be on my property on Wednesday and impact my Wednesday decisions and then impact my Thursday decisions, I really need to make my decisions for that whole week simultaneously versus one at a time. This moves us to this framework of simultaneous decision- making. One of the common aspects of this simultaneous decision- making framework is that most of these settings have some sort of limited resource. This limited resource might be, as in our earlier example, how many rooms we have available on Wednesday and Thursday or it might 15
be how much cash you have on hand to purchase items or it might be how many items you have in stock which you can use to manufacture goods and sell to consumers. The thing that s common across this framework is this constrained or limited resource. Our goal is to mathematically model these and as a function of that we need to be able to evaluate performance. And the easiest way to evaluate performance is to have some sort of single unifying objective. So from our context we re going to maximize revenue or maximize profit, but in other contexts you might want to minimize cost, right? We have to be able to map this performance metric, revenue, to our decisions, how many rooms to accept across each of the rate classes and lengths of stays. In addition to having both this sort of unifying objective, which is a function of these decision variables, we re also going to have these constraints, right? I only have 100 rooms available on Wednesday and 100 rooms available on Thursday. We re going to add some other sort of logical constraints; those logical constraints are things like, I can t accept negative reservations, right? So that s pretty easy for you to think logically, but again we re going to do this computationally so we have to define those things as well. Transcript: Optimization at Snap Électrique Excel Solver is a tool that we can use in our simultaneous decision making process. To use Solver, we must build a model that specifies: The decisions we need to make; we refer to these as decision variables 16
The measure to optimize, called the objective for example, maximize profit or minimize costs Limitations on how we make decisions, called constraints for example, limited resources Solver will find values for the decision variables that satisfy the constraints while optimizing (maximizing or minimizing) the objective. We will use Snap Électrique to help describe how to use Solver. We begin with the decision variables. They usually measure the amounts of resources to be allocated to some purpose, or the level of some activity, such as the number of products to be manufactured. For Snap Électrique, we need to decide how many of each of the four products to make. Once we define the decision variables, the next step is to define the objective, which is normally some function that depends on the decision variables. For Snap, the objective is to maximize profit. We know that each LCD touch screen yields a profit of 29, each integrated audio system 32, each voice and audio processor 72, and each custom kiosk 54. Then our objective function might be: ( 29 times the number of LCDs) + ( 32 times the number of integrated audio systems) + ( 72 times the number of voice and audio processors) + ( 54 times the number of custom kiosks). We d be finished at this point, if the model did not require any constraints. In most models constraints play a key role in determining what values can be assumed by the decision variables and what sort of objective value can be attained. It is the constraints that require us to use optimization models like Solver. 17
Constraints reflect real- world limits on production capacity, market demand, available funds, and so on. To define a constraint, you first compute a value based on the decision variables. Then you place a limit (, =, or ) on this computed value. Many constraints are determined by the physical nature of the problem. For example, if our decision variables measure the number of products of different types that we plan to manufacture, producing a negative number of products would make no sense. This type of non- negativity constraint is very common. Often we have constraints that require decision variables to assume only integer (whole number) values at the solution. Integer constraints normally can be applied only to decision variables, not to the quantities calculated from them. For Snap, we cannot allocate more resources to production than we have in inventory. Also we cannot produce negative or partial products. Now let s look at the model we created for Snap Électrique. In the worksheet, we have reserved cells B4 though E4 to represent our decision variables the optimal mix of products to produce. Solver will determine the optimal values for these cells. The profits for each product ( 29, 32, 72, and 54) are entered in cells B5, C5, D5, and E5. This allows us to compute the objective in cell F5. Remember, our objective is the sum of the number of products made times the profit margin. In cells B8:E10, we've entered the amount of resources needed to produce each type of product. With these values, we can enter a formula in cells F8 to F11 that computes the total amount of resource used for any number of products produced. Now open Solver. This may be under the Tools menu or the Data menu depending on what version of Excel you are using. 18
We must let Solver know which cells on the worksheet represent the decision variables, constraints, and objective function. In the Set Objective box, type or click on cell F5, the objective function. In the By Changing Variable Cells edit box, type B4:E4 or select these cells with the mouse. To add the constraints, click the Add button and select cells F8:F10 in the Cell Reference edit box (this will show the number of units or hours needed), and select cells G8:G10 in the Constraint edit box (the number of units or hours available). We can only use equal to or less than the amount of units or hours we have in stock. The constraint is set to. Define the non- negativity constraint on the decision variables. Depending on the version of Excel, we do this by making sure the Make Unconstrained Variables Non- Negative box is checked or click Options then Assume Non- Negative. 19
Also click on Assume Linear Model or use Simplex LP, depending on your version of Solver. To find the optimal solution click Solve. When the next window appears click OK. After a moment, the Solver returns the optimal solution in cells B4 through E4 and a new window appears. Here are the results. This shows that we should build zero LCD Touch Screens. Transcript: Marginal Value of Last Room Sold What happens when I accept a reservation? When I accept a reservation, assuming the guest shows, I receive the revenue from that individual. I also decrease my capacity to sell to subsequent consumers by that reservation. The act of accepting a reservation really decreases the available capacity to your hotel. Thinking about this from a marginal value standpoint, I don t want to accept a reservation unless it's at least as high as the marginal value of that room. Here we determine how many reservations to accept across our two rate classes of 350 and 250 where guests can stay one, two, or three nights. 20
We decided which reservations to accept with the goal of maximizing revenue. In that context we made almost 515,000 ( 514,850). Now let s step back and say Well, what if I had one more room on the 14th? On the very first day, if I had 179 rooms, what if I had 180 rooms? We ll just simply change the rooms that we have available from 179 to 180 and rerun our optimization mode. If we rerun our optimization model, it turns out that our revenue now is 515,000. So by having one more room we can make 515,000 versus earlier we were making 514,850. So, in essence, that one incremental room generated 150 incremental Euros. Our goal now is to take that idea from 179 to 180 and sort of automate that. It turns out, given we re doing things computationally, that s relatively easy. When our results come back, we simply click on the sensitivity report on the right side, and by doing that we generate what is referred to as the shadow prices. What we see here in the very first row of that shadow price table is 150. So, corresponding to cell H4, was the rooms that were available on December 14th, we have a shadow price of 150, which before we calculated manually. 21
So if you think about things on the 14th, if I had 180 rooms versus 179 rooms I would have made 150 more. If I had 178 rooms versus 179 rooms, I would lose 150. If we go back and compare the solutions to having 179 versus 180 rooms, we see some very interesting results. When we had 179 rooms available on the 14th, we accepted 44 reservations for three- night stays at 250. When we had 180 rooms on the 14th, we actually accepted 45 of those three- night- stay 250 requests. Because those are three- night requests, those individuals are now going to stay into the 15th and into the 16th. Because of that, if I accept that three- night stay on the 14th, I have to accept less stays on subsequent days. It turns out on the 15th I accept one less 350 one- night stay. If you look at the 16th, on the 16th before I accepted one three- night stay at 250, now I accept no three- night stays at 250.On the 17th before I accepted 19 two- night stays at 250; now on the 17th I ve accepted 20 of those two- night stays at 250. 22
You see, the simple act of having one more room available on the 14th has this massive chain reaction on subsequent stay days. It s this chain reaction that creates this odd marginal value. We see, then, that we can generate those shadow prices for all subsequent days. It turns out for the subsequent days the shadow prices are much more straightforward, either 350 or 250. The next part is how we use these shadow prices. Just like having one more room on the 14th we generate 150. Having one less room would decrement us by 150. The same thing on the 15th- If I had one more room I could increase my revenue by 350. If I had one less room I would lose 350. My focus is now is back to our marginal analysis, thinking about accepting our reservation. If I accept a reservation for the 14th that means instead of having 179 rooms I have 178 rooms. If I only have 178 rooms, I m going to lose 150. Logically, I would not accept any reservation unless it brought in at least 150. 23
That s fairly straightforward for us it means we re going to accept reservations at 250 and 350. If you look at the 15th, now it says if we had one less room on the 15th, our revenue would go down by 350. That tells us is we re going to close the 15th to 250 reservations, specific to 250 one- night stays. The marginal value on the 15th is 350, whereas a one- night request for a 250 only brings in 250. If we go back to the 14th, if a guest was going to stay two nights on the 14th, so he is going to consume one room on the 14th and one room on the 15th, so logically he has to bring in revenue in access of those two marginal values that is, the 150 plus the 350, which is a total of 500. That means while everything is open on the 14th and I have closed the 250 one- night stays on the 15th, I m actually going to sell some multi- night 250s on the 14th, i.e. I would allow reservations to be made to the 250 rate for a two- night stay on the 14th because that would bring in 500 worth of revenue. Keep in mind the marginal value here is the 150 plus the 350 for a total of 500. Transcript: Using Rate And Availability Controls In this lesson we examine rate and availability controls at the Hotel Ithaca. You will have an opportunity to practice in the following lesson. 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. 24
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 constraint 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. Click Solve. Once the solution comes back, click Sensitivity. Click OK. In Excel, we navigate to the Sensitivity report tab and copy the shadow prices. Navigate to the Restrictions tab. We have already created a table to use in calculating our demand. Paste the copied shadow prices into the shadow price column. Now we can determine our minimum available rates by using the shadow prices. The bid prices, the average of the appropriate shadow prices, become our minimum daily rates. For a one- night stay, the bid price is equal to the minimum daily rate. The bid price for a two- night stay is the average of the first two nights shadow prices. The bid price for a three- night stay is the average of the shadow prices for all three nights of the stay. Copy these three formulas down to fill columns C, D, and E. Now we want to check to see if our rate ( 195, 250, or 350) is greater than these bid prices. If our rate is greater than the bid price, then the rate is available. If the rate is less than the bid price our rate is not available. In F3, G3, and H3 we enter these formulas. The formula will place an X in the cell if the rate is closed and leave the cell blank if the rate is open. Copy the columns and paste into the remaining cells for the 250 and 350 rates. We can take this one step further and use Excel s conditional formatting to color- code the cells and make it easier to read. The green cells indicate the rate is available. The red cells indicate the rate is closed. For example, on Oct. 20th we will accept a one- or two- night reservation at 195, but a three- night reservation is closed at the 195 rate. The lowest rate we can offer for a three- night reservation is 250 as the bid price is 233. 25
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