And. Maria Bernarda Serrano B.A. International Business, ITESM Queretaro, 2012.

Transcription

1 Intermodal Variability and Optimal Mode Selection By Tianshu Huang M.Eng. Industrial Engineering and Operations Research, University of Toronto, 2013 B.A.Sc. Engineering Science, University of Toronto, 2012 And Maria Bernarda Serrano B.A. International Business, ITESM Queretaro, Submitted to the Supply Chain Management Program in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in Logistics and Master of Engineering in Supply Chain Management At the Massachusetts Institute of Technology June Tianshu Huang and Maria Bernarda Serrano. All rights reserved. The authors hereby grant to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature redacted Signature of Author...Signature.red.ac Master of Engineering in Logistics Program Signature of Author... C ertified by... C ertified by... Accepted by... S ig ARCHIVES MASSACH MS rm ITUTE OF TECHNOLOGY AUG LIBRARIES Q irinn"irx rxmr nr-xr1 May 12,2017 ~.JI'4I I~4LLII ~ I ~ Master of E*ine g in Suppl hain_' agement Program Signature redacted May 12, Dr. Chris Caplice Executive Director, Center for Transportation and Logistics Signature,redacted Thesis Supervisor..... Dr. Francisco Jauffred Research Affi~hatr-Center for Transportation and Logistics Thesis Supervisor nature red acted Dr. Yossi Sheffi Director, Center for Transportation and Logistics Elisha Gray II Professor of Engineering Systems Professor, Civil and Environment Engineering

2 Intermodal Variability and Optimal Mode Selection By Tianshu Huang And Maria Bernarda Serrano Submitted to the Supply Chain Management Program on May 12, 2017 in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in Logistics and Master of Engineering in Supply Chain Management. ABSTRACT Transportation cost is one of the major costs in supply chain. Companies need to optimize every aspect of the transportation process to reduce the total logistics cost. A key aspect is optimal mode selection to minimize the cost of every lane in a company's transportation network. The traditional approach is to select the mode based on freight cost and average transit time. Besides these two factors, the transit variability associated with each mode choice also impacts the transportation cost in an indirect way. In particular, higher variability of transit time will lead to a higher safety stock level in order to keep up with service level, resulting in higher inventory holding cost. To study the impact of transit time variability, we first generated transit time distribution from data provided by a larger retailer. Then we constructed a total logistics cost equation based on transportation cost, inventory cost that incorporates both average transit time and transit time variability from the transit time distribution. Lastly, we conducted sensitivity analysis using the total logistics cost equation with respect to changes in service level, load value, and volume. Beside mode selection problem, our approach of including cost of variability in total cost calculation can be applied to general problems that deals with uncertainties. Thesis Supervisor: Dr. Chris Caplice Title: Executive Director, Center for Transportation and Logistics Thesis Supervisor: Dr. Francisco Jauffred Title: Research Affiliate, Center for Transportation and Logistics 2

3 Acknowledgments First and foremost, we would like to express our deepest appreciation to Dr. Chris Caplice and Dr. Francisco J. Jauffred, under whose supervision this project has been carried out. From defining research scope to the conclusion, their guidance has been vital to the completion of this thesis. In addition, we would like to thank our sponsor company and the internal team members for their continuous support and valuable resources provided for this research. First, I would like to thank my thesis partner, Tianshu, for his commitment and contribution to this project. A big thank you to Kirsten, Bruce, Sue, and all the SCM staff for their support and guidance. I would also like to thank my SCM cohort for a wonderful year. Lastly, and most importantly, I would like to thank my family and friends for their permanent love and support, I owe all my achievements to them. - Bemarda I would like to take this opportunity to thank my partner Bernarda, without whom the thesis would not be completed. I also want to thank Dr. Chris and Dr. Francisco, who guided us with their incredible expertise from start to the end. Lastly, I want to thank my family, especially my wife Nina, for their support on all aspects of my life. - Tianshu 3

4 Table of Contents A BSTRA C T... 2 A cknow ledgm ents... 3 List of Figures... 6 List of Tables Introduction Literature R eview Transit tim e M ean and V ariability Sources of variability in lead tim e M ode selection Total C ost Function - C ase Study Sum m ary M ethodology D ata Profiling Tim e/d istance Probability Distribution R esults D ata Profiling Im pact of D istance Im pact of Transit Tim e Im pact of Pickup and Delivery Tim e Shipping Frequency Tim e/d istance Probability D istribution Total C ost Equation Transportation Cost R equired Tim e/d istance Inventory Cost Total C ost Equation D iscussion Total C ost Equation M ode Selection C om parison

5 5.3. Sensitivity Analysis Im pact of Load Value Im pact of Volum e Im pact of service level Sim plifying the m odel G eneralizing the m odel Lim itations Conclusion Future Im provem ents References Appendix

6 List of Figures Figure 1: TL Average Transit Time vs. Distance Figure 2: IM Average Transit Time vs. Distance Figure 3: Speed vs. Distance Figure 4: Average Time/Distance vs. Distance Figure 5: Speed vs. Transit Time Figure 6: TL Average speed vs. Pickup Time Figure 7: TL Average speed vs. Delivery Time Figure 8: TL Average Time/Distance vs. Pickup Time Figure 9: TL Average Time/Distance vs. Delivery Time Figure 10: TL Time/Distance Distribution (h/ mi.) Figure 11: IM Time/Distance Distribution (h/ mi.) Figure 12: Finding Required Time/Distribution for Non-normal distributions Figure 13: Sensitivity Analysis based on Load Value Figure 14: Sensitivity Analysis based on Volume Figure 15: Sensitivity Analysis based on Service Level Figure 16: Sensitivity analysis based on load value for the initial model (MP) vs. the new model (O P ) Figure 17: Sensitivity analysis based on volume for the initial model (MP) and the new model (O P ) Figure 18: Total cost of Truckload/ Total cost of Intermodal by load value Figure 19: Total cost of Truckload/ Total cost of Intermodal by service level Figure 20: IM Average speed vs. Pickup Time Figure 21: IM Average speed vs. delivery Time Figure 22: IM Average Time/Distance vs. Pickup Time Figure 23: IM Average Time/Distance vs. Delivery Time Figure 24: Shipment frequency by transportation mode Figure 25: TL Time/Distance vs. Transit Time Figure 26: TL Time/Distance vs. Transit Time Figure 27: Example of Chainalytics rate estimator

7 List of Tables Table 1: Time/Distance Lognormal and Normal Distribution Parameters - Truckload Table 2: Time/Distance Lognormal and Normal Distribution Parameters - Intermodal Table 3: % of lanes assigned to each mode by ABS Stores vs. our model Table 4: Goodness of fit for Normal and Lognormal distributions (TL) Table 5: Goodness of fit for Normal and Lognormal distributions (IM) Table 6: Time/Distance Lognormal converted parameters for Truckload Table 7: Time/Distance Lognormal converted parameters for Intermodal Table 8: Normal distribution parameters by mode

8 U' 1. Introduction Transportation cost is one of the major drivers of total costs in any retailer's supply chain. Since the transportation cost is dependent on the mode of transportation, optimizing mode selection is imperative to minimize costs. Different transportation modes, and different carriers within a mode offer varying rates, lead times and service level. The traditional approach to the mode selection process is to choose the carrier that offers the lowest rate or the shortest delivery time. However, each mode has an associated transit variability that impacts the total logistics cost. Given this uncertainty, retailers need to increase the safety stock in distribution centers to maintain a high service level, resulting in higher inventory holding costs. Our research proposes to incorporate additional variables, such as lead time uncertainty and service level, into the mode selection process. We developed a model that calculates the total logistic cost incurred by the company for two transportation options; over the road truckload (TL) and intermodal (IM). A major retailer in the US, ABC STORES, manages its inbound logistics. Currently, the company employs truckload and intermodal to move goods from vendor facilities to distribution and mixing centers. Intermodal transportation refers to the use of multiple modes to move freight from the source to the destination point (Lam & Gu, 2016). The scope of this research only deals with inland transportation, therefore intermodal only includes train and truck. The company assigns most of the shipment to truckload, but they believe that there is a cost savings opportunity by favoring intermodal more often. ABC STORES wants to know what the tradeoff between costs, lead time, reliability and inventory levels is for each mode choice. 8

9 We addressed this challenge by incorporating uncertainties in transit time into the total logistics cost. With this method, it is possible to quantify the impact of lead time variability on the inventory costs. We developed a function that calculates the total transportation and inventory costs that the company would incur by selecting each transportation mode. Our model will help the company evaluate the best option not only in terms of freight rates but also in terms of transit time reliability. In Chapter 2 we present the literature review of transit time, transportation mode selection process and the total cost function that served as the base for our model. In Chapter 3 we discuss our methodology. In particular, we present our approach to profiling the data, defining the appropriate probability distribution for the transit time, and developing the total cost equation. The results and discussion are reviewed in Chapter 4 and 5, respectively. Our conclusion and recommendations are explained in Chapter 6. 9

10 El 2. Literature Review In this chapter, we present the existing studies on how to define lead time in terms of expected value and standard deviation and explore sources of variability. Following that, we discuss how disturbances in lead time affect the supply chain performance. Later, we focus on the mode selection processes proposed in past studies. We provide an alternative to the total cost equation considering uncertainties in demand and transit time. Finally, we summarize how these findings relate to our thesis topic and what gap on the existing literature we attempted to fill. 2.1 Transit time Mean and Variability Transit time can be characterized by the expected lead time (mean) and the variability (variance). The mean defines how fast products move from origin to destination, while the variance explains how predictable the lead time is (Chaharsooghi & Heydarti 2010). According to Chopra and Meindl (2010) to reduce safety stock the average lead time has to decrease. Meanwhile, He (2009) demonstrated that inventory levels and total relevant costs are impacted by the variance. Results in a study by Chaharsooghi and Heydari (2010) confirm that transit time variability has a greater impact on inventory holding cost than the mean. These findings give a satisfactory explanation of the differences between transit time and transit time uncertainty. Furthermore, they support one of the motivations for our research: lead time variability impacts inventory costs. Given that this variability differs between truckload and intermodal, it is important to consider its effect on the total logistics costs when selecting the transportation mode. 10

11 2.3.2 Sources of variability in lead time Some of the sources of variability in truckload transit time can be extracted from the regulation in this industry. The Federal Motor Carrier Safety Administration (FMCSA) is the agency in charge of regulating commercial motor vehicles in order to reduce accidents on the road ("FMCSA," 2016). The most important regulation for the purpose of this research refers to the hours of service. According to the Code of Federal Regulations, a driver can only drive up to 11 consecutive hours after a period of 10 hours off-duty (e-cfr, n.d., sec. Part 395-Hours of Service of Drivers). In terms of lead time, this has implications for distances that cannot be covered in 11 hours. Truck drivers will necessarily incur idle time due to the required 10-hour break. Extensive research on the sources of transit time variability for rail transportation can be found in the existing literature. B. Riessen et al. (2013) discuss transit disruptions in container transportation and how adjusting transportation planning to these disruptions affect the costs. Some of the disruptions studied in this paper are a late departure, an early departure or service cancellation. Other sources of variability in rail transportation relate to scheduling. According to Strasser (1992), scheduling comprises three decisions: frequency, dispatching policy and time in the yard. Frequency refers to how often trains run on a certain lane (e.g. every 12 hours, every 24 hours). The policy in terms of dispatching can be to hold trains for late-arriving loads or ship trains ontime. Yard time refers to the amount of time a load has to wait in the yard before being shipped. The above-mentioned sources of variability in each transportation mode are just a sample of where uncertainties arise. Nevertheless, they provide an important background in the process of 11

12 interpreting of ABC STORES's historical records and understanding why the reliability varies between modes. 2.2 Mode selection Transportation mode choice requires a deep understanding of shipper's preferences in terms of costs, transit time reliability, and service. According to Strasser (1992), mode selection is based on carrier's performance. Performance is measured by transit time, transit time reliability (% late) and rates. Furthermore, it is critical that companies use a freight transportation model that correctly and efficiently represents all the fundamental components of a multi-modal transportation system. Crainic et al. (2007) believe that a general transportation model is considered valid if it includes demand and supply requirements, performance measures, and decision criteria. Sheffi et al. (1988) expand more on this topic by analyzing the relationship between transit time and inventory. The transportation mode choice is based on the total cost of freight rate and level of service provided. The service components include transit time and transit reliability, among others. Shippers may want to protect themselves against unreliable transit time by keeping extra inventory as safety stock. The cost of the safety stock is a function of the holding cost rate, the inventory value, and the amount of time the inventory is stored. The paper proposes a model that calculates the total logistics costs considering the transit time as a random variable rather than a deterministic one. The first component is the transportation cost per shipment, which is defined by the rate per shipment and the shipment size. The second component is the stationary inventory costs. This is determined by the inventory holding cost per unit, the inventory level and the number of days the inventory is stored. The last two can be 12

13 calculated from the transit time distribution and customer fill rate. The holding cost rate also impacts the in-transit inventory cost. These studies are extremely relevant for our research topic because they provide a framework of what components should be include in our model. Also, they support our premise that transit time variability has an impact on the total logistic costs and should also be considered when selecting a transportation mode. 2.3 Total Cost Function - Case Study Sheffi et al. (1988) developed an approach to the mode selection process based on the total logistics costs. They created a model to be used by the Burlington Northern Railroad. By incorporating various service elements to the total cost calculation, the model fulfilled multiple objectives. The first one was to train the sales force in evaluating the mode choice from the shipper's perspective. The second objective was to empower the marketing team with a tool that could be used with customers in identifying situations in which shipping by rail is more convenient. The model also intended to instruct the operating department in the importance of customer service. The concept of protected time is incorporated. It is defined as the number of days of supply that the company keeps in inventory to guard against stock-outs. To model the transit time, the authors use a triangular distribution with a minimum, a typical and a maximum value. Using these values, the average transit time, L, and the protected time, t, are calculated. The authors constructed a total cost function that includes transportation, cycle stock, in-transit inventory, and safety stock. It is based on the economic order quantity (EOQ). * Transportation Cost: Annual demand, D (units/year), divided by the EOQ, to get the number of shipments. This figure is multiplied times the rate, a ($/shipment). " Cycle inventory (CS): The average inventory held by the company during a replenishment 13

14 cycle. It is calculated by dividing the EOQ, Q*, by 2. " In-transit inventory (PI): The inventory necessary to cover the demand during the transit time. It is calculated by multiplying the average transit time by the demand in the unit of time in which the transit time is measured. * Safety Stock (SS): The inventory necessary to protect the company against unreliability in the transit time. It is calculated by multiplying the protected time by the demand in the unit of time in which the transit time is measured. " Inventory holding Cost: It is calculated by adding the cycle stock, the in-transit inventory and the safety stock and multiplying the total by the price per unit, p, and the annual holding rate, r. Putting these variables together, the equation is set as follows: Total Cost = - x a] + [h x p x (CS + PI + SS)] In the case study mentioned in this paper, the lead time is measured in days, therefore, the equation can be expressed as follows: Total Cost= xa] + [hx px (+ x L+ t Where, D = Annual demand (units) Q *= Economic Order Quantity (units/shipment) a shipping rate ($/shipment) h Annual holding rate (%). p= Price per unit ($/unit) L= Average transit time (days) t = protected time (days) CS P1 SS This case study is extremely useful for our research since it explains how to calculate the transportation cost and how to quantify the impact of transit time on the inventory cost. However, this model assumes that the transit time follows a triangular distribution. Our calculation of 14

15 inventory costs will have to be adapted to the best probability distribution we define for the set of data that ABC STORES provided. 2.4 Summary A lot of research has been done on transportation mode choice and the factors that affect this choice. Nevertheless, there are some gaps in the existing literature that we expect to fill with our research. There are only few transportation mode selection studies that incorporate transit time as a stochastic variable. Among these models, none included a detailed methodology on how to determine the probability distribution of transit time. Our thesis focused on finding a precise distribution function based on actual data. Furthermore, according to the case study presented in the existing literature review, the shipment size is what determines the tradeoff between transportation and inventory costs. In our research, we analyze the tradeoff based on the transportation mode. 15

16 3. Methodology The main goal of this research was to develop an approach that optimizes the transportation mode selection process. We focused on finding an appropriate distribution for the transit time to quantify its impact on the inventory cost. This section provides an overview of the steps followed to create this model. The method involves three steps: 1) Data profiling to find the factors that are relevant to transit time 2) finding the right distribution to model transit time 3) building the total cost function based on the relevant cost factors and transit time distribution. Once the total cost function is built, it is used to compare the total cost of using truckload and intermodal Data Profiling To find the factors that are relevant to transit time, data profiling was performed on about 70,000 full truck loads (FTL), carrying ambient products, shipped between October 2015 and November 2016 in approximately 1,600 lanes. For each load, the database contains the following information: * Transportation mode: Truckload or intermodal " Origin and destination points: State code, postal code. " Distance: Total distance from origin to destination point in miles. " Pickup and delivery time: In mm/dd/yy hh:mm:ss format. Using this information, the transit time and speed were calculated for each load. For the purpose of this research, the transit time is defined as how long a load spends in transit between it is picked up and its delivery. The total transit time was computed by calculating the difference between pickup and delivery time. Changes in transit time for different distances for truckload and intermodal are shown in Figures 1 and 2, respectively. 16

17 =Mean Distance (mi) Figure 1: TL Average Transit Time vs. Distance inmeon ~' so D 60D 70D SDD 90D 1I0D I ~I Distance (mi) Figure 2: IMAverage Transit Time vs. Distance 17

18 For truckload, it can be observed that transit time increases as the distance increases. For intermodal, the transit time has a more stable trend, with slight peaks at 800, 1200, and 1900 and 2400 miles. However, the relationship between these variables does not provide insights related to the sources of the variability in transit time. Furthermore, we cannot compare the transit time for different lanes because it is highly influenced by the distance, especially for truckload. Therefore, we removed the effect of distance from the transit time. Instead, the transit time per mile was used in the analysis. The transit time per mile is defined as Time/Distance and measured in hours per mile. We used the total transit time and the distance to calculate the speed. This variable states how fast the shipment moves from the origin to the destination point, it does not refer to the velocity of the truck/train. Because our model focuses on incorporating the impact of transit variability into the total cost equation, our first step was identifying the relevant variables that influence the transit time. We analyzed the relation between Speed, Distance, Transit Time, Time/Distance, Pickup/Delivery Time, among others. The results of this analysis are presented in Chapter 4. Once we identified the relevant relationships, we selected the variables that impact the speed and transit time to build the total cost function Time/Distance Probability Distribution The next step was to characterize the probability distribution of the transit time per mile and set the distribution parameters. We tested the goodness of fit for each transportation mode to determine how well-fitted the data was against common continuous probability distributions. The parameters of two distributions with the best results were incorporated in the total cost function. 18

19 3.3. Total Cost Function Once all relevant factors and the best-fitted Time/Distance distributions were identified, the total cost function was built. It incorporates both transportation cost and inventory cost. A sensitivity analysis was performed to analyze how the results varied using both distributions. Finally, we evaluated several limitations of our model and ways to simplify it. 19

20 4. Results This chapter provides an overview of the generated results after following the steps detailed in the Methodology section. First, we present the relevant factors identified through profiling the data. Later, we explain our approach to defining the probability distribution for Time/Distance. The last section shows the components of the total cost function and how we incorporated the results from the previous sections Data Profiling Impact of Distance In terms of the impact of distance on the speed, the expectation was that speed would be lower for longer distances. Results that confirm the previous hypothesis are shown in Figure Transportation Mode " IM " : U : J& *:j I _ 4' *fs.~r. :' 3 a 4 S *0 4S* I. a I... I..4, a a lit; Distance (mi) Figure 3: Speed vs. Distance 20

21 It can be observed that the average speed decreases as distance increases. One thing to note from the graph is that truckload is used more common for shipments on lanes of less than 700 miles. Intermodal shipments become more common as distance increases. Since Time/Distance is the inverse of speed, the expected result was that for shorter distances the average time to move a load over one mile would be lower. Results shown in Figure 4 ratify that the impact of distance on Time/Distance is the opposite than the impact on speed Transportation Mode 0.2D I T Distance (mi) Figure 4: Average Time/Distance vs. Distance Truckload (red bars) dominates for shipments of less than 700 miles and has, on average, shorter values for Time/Distance. Intermodal (blue bars) dominates for the longer hauls and the values for Time/Distance are higher. 21

22 Impact of Transit Time For truckloads transportation, drivers take mandatory breaks after 11 hours on the road. For intermodal, lengthy lanes might require the carrier to stop at multiple yards or consolidate shipments. Therefore, one of the initial hypothesis was that the speed would increase significantly for transit times over 11 hours for truckload and 24 hours for intermodal. Figure 5 shows the impact of transit time on speed for each transportation mode. 60, TRANS MODE 9 IM 55- e TL *i 40~ * IA Transit Time (h) Figure 5: Speed vs. Transit Time A clear trend can be observed where speed reduces as transit time increases. However, the speed for truckloads (red dots) varies in a range of about 5 miles per hour to almost 60 miles per hour, even for transit times of less than 10 hours. For intermodal (blue dots), transit times start at 22

23 around 2 days (48 hours). The variability of speed, even for the shortest lead times, is still significant (between 15 and 30 mi. /h) Impact of Pickup and Delivery Time The impact of pickup and delivery time on average speed and average transit time per mile (Time/Distance) was studied in detail. Findings show that the behavior of speed varies by transportation mode. Findings also show that pickup and delivery times have different effects on the speed, as presented in Figures 6 and 7. Truckloads that are picked up early in the morning (3:00am to 6:00am) are delivered faster and the slowest loads are picked up at night (6:00pm to 1:00pm) Mean w H PU Time Figure 6: TL Average speed vs. Pickup Time 23

24 E24- S H i -Mean 4 2 J 01T DEL Time Figure 7: TL Average speed vs. Delivery Time Consistent with the findings in section of the Literature Review, pickups that happen in the morning are most likely to be handled by drivers who are starting a shift. Therefore, they would be able to drive without long breaks for at least 11 hours. Drivers that pick up loads at night are probably about to end their shift and take the mandatory break. The opposite trend occurs for the average speed at different delivery times. Figure 7 shows that truckloads that are delivered early in the morning have the lowest speed and the fastest loads are delivered between 6:00pm and midnight. As Time/Distance is the inverse of speed, a maximum speed point in figures 6 and 7 present a minimum time/distance point in figure 8 and 9, respectively. For example, the average speed of a truckload that is picked up at 3 am is about 38 mi. /h, and the Time/Distance for the same pick up time is approximately 0.03 h/ mi. 24

25 & V C 4, *1= , H o i l -Mean PU Time Figure 8: TL Average Time/Distance vs. Pickup Time Mean H II. 1 I I1 I L I'l 0.06] ~ I I II I t I 4L,,&LIiI (o DEL Time Figure 9: TL Average Time/Distance vs. Delivery Time 25

26 Interestingly, the average speed for intermodal loads is very consistent for different pickup/delivery times (Appendix A). Intermodal speed - and Time/Distance - are not impacted by either pickup or delivery time Shipping Frequency Analyzing shipping frequency by transportation showed that both truckload and intermodal are used consistently throughout the year, although truckload is significantly much more common (Appendix B) Time/Distance Probability Distribution First, we analyzed the distribution of Time/Distance for each mode. A frequency histogram of this variable for truckload and intermodal is shown in Figures 10 and 11, respectively. I Figure 10: TL Time/Distance Distribution (h/ mi.) Figure 11: IM Time/Distance Distribution (h/ mi.) 26

27 In both the histogram and the box-whisker plot, we observe that the distribution has a long right tail. This indicates that the values of Time/Distance are not symmetrically distributed around the mean and that many loads in the dataset have Time/Distance that are larger than the mean. As both histograms have positive skewed long tails, we hypothesized that the best distribution in terms of goodness of fit would be the lognormal distribution. We tested different continuous distributions and evaluate the goodness of fit of each one. The results (Appendix C) show that the probability that the data do not follow the normal or lognormal distributions for Truckload is less than 1%. For Intermodal, the probability that the data do not follow a normal distribution is less than 1%, and the probability it does not follow a lognormal distribution is less than 4%. Neither number is statistically significant. Therefore, both distributions were used for modelling the transit time. The following step was to generate parameters of each distribution. From the data profiling results, we concluded that the distance has a big impact on the performance of transit time. The trend of Time/Distance by distance for each transportation mode are shown in figures 23 and 24 (Appendix D). We can observe in Figure 23, for example, that the slope of the trend line changes almost every 100 miles increment. Hence, we generated multiple sets of distribution parameter. The generated sets of parameters are shown in table 1 for Truckload and table 2 for Intermodal below. 27

28 Table 1: Time/Distance Lognormal and Normal Distribution Parameters - Truckload. Distnce umbe oflognormal Distribution jnormal Distribution Distance Number of Scale Shape Mean Stdev (ni.) observations (b/ M.) <100 11,913 (3.1926) ,869 (3.1353) ,619 (3.0740) ,027 (3.1263) ,912 (3.0352) ,353 (3.0727) ,348 (2.9644) (3.0034) ,284 (3.0340) (3.0962) (3.0518) (2.9697) > (3.1276) Table 2: Time/Distance Lognormal and Normal Distribution Parameters - Intermodal. Distance Distnce oflogormnal Distribution Number SaeSjMa Normal Distribution te (mil) observations (h/i. < (2.6601) (2.0280) ,267 (2.1570) ,119 (2.1377) ,366 (2.3073) (2.3607) (2.4356) _ (2.6869) (2.7293) (2.5606) (2.6338) (2.7371) (2.7867) > (2.8457)

29 The number of sets for each transportation mode was different based on the changes in the trend of Time/Distance. It was also determined by the number of observations in each distance range. For example, for Truckload the first range goes from zero to one hundred miles (11913 observations), whereas for intermodal it goes up to six hundred miles (81 observations). It can be evidenced in Table 1 - which corresponds to Truckload - that the scale of the Log Normal distribution and the mean of the Normal distribution vary little among distance ranges. However, the shape and standard deviation have a significant variation. Interestingly, the coefficient of variation is high for short distances and decreases as the distance increases. We observe the same pattern for Intermodal loads in Table Total Cost Equation Having conducted data analysis and selected Time/Distance distributions, the total cost equation is constructed based on the findings in sections 4.1 and 4.2. The total cost is determined by two major components: (1) transportation cost and (2) inventory cost Transportation Cost The transportation cost is a function of the carrier's cost and the volume of the lane. This rate is provided by each carrier and it varies between lanes. It considers not only the distance between the origin and destination points but also geographic factors that could impact the transportation mode performance. The rate is also dependent on the volume of demand. For our model, the transportation cost is calculated as follows: Transportation Cost = CPL x D Where: CPL= Carrier cost per load ($/I) D = Annual demand of the lane in number of loads (1) For the purpose of this analysis, the cost per load (CPL) was calculated by using a rate estimator 29

30 provided by Chainalytics Freight Market Intelligence Consortium (2016). This estimation model was used in lieu of actual rates from the shipper. The estimator integrates freight market data from multiple sources to calculate different cost parameters. These parameters vary for short-haul truckloads (less than or equal to 250 miles), long-haul truckloads (greater than 250 miles) and intermodal loads. The primary cost driver is the distance of the lane. It is multiplied by a distance rate, k. The second and third components incorporate the geographic impact due to balancing issues between linehauls and backhauls. These components depend on the state of origin and the state of destination, respectively. The fourth component is a factor of the inverse of the volume. This variable is capturing the impact of economies of scale on a high volume corridor. The last component is a fixed cost, a constant value regardless the distance or volume of the lane. The computation of the rate per load is done as follows: CPL = (d x k) + (0_S) + (DS) + ICV x + C Where: d = Distance (mi.) k = distance rate ($/ mi.) O_S = State of Origin factor ($) D_S = State of Destination factor ($) Icy = InverseCorridor Volume ($) V = Annual volume (1) C = Constant ($) An example of the estimator is presented in Appendix F. The data has been disguised for confidentiality issues. Likewise, in this analysis, the demand (D) was calculated by adding all the loads per lane. In the case where the dataset had records for both transportation modes we added the loads. 30

31 4.3.2 Required Time/Distance The required Time/Distance, t(m, a, service level), represents the required transit time over unit distance given a probability distribution and a specific service level. It is measured in hours per mile. The letter I represents the mean of the distribution of Time/Distance, a represents the standard deviation. The service level represents the percentage of time that an order is delivered on time. For example, for a normal distribution, t(0.05, 0.02, 95%) = 0.08 means that if the company has stored enough inventory to cover for a transit time per mile of 0.08 h /mi. it is able to deliver on-time 95 percent of the time. From another perspective, to deliver on-time 95 percent of the shipments, they have to move faster than 12.5 miles per hour (! 0.08 h /mi.), when Time/Distance is normally distributed with a mean of 0.05 h /mi. and standard deviation of 0.02 h /mi. For a normal distribution, the t(m, u, service level) can be found using the standard normal table given a mean, a standard deviation, and a service level (probability). For other distributions, the t(m, a, service level) can be found by calculating the area under the distribution curve that covers the required service level. For example, in Figure 12 below, the transit time does not follow a normal distribution. 31

32 Time'Distance Required Time/Distance Figure 12: Finding Required Time/Distribution for Non-normal distributions The required time/distance can be found by finding the point in the X axis that covers 95% of the total area under the curve Inventory Cost The inventory cost is determined by the level of cycle stock and safety stock (SS) that the company should maintain in order to protect themselves against transit variability. The safety stock is a function of the demand during the transit time plus a buffer to cover for the transit variability. The transit time and its variability are given by the distance and the parameters we set for the Time/Distance probability distribution. SS = D x d x t(p, u, service level) Where: D Annual demand (1). d= Distance (mi.). t(p, a, service level) = Required Time/Distance (h/ mi.). p = Mean of the normal distribution. c-= Standard deviation of the normal distribution. To convert the scale and shape (lognormal parameters) to mean and standard deviation, respectively, we applied the following formulas:,1 2 it= e V+2 a = V(e2v+,1 2 ) x(e 1 2 ~ 32

33 Where: k= Scale of the lognormal distribution. v = Shape of the lognormal distribution. The converted parameters are presented in Appendix E. To calculate the cost of the safety stock we included the monetary value of a load and the inventory holding rate defined by the company. Unlike Sheffi et al., we are not including cycle stock or pipeline inventory because these portions of the total cost equation are not affected by the freight rate or the transit time. Therefore, it is not relevant for this analysis. The inventory cost function was determined as follows: Inventory Cost = h x C x SS h Inventory Cost = x C x D x d x t(p, a, service level) 8760 Where h 8760 = Inventory holding rate ($/$/h). C = Value of the load ($/1). D = Annual demand (1). d = Distance (mi.). t(p, a, service level) = Required Time/Distance (h/mi.) Total Cost Equation By adding the two components together, we were able to calculate the total cost for each transportation mode for a given lane. The total cost equation is set as follows: Total Cost: [CPL x D] + [7 x C x D x d x t(, a, service level) Where: CPL= Carrier cost per load ($/1). D = Annual demand of the lane in number of loads (1). = Inventory holding rate ($/$/h) C = Value of the load ($/I). D = Annual demand (1). d = Distance (mi.). t(p, a, service level) = Time/Distance for a given service level (h/mi.). 33

34 5. Discussion 5.1. Total Cost Equation As discussed in the Results Section, the total cost is calculated as [CPL X D] + x C x D x d x t(p, a, service level)]. The cost equation requires six input parameters: CPL (carrier cost per load), D (annual demand), h (annual inventory holding rate), C (load value), d (lane distance), and service level. The distribution parameters used for computing the required transit time, t(p, -, service level), can be obtained from the two tables listed in section Mode Selection Comparison There are 1662 different transportation lanes in ABC Store's dataset. Out of these 1662 lanes, ABC Store uses truckload more frequently for 64% of the lanes, intermodal more frequently for 35%, and uses both modes with the same frequency for less than 1% of lanes (13 lanes). This last set of lanes was excluded from the analysis. Having constructed the total cost equation, we applied the equation to ABC Store's dataset to generate transportation mode recommendation for 1649 lanes. For this initial comparison, we used the actual demand of each lane provided in the dataset. For the load value, we assumed an average of $25,000. Further analysis on the impact of changes on the load value and the volume are presented in section 5.3. The confusion matrix presented in Table 3 shows that our model's recommendation coincides with ABC Store's mode choice on about 74% of the lanes. 34

35 Table 3: % of lanes assigned to each mode by ABS Stores vs. our model Model Reconmendation TL IM TOTAL ABCSts TL 60% 4% 65% ABC Stores IM- 21% 14% 35% TOTAL 81% 19% 100% For 4% of the lanes, our model recommends intermodal while ABC Store uses truckload and 21 % of lanes were assigned to truckload by our model while ABC Store uses intermodal. These results show that the total cost equation recommends truckload more often than what ABC Store selects Sensitivity Analysis We calculated the cost of using intermodal and the cost of using truckload for each lane by applying the total cost equation to the dataset provided by ABC STORES. The ultimate output of the model is a recommendation to use the transportation mode that has the lower total cost. If the cost of intermodal is greater than the cost of truckload use the latter and vice versa Impact of Load Value The load value represents the total monetary value of a load. Based on the total cost equation introduced in the Results section, the load value is a multiplier for calculating the total inventory cost. Therefore, an increase in load value would have a multiplicative effect on the total inventory cost and enlarge the cost difference between each transportation option. Specifically, an increase in load value would give the transportation option that has a lower total inventory cost bigger cost advantage, therefore making it more favorable. 35

36 To investigate the impact of different load values on mode selection, a wide range of load values, from $1,000 to $120,000 were used to compute the total cost using the total cost equation introduced in section Then, the model generated a mode selection for each lane based on the mode with the lower total cost. The dynamics of mode selection changes with respect to different load values are presented in figure % 90%M 80% 70% 60% S50% -- TL (ND) 40% -IM (ND) 30% -- TL (LnD) 20% 10% 0% Load value ($) -0- IM (LnD) Figure 13: Sensitivity Analysis based on Load Value The horizontal axis represents the load value measured in dollars per load and the vertical axis represents the percentage of lanes assigned to a specific mode. The blue (TL(ND)) and grey (TL(LnD)) lines represent the percentage of lanes assigned to truckload using normal and lognormal distribution, respectively. The orange (IM(ND)) and yellow (IM(LnD)) lines represent the percentage of lanes assigned to intermodal using normal and lognormal distribution, respectively. As can be seen from Figure 13, the difference in mode selection between using normal and using lognormal distribution is insignificant. However, under both distributions, the percentage of 36

37 truckload selected increases as the load value increase. This is because the inventory cost for truckload is lower than that of intermodal in general. As discussed above, the load value has a multiplicative effect on the total inventory cost. Therefore, an increase in the load value would enlarge the difference in inventory cost, increasing truckload's cost advantage. As a result, an increase in load value makes truckload more favorable than intermodal Impact of Volume The volume represents the number of loads demanded on each lane. Based on the total cost equation discussed in section 4.3.4, the volume is not only a multiplier of the total cost but also inversely related to the rate (based on the carrier rate equation discussed in section 4.3.1), thus inversely related to the transportation cost. Values ranging from 1 to 100 were used to evaluate how changes in the volume affect the percentage of lanes assigned to each transportation mode. The dynamics of mode selection changes with respect to different volumes are shown in Figure % 90% 80% V 70% 60% 50% 40% 30% 20% 1u 4-0 -*- TL (ND) -*- IM (ND) -4-TL (LnD) -e-im (LnD) 10% 0% Volume (1) Figure 14: Sensitivity Analysis based on Volume 37

38 The horizontal axis represents the volume measured in loads per year, and the vertical axis represents the percentage of a specific mode selected. The grey (TL(ND)) and blue (TL(LnD)) lines represent the percentage of lanes assigned to truckload using normal and lognormal distribution, respectively. The yellow (IM(ND)) and orange (IM(LnD)) lines represent the percentage of lanes assigned to intermodal using normal and lognormal distribution, respectively. As can be seen from Figure 14, there is an increase in intermodal selection as the volume increases between 0 and 20 loads per year. This indicates that between 0 and 20 loads, the transportation cost of intermodal decreases in a greater proportion than that of truckload, according to the rate estimator used in this analysis. The mode selection gets stable after 20 because the change in carrier rate is minimal for a volume greater than 20 loads for both modes, according to the carrier cost equation Impact of service level The service level represents the percent of shipments delivered on time. Based on the total cost equation discussed in section 4.3.4, an increase in service level leads to an increase in the required safety stock, and therefore an increase in inventory cost. The dynamics of mode selection changes with respect to changes in the service level is shown in Figure 15. The horizontal axis represents the service level and the vertical axis represents the percentage of a specific mode selected. The grey (TL(ND)) and blue (TL(LnD)) lines represent the percentage of lanes assigned to truckload using normal and lognormal distribution, respectively. The orange (IM(ND)) and yellow (IM(LnD)) lines represent the percentage of lanes assigned to intermodal using normal and lognormal distribution, respectively. 38

39 80% 70% 60% 50% 40% -- TL (ND) 30%1Fl- - IM (ND) -- TL (LnD) 20% -e- IM (LnD) 10% 0%: 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Service Level Figure 15: Sensitivity Analysis based on Service Level It can be seen in the Figure 15 that under both probability distributions the percentage of truckload selected increases as the service level increases and vice versa. This is because truckload has a higher transit time variability than intermodal. To cover the increased service level, using intermodal requires a higher increase in safety stock inventory level to buffer against the bigger transit time variability. As such, a higher service level makes truckload more favorable than intermodal. The difference in mode selection between using normal distribution and log-normal distribution is very small, especially when the service level is low (less than 80%). The difference becomes bigger as the service level increases. This is because the lognormal has a longer tail. In order to cover the longer tail, the mode that has a higher transit time variability (intermodal) is penalized more than the mode with a lower transit time variability. Therefore, the percentage of intermodal selected using lognormal decreases faster than that of using normal. 39

40 5.4. Simplifying the model Even though the lognormal distribution was the best in terms of fit, the sensitivity analysis showed that there is no significant difference when using the normal distribution. Since the latter is more common and therefore better understood, the final version of our model uses normal distribution parameters. Furthermore, our initial model uses parameters for multiple distance ranges. As we explained in section 4.2, the ranges were determined based on the trend of Time/Distance for different distances. Therefore, if we want to apply the model to a different set of data, we would need to identify new ranges and find their parameters. A relevant amount of data for each range would be required and it might not always be possible to obtain this data. However, a single set of parameters for each transportation mode would make the application of this model much simpler. We performed a comparison analysis of the performance of our model using multiple sets of normal distribution parameters and a new version of the model using only one set, for each transportation mode. The new set of parameters is presented in Appendix G. By replicating the same sensitivity analysis based on load value and volume, we were able to confirm that there is no significant difference in the performance of both the initial and the new model. The blue (TL (MP)) and grey (IM (MP)) lines in Figure 16 correspond to the initial model and the orange (TL (OP)) and yellow (IM (OP)) lines to the new version. 40