Estimating the Value of Truck Travel Time Reliability (2019)

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22 This chapter describes how the value of reliability (VOR) was estimated with the data col- lected with the stated-preference survey. Statistical models were estimated to represent the respondents’ selections, capturing how they made trade-offs between costs, time, and reliabil- ity. Because a wide range of models could have been used, each with different assumptions and properties, this chapter first describes theoretically how unreliability might affect motor carri- ers and shippers. This theory was helpful in specifying statistical models that are realistic and in capturing the main relationships at play. Several types of interaction effects and controls were ruled out because they were theoretically unlikely to have a large effect on reliability valuation. Lessons from the literature also informed this understanding. The statistical models estimated were of the discrete choice variety, which is widely used to analyze stated-preference data. Different specifications for these models were explored, and their strengths and weaknesses were assessed. Subgroup models were also estimated to explore how VOR estimates vary with the characteristics of motor carriers and shippers. 4.1 Theory 4.1.1 Reliability Assume that the travel time of a shipment starting at time h is given by a random variable, th. Part of this trip time is expected by truck operators, t–h, and another part is random, rh, with a probability distribution function, f(⋅), such that While there is no standard way that truck operators arrive at t–h, most in the industry rely on a combination of travel applications and experience. For modeling purposes, assume that truck operators approximate t–h as the average trip time of previous comparable trips. (Chapter 5 dis- cusses in more detail how to calculate this measure from available data). Therefore, the expected travel time can be calculated simply with where ti,h is the travel time in day i at time of day h and N is the number of comparable trip times considered. A more elaborate model of expectations could be used instead of Equation 2; however, this formulation is adequate for reliability measurements. (1)t th h h= + r 1 (2), 1 t N th i h i N ∑= = C H A P T E R 4 Modeling

Modeling 23 As seen previously, most research, particularly in Europe, has modeled reliability by using the standard deviation of travel times. Using the notation adopted for the present study, this could be calculated as However, this measure has several disadvantages. Most important, the freight industry does not think about reliability in these terms, so that assumptions and transformation are required to con- vey reliability information to stakeholders (particularly in surveys). Freight planners in the United States also do not consider reliability in this way, which leads this measure to be incompatible with existing planning efforts. The standard deviation also has the drawback of being less sensi- tive to the tails of the distribution than other measures and, therefore, potentially under represents how much truck operators care about rare but significant delays. To address these and other concerns, this study instead opted to measure and model reliability through the 95th percentile delay (sometimes called the “buffer time” in the literature). This measure can be calculated as where the x%y notation indicates the x percentile value of random variable y. This measure is different yet complementary of the delay measures used in traffic engineer- ing, which typically compare average travel times throughout the day, t–h, with the free-flow travel time to estimate the extra time spent in the system because of congestion. Therefore, the 95th percentile delay measure does not overlap with traditional delay measures, and, therefore, both can be considered simultaneously in planning analyses. The 95th percentile delay measure also has the advantage of being able to be used to calcu- late the Travel Time Index, which is the reliability measure most commonly used in bottle- neck analyses and performance monitoring around the United States. This index is typically defined as the ratio of the 95th percentile travel time to the median travel time. 4.1.2 Basic Trucking Company Model Assume that a trucking company moves Q tons of goods per year on a route that is l miles long and takes on average t– hours to complete. The time required to turn around the truck for it to complete the next shipment, including loading, unloading, and repositioning, is defined as γ. Also assume that each shipment moves q tons and that the size of the fleet is F. The total cost per year for this idealized company can be calculated as where cl captures the costs that depend mainly on distance (e.g., fuel, maintenance), ct captures the costs that depend mainly on time (e.g., driver wages), Q/q is the number of truck trips required per year, and cF represents the fixed costs of truck ownership (e.g., depreciation, parking). The number of shipments that a single truck can complete per year is l/( t– + γ), where l rep- resents the number of hours that the truck is available in the year. With these definitions, the size of the truck fleet required to complete Q/q trips is 1 (3) , 2 1 t t N h i h hi N∑ ( )s = − − = 95% 95% (4),t th h i h hj = r = − (5)C c l c t Q q c FT l t F[ ]( )= + + γ + ( )= + γ l (6)F Q t q

24 Estimating the Value of Truck Travel Time Reliability Substituting Equation 6 into Equation 5 and collecting terms leads to The per-ton costs can be calculated as One way to consider reliability in this model is to assume that firms pick a larger γ to buffer against the risk of late deliveries having spillover effects. Hirschman et al. (2016) found that this was one of the main responses of motor carriers to unreliability, which effectively decreases the utilization of trucks. In this sense, γ can be interpreted as a function of the dispersion of r. For simplicity, it is assumed that motor carriers select a γ large enough so that the risk that delays will affect operations is very small. 4.1.3 Basic Shipper Model Assume that the movement of Q goods is part of a supply chain operated by a single shipper. This shipper faces two types of costs: holding costs and broader supply chain costs. Holding costs include warehousing costs and inventory costs, which result from the value of the goods depreciating at φ per year. The total shipper costs per ton shipped can be expressed as where v is commercial value per ton and w(⋅) is a function that specifies the costs per ton of being late by r. This captures the impact of delays on production and other downstream supply chain activities. 4.1.4 Value of Reliability The total expected costs per ton shipped can be calculated by considering the likelihood and impact of different levels of delay: which, using Equations 8 and 9, leads to The amount that costs increase at the margin because of unreliability is known as the VOR. When reliability is measured as the standard deviation of travel times, the VOR can be calculated as (7)C c l c c t Q q T l t F[ ]( )( )= + + l + γ (8)C c l c c t q T l t F ( )( )= + + l + γ 2 (9)c v q Q vt wS ( )= φ + φ + r ; 0, ; 0, (10)E c c f d c f dT S∫ ∫[ ] ( ) ( )= r s r + r s r−∞ ∞ −∞ ∞ ∫[ ] ( ) ( ) ( ) ( )= + + l + + l γ + φ + φ + r r s r −∞ ∞ 2 ; 0, (11)E c c l c c t q c c q v q Q vt w f d l t F t F VOR 1 ; 0, (12) dE c d q c c d d d d w f dt F ∫( )[ ] ( ) ( )= s = + l γs + s r r s rs −∞∞

Modeling 25 In this simple model, the component of VOR due to trucking is a function of how a marginal increase in uncertainty, s, decreases the utilization of vehicles (as γ is increased to add slack to the system), leading to more trucks being needed to move the same freight and increasing time-related costs. Because the VOR in Equation 12 is specified per ton moved, the larger the shipment, q, the smaller the contribution of trucking costs to VOR. On the shipper side, VOR captures how a marginal increase in s increases the frequency and magnitude of delayed shipments, leading to greater supply chain and production costs. Differ- ent functional specifications were used for γ and w to develop analytical formulations for VOR; however this did not provide insights that were general enough to be useful during statistical modeling. For the reasons mentioned previously, this study measured reliability as the 95th percentile delay, instead of as the standard deviation. Theoretically, the VOR estimated for the 95th percen- tile delay measure can be calculated just as in Equation 12, but differentiating with respect to j The VORs and VORj are defined per ton of commodity moved. The effect on total costs per year can be found through VORsQ and VORjQ. With these definitions, the value of time can be calculated as 4.1.5 Abatement Actions In actuality, motor carriers and shippers take many actions to mitigate the costs of unreli- ability. Assume that the shipper can implement action a that reduces the expected costs of travel time unreliability, but at an increasing additional cost. In this case, the shipper will select an opti- mal level of a that minimizes expected costs in the long-run, over many shipments. Assume that the trucking company can similarly implement an abatement action b that reduces the impacts of unreliability. Finding the optimal levels of a and b that minimizes costs can be formulated as where r has a standard deviation, s, and an expectation of zero. The optimal level investment in a and b is defined by the point where the marginal costs of a and b are equal to the marginal savings in unreliability costs. Costs are minimized at this point. The VOR in this case can be expressed as which indicates that the VOR is simply the rate at which expected costs change with respect to reliability, while shippers and trucking companies endogenously reoptimize their operations to reduce these costs. This reoptimization has the effect of reducing VOR estimates. VOR (13) dE c d [ ]= j j [ ] ( )= = + l + φVOT (14)dE c dt c c q v t F min , , (15) , c E c a c b a b S T[ ]{ }( ) ( )∗ = r + rs VOR min , , (16), dc d d E c a c b d a b S T{ }[ ]{ }( ) ( ) = ∗ s = r + r s s s

26 Estimating the Value of Truck Travel Time Reliability 4.1.6 Lessons for Modeling The simple analytical model presented above and the findings from the literature provided the following lessons for the statistical modeling: • Unreliability does not increase the direct costs of operating trucks, in terms of fuel consump- tion, maintenance, and so forth. Instead, it makes it more difficult for truck operators to plan their delivery schedules and thus leads them to build slack into their operations in case of unforeseen delays. This slack manifests itself in trucks arriving early and idling near receivers or in having additional trucks and drivers standing by to pick up after a truck that has been significantly delayed. Consequently, unreliability decreases truck utilization rates and raises costs per shipment. • Unreliability does not directly increase shippers’ inventory costs, and shippers are generally unwilling to increase their inventories to mitigate the potential impacts of delayed shipments (Hirschman et al. 2016). The factors that are most likely to affect reliability valuations for shippers are commodity type, supply chain type, and shipment size. • VOR estimates should consider the actions that shippers and motor carriers might take to mitigate the costs of unreliability, or the estimates will be higher than they should be. The stated-preference survey should stress that participants should assume they implement contingency plans and reoptimize their operations as they consider different alternatives. • The ability to implement mitigating actions likely has a large impact on VORs. Shorter ship- ments are likely to have lower VORs because delays are easier to correct or mitigate. Similarly, large companies are also hypothesized to have lower values of reliability, because they have more trucks available to reposition and respond to delays. Shippers with in-house transporta- tion likely also have greater control in responding to unreliability and, therefore, could have lower values of reliability. Shipments that are internal to the company likely have lower VORs because the company has more time to adapt and implement contingencies. • Penalties or fees in the contract for late delivery should not be included as unreliability costs. Only resource costs should matter in estimating VOR. These transaction costs cancel out throughout the supply chain (Andersson et al. 2017). • The effect of unreliability on costs is likely to be nonlinear. Unreliability levels below a certain threshold are not likely to cause significant disruptions; however, as unreliability increases, the contingencies and precautions that need to be implemented increase exponentially, up until a point at which contingencies have been deployed and further delays do not cause incre- mental costs. • Commodity type is more likely than commodity value to have an impact on reliability valu- ation. The costs of unreliability faced by trucking companies do not depend on the value or type of the commodity. For shippers, the costs of unreliability depend mostly on commodity type. The value of a commodity is not a good proxy for the importance of the commodity in the production process. A low-value commodity, as measured by market prices, could cause a bigger disruption in a supply chain than a higher-value commodity. • The representativeness of the VOR estimates is paramount for using the results in planning analyses. The sample received should be reweighted by using population shares to improve the representativeness of the results. Some of the variables that should be considered include commodity type, shipment distance, and supply chain type. 4.2 Exploratory Statistical Models This section explores how well different statistical models captured respondents’ choices in the stated-preference survey. Different specifications and structures were considered to iden- tify the models that best fit the data and most accurately described the trade-offs between costs

Modeling 27 and shipment reliability. However, not all models presented in this section were robust enough for use in planning analyses. Section 4.4 summarizes the model results recommended for this purpose. The simplest model estimated was the multinomial logit (MNL) model. With this structure, the utility of selecting an alternative was formulated as where asc = alternative specific constant that captures whether respondents systematically prefer an alternative that is on the left of the screen, βc = parameter coefficient for cost, βt = parameter coefficient for time, and βj = parameter coefficient for reliability, measured in terms of 95th percentile delay. Models that measure reliability with the standard deviation of travel times, s, were also esti- mated so that the results could be compared with the literature. The error term e in an MNL model has a specific distribution that gives the model specific properties, some of which will be relaxed in other models to improve fit (for a review, see Train 2003). Adding an alternative specific constant was important, because even though the choices were unlabeled—an alternative should have the same utility whether it is presented as A or B—some respondents might tend to select the alternative they saw first. Studies have found that including this constant term improves model fit (Jin and Shams 2016). Table 4-1 shows the results of estimating MNL models for different ways of defining reli- ability and for samples that had undergone different levels of data cleaning. The parameter estimates were used to calculate the value of reliability VORj when reliability was measured as the 95th percentile delay and the value of reliability VORs when reliability was measured as the asc + (17)U C tc t= β + β + β j + ej Parameter Outliers Removed Outliers + Illogical Removed Outliers + Illogical + Low Relevance Removed Model A (MNL additive) Model B (MNL additive) Model C (MNL additive) Model D (MNL additive) Model E (MNL additive) Model F (MNL additive) Alternative A constant –0.1581*** –1.5591*** –0.2904*** –0.2885*** –0.3064*** –0.3046*** Cost ($000) –0.4539*** –0.4530*** –0.8799*** –0.8791*** –1.0389*** –1.0389*** Time (h) –0.0308*** –0.0309*** –0.0487*** –0.0489*** –0.0530*** –0.0534*** SD time (h) — –0.5529*** — –0.6416*** — –0.6705*** 95th percentile delay (h) –0.2876*** — –0.3343*** — –0.3495*** — Log likelihood –4,181 –4,165 –3,562 –3,545 –2,449 –2,436 No. respondents 976 976 898 898 631 631 No. observations 15,364 15,364 14,200 14,200 9,992 9,992 VOT ($/shipment-hour) 67.8 68.2 55.3 55.6 51.0 51.4 VOR ($/shipment-hour) — 1,220.2 — 729.8 — 645.4 VOR ($/shipment-hour) 633.5 — 379.9 — 336.4 — Note: SD = standard deviation; — = model parameter was not estimated. *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. σ ϕ Table 4-1. Basic models by data-cleaning actions.

28 Estimating the Value of Truck Travel Time Reliability standard deviation. All of these models were estimated on the sample with the outliers removed, as described in Section 3.4. The other data-cleaning actions undertaken were • Removing respondents who responded illogically to two or more trivial questions (i.e., selected an alternative that was inferior in all dimensions) and • Removing respondents who rated the relevance of the stated-preference questions to their own operations at 2 or lower (on a 5-point scale). The results indicated that removing outliers was important in obtaining interpretable esti- mates. Keeping outliers in the sample led to insignificant parameter estimates (not shown in the table). Removing respondents who responded illogically to two or more questions also improved model fit considerably. These respondents were likely not taking the survey seriously or did not understand the choice situations presented. This improvement was more significant in some of the more detailed models estimated later in this section. Further removing respon- dents who said the questions were not relevant did not improve model fit significantly (at a large loss of sample). Respondents could still have provided well-reasoned answers, even if the questions were less relevant to their situation. Overall, it was judged that removing outliers and illogical respondents was the best strategy to improve the quality of the sample, and all future models were estimated on this cleaned sample. VORs estimates were slightly less than twice as high as VORj estimates. The relationship between j and s was close to linear (exactly linear if travel times were normally distributed), although with real data, the relationship can be more complex, especially if the distribution is multimodal (as tends to happen on arterials). However, the tendency for this relationship to be linear implies that models that use these two metrics are functionally similar. Therefore, because of the advantages of the 95th percentile delay measure described in Section 4.1.1, only this measure is used in the remainder of this chapter. 4.2.1 Comparison to Previous Estimates While the VOT estimates were roughly in line with the literature, the VORs estimates were higher than most previous studies. The estimates did decrease considerably in the more detailed models presented later in this section; however they remained higher than the estimates in the recent literature. For a comparable model, Jin and Shams (2016) estimated a VORs of $59.5/ shipment-hour, and de Jong et al. (2014) estimated a VORs of €14.0/shipment-hour (for a review of previous estimates, see Shams et al. 2017). Many factors can explain why the estimates in the present study are higher. 4.2.1.1 Presentation of Reliability The main factor is probably how reliability was described to respondents. De Jong et al. (2014) described reliability in terms of five equally probable travel times, where one was significantly higher than the rest. The main issue with this approach is that it underrepresents unreliability by not describing what could happen 1 out of 10 times or 1 out of 20 times (95th percentile), which are the levels of certainty relevant to modern-day shippers. The worst travel time presented in this approach had a 20 percent chance of occurring, which is too frequent to capture the rare but large delays that shippers care about. It is possible that many respondents took the highest value presented on the screen as indicative of the worst-case delay associated with an alternative, which would lead the estimated values of reliability to be much lower. A similar issue likely occurred with Jin and Shams (2016, p. 79), who described reliability to respondents as 1 out of 4 times “on-time” and 1 out of 5 times “with possible delay of x hours.” Not only does this approach also ignore the consequences of rarer but larger delays that are criti- cal, but it further dilutes their impact by adding the word “possible” in front of the consequence. It is likely that this presentation of reliability also leads to lower estimates.

Modeling 29 4.2.1.2 Sample Differences The differences in the estimates could also be attributed to the composition of the sample. As shown later in this chapter, company size and shipment distance were found to have a very large effect on VOR estimates. For example, smaller companies had VORs that were signifi- cantly larger (by up to 75% more), and long-haul shipments had VORs that were also significantly larger than short urban shipments (by up to 400% more). However, only 22.7 percent of Jin and Shams’ (2016) respondents reported shipments longer than 300 miles, while in the pres- ent study, around 50 percent of shipments were longer than 500 miles. This would naturally lead the VOR estimates from the present study to be larger than those of Jin and Shams (2016), even if the present study had measured the same effect. The same occurred with company size. Around 50 percent of the respondents of the present study worked in small companies with one to four employees (most of these were truck owner–operators). In contrast, in Jin and Shams (2016), only 25 percent or so of the companies surveyed had fewer than 20 employees. Jin and Shams (2016) focused on larger companies, which generally have lower VORs, according to the findings of the present study. 4.2.1.3 Framing of Choice Questions Another factor that could have caused previous studies to estimate lower values of reliability is not making a clear distinction between travel time variability that is anticipated and variability that is unanticipated. For example, the terminology used could have been interpreted by some respondents as referring to delays relative to free-flow travel times. Respondents might not have understood that delays are unexpected. This interpretation would lead VOR estimates to be lower because some of the unreliability would be attributed to recurring congestion, which has fewer adverse impacts because it can be anticipated. 4.2.2 Taste Heterogeneity One of the main limitations of the MNL model is that parameter coefficients are assumed to be fixed. All differences between individual-level preferences and the estimated coefficients are accounted for in the error term. There are various ways of relaxing this assumption and estimat- ing models that explicitly consider heterogeneity in preferences. One popular alternative is to use mixed logit (ML) models in which parameters are defined by a probability distribution instead of a fixed value. This type of model is vastly more flexible and has been proven to be capable of approximating any distribution of preferences without imposing restrictions on choice behavior (Hess and Train 2017). Using the ML formulation, the utility that a respondent, n, gets from selecting an alternative can be formulated as where parameters βn,t and βn,j are now normally distributed with means and standard deviations that are estimated by the model, and the error term en can have a different variance for different decision-makers and choice situations. Table 4-2 shows the estimation of MNL and ML models for different types of respondents. The ML models have higher log likelihood values than the MNL models, which indicates that they fit the data better, which is unsurprising, given that these models have more degrees of freedom. Parameter estimates for the ML models were only significant for motor carriers, which received a larger number of responses. However, more refined ML models shown later in this chapter have significant parameters for all coefficients. All ML models were estimated by using simulation with 10,000 draws. asc + (18), ,U C tc n t n n= β + β + β j + ej

30 Estimating the Value of Truck Travel Time Reliability 4.2.3 Sample Weighting When estimating MNL or ML models, weights can be introduced in the log likelihood func- tion that give greater weight to certain survey responses. This approach was used to reweight the sample so that it is more representative of the population being modeled. The Freight Analysis Framework (v. 4.4) data set was used to calculate the shares of commodities moving by truck in the United States by shipment length. These shares were then used to reweight the sample so that the results better reflected conditions nationwide. Correcting for shipment distance and com- modity type was important because, in the literature, these two factors were found to have a large impact on reliability valuation (corroborated in the authors’ own analysis). The results of these reweighted models can be found in Table 4-3. Reweighting increased substantially the log likeli- hood values of all models, but more importantly this correction now led the ML coefficients for shippers to become significant, suggesting that the survey received better results (lower noise) for respondents who were reweighted more heavily. 4.2.4 Parameter Correlation and Scale Heterogeneity The ML models in Table 4-3 assumed that the random parameter coefficients for time and the 95th percentile delay are independent. This is unrealistic, as respondents who have a high disutility of travel time are also likely to have a high disutility of unreliability. To account for this, an additional parameter was introduced that captured the correlation between these two variables. Hess and Train (2017) noted that this formulation, with correlation between random parameters, has the added advantage of considering scale heterogeneity, which is potentially a factor in this study’s sample. Heterogeneity in the scale of the utility function is caused by unobserved variables playing a larger role for some survey participants than others. That is, this occurs when one or more of the subgroups has greater random variation in its choices that cannot be explained by the model. This is likely the case in this study’s sample, given that it came from a wide range of respondents around the country. As can be seen in Table 4-4, using this more flexible version of the ML model improved the estimates, which increased log likelihood scores and led some parameters to become significant. Parameter Motor Carrier Shipper w/o Transportation Shipper w/Transportation Model G (MNL) Model H (ML) Model I (MNL) Model J (ML) Model K (MNL) Model L (ML) Alternative A constant –0.20064*** –0.01184 –0.65740*** –2.6890 –0.36860*** –0.40436 Cost ($000) –0.26447* –0.88778** –1.50211*** –8.7230 –2.79190*** –18.9473 Time (h) –0.05057*** –0.23440*** –0.04784*** –0.3073 –0.04910*** –0.51008 95th percentile delay (h) –0.30850*** –1.24058*** –0.41364*** –2.6598 –0.38174*** –3.30001 SD time (h) — 0.30838*** — 0.5329 — 1.11131 SD 95th percentile delay (h) — 1.32146*** — 2.2431 — 3.16557 Log likelihood –2,110 –2,031 –346 –326 –1042 –975 No. respondents 505 505 106 106 287 287 No. observations 7,990 7,990 1,664 1,664 4,546 4,546 VOT ($/shipment-hour) 191.2 264.0 31.9 35.2 17.6 26.9 VOR ($/shipment-hour) 1,166.5 1397.4 275.4 304.9 136.7 174.2 *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. ϕ Table 4-2. Models by respondent type.

Modeling 31 Parameter Motor Carrier Shipper w/ Transportation Shipper w/o Transportation Model S Model T Model U Model V Model W Model X (ML + com. & dist. weighting) (ML correlation + com. & dist. weighting) (ML + com. & dist. weighting) (ML correlation + com. & dist. weighting) (ML + com. & dist. weighting) (ML correlation + com. & dist. weighting) Alternative A constant –0.2136*** –0.2572*** –1.2855*** –1.3806*** –0.8984*** –0.3914*** Cost ($000) –0.4931 –0.6788* –2.9029*** –3.6284*** –34.3629*** –25.2386*** Time (h) –0.3578*** –0.2794*** –0.0729*** –0.0526** –1.2643*** –0.3850* 95th percentile delay (h) –0.6452*** –0.5780*** –0.6435*** –0.6764*** –3.6671*** –2.1374*** SD time (h) 0.5723*** 0.7268*** 0.0873** –0.1724*** –1.0748* –1.5924*** SD 95th percentile delay (h) 0.5243*** 0.3082*** 0.4073*** 0.0012 3.7167*** 3.7167*** Time: 95th percentile delay correlation (h) — –0.3317*** — 0.4433*** — 1.0422*** Log likelihood –2,003 –1,963 –332.87 –329.39 –967.26 –957.75 No. respondents 505 505 106 106 287 287 No. observations 3,995 3,995 832 832 2,273 2,273 Average tons per shipment 19.9 19.9 14.1 14.1 12.7 12.7 ($/shipment-hour) — 411.6 25.1 14.5 36.8 15.3 ($/ton-hour) — 20.7 1.8 1.0 2.9 1.2 ($/shipment-hour) 1,308.5 851.5 221.7 186.4 106.7 84.7 ($/ton-hour) 65.8 42.8 15.7 13.2 8.4 6.6 *Statistically significant at 95% level; **statistically significant at 99% level;***statistically significant at 99.9% level. VOT VOT VOR VORϕ ϕ Table 4-4. Additional ML models by respondent type. Parameter Motor Carrier Shipper w/ Transportation Shipper w/o Transportation Model M Model N Model O Model P Model Q Model R (MNL + com. & dist. weighting) (ML + com. & dist. weighting) (MNL + com. & dist. weighting) (ML + com. & dist. weighting) (MNL + com. & dist. weighting) (ML + com. & dist. weighting) Alternative A constant –0.20357*** –0.2136*** –1.0012*** –1.2855*** –0.3295*** –0.8984*** Cost ($000) –0.25901* –0.4931 –1.9483*** –2.9029*** –4.6013*** –34.363*** Time (h) –0.11363*** –0.3578*** –0.0426*** –0.0729*** –0.1522*** –1.2643*** 95th percentile delay (h) –0.32811*** –0.6452*** –0.4217*** –0.6435*** –0.3823*** –3.6671*** SD time (h) — 0.52426*** 0.40728** — 3.71665*** SD 95th percentile delay (h) — 0.57226*** 0.08733*** — –1.0748* Log likelihood –2,045 –1,977 –337.11 –332.87 –1,054 –967.26 No. respondents 505 505 106 106 287 287 No. observations 3,995 3,995 832 832 2,273 2,273 Average tons per shipment 19.9 19.9 14.1 14.1 12.7 12.7 VOT ($/shipment-hour) 438.7 –– 21.8 25.1 33.1 36.8 VOT ($/ton-hour) 22.1 –– 1.5 1.8 2.6 2.9 VOR ($/shipment-hour) 1,266.8 1,308.5 216.5 221.7 83.1 106.7 VOR ($/ton-hour) 63.7 65.8 15.3 15.7 6.5 8.4 Note: com. = commodity; dist. = distance. *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. ϕ ϕ Table 4-3. Models by respondent type adjusted by commodity and distance shares.

32 Estimating the Value of Truck Travel Time Reliability The models recommended for planning analysis have the specification used in Models T, V, and X. These models are flexible, in that parameters are defined as random variables that can be correlated. Moreover, these models reweight the sample to improve the representativeness of the results. 4.3 Subgroup Models This section describes how the VOR and VOT estimates varied for different subgroups of respondents. The results are shown primarily for the type of model recommended for planning analysis; however, for some subgroups, MNL models are shown as well to facilitate comparisons with the literature, most of which has not successfully estimated ML models. 4.3.1 Commodities Table 4-5 shows the VOT and VOR estimates for 10 commodity groups, using only ML models. The highest VORs were found for agriculture products and fish, conceivably because of perish- ability. Furniture, mixed freight, and manufactured products come in second. As expected, the lowest VOR was estimated for stones, nonmetallic minerals, and metallic ores. 4.3.2 Shipment Distance Table 4-6 shows the effect of shipment distance. For both MNL and ML models, shipment distance was observed to have a strong effect on VOT and VOR. As shipments get longer, the importance placed on reliability increases substantially. Shipments of 500 miles or more had a VOR 4 times greater than that of shipments of 75 miles or less. Commodity (SCTG classification) VOT ($/shipment-hour) ($/shipment- hour) P-Value of Parameter Price Time 95th Percentile Delay 01-05 Agriculture Products and Fish 183.6 271.3 0.000 0.000 0.000 06-09 Grains, Alcohol, and Tobacco — — 0.736 0.096 0.005 10-14 Stones, Nonmetallic Minerals, and Metallic Ores 169.2 67.5 0.001 0.000 0.000 15-19 Coal and Petroleum Products — 88.0 0.010 0.933 0.006 20-24 Basic Chemicals, Chemical, and Pharmaceutical Products — — 0.196 0.709 0.187 25-30 Logs, Wood Products, and Textile and Leather 57.5 120.8 0.000 0.054 0.000 31-34 Base Metal and Machinery 202.6 97.6 0.000 0.000 0.000 35-38 Electronic, Motorized Vehicles, and Precision Instruments — — 0.408 0.864 0.403 39-43 Furniture, Mixed Freight and Miscellaneous Manufactured Products 43.4 133.1 0.000 0.001 0.000 Unknown — — 0.459 0.378 0.085 Note: VOT and VOR estimated with ML models with normal parameters and correlation between time and reliability coefficients. Sample reweighted to match shares of U.S. truck shipments by commodity and distance per Freight Analysis Framework v. 4.4. All values shown calculated with parameters significant at the 90% level. SCTG = Standard Classification of Transportable Goods. VORσ Table 4-5. Commodity models, ML formulation.

Modeling 33 4.3.3 Company Size Table 4-7 explores the effect of company size on model estimates. Larger companies were observed to have lower VOR values, likely because these companies have a greater ability to manage the impacts of traffic unreliability. 4.3.4 Shipment Characteristics Table 4-8 and Table 4-9 show model estimates by shipment characteristics. Shipments that respondents indicated had perishable commodities resulted in very high VOR estimates, although these were not statistically significant because the sample was not large enough. The sample also did not include enough shipments with delivery windows of less than 5 min- utes or just-in-time (JIT) supply chains to estimate statistically significant VORs. Shipments involving high-value commodities and less-than-truckload shipments were also observed to have higher than average VOR estimates. Contrary to expectations, shipments involving an intermodal transfer had lower VOR estimates, indicating that the risk of missing a connec- tion does not affect reliability valuations. These shipments, however, had some of the highest VOT estimates. 4.3.5 Receiver Type Table 4-10 explores the effect of receiver type on reliability valuations. As expected, shipments intended for customers had VOR estimates 2.4 times greater than internal shipments (i.e., ship- ments to own company). A similar effect was also found for VOT. 75 miles or less 75 miles to 500 miles 500 miles or more Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A constant –0.33850*** –0.5911** –0.30350*** –0.4786* –0.3032*** –0.4133*** Cost ($000) –5.64710*** –33.637** –1.81560*** –12.876* –1.0529*** –2.7848*** Time (h) –0.58300*** –0.85 –0.17170*** –0.3234 –0.0471*** –0.0398** 95th percentile delay (h) –0.38390*** –2.2279** –0.33300*** –2.4816* –0.3088*** –0.7262*** SD time (h) — –3.2122** — –1.9468* — –0.2483*** SD 95th percentile delay (h) — –0.0159 — 1.9354* — 0.2885** Time: 95th percentile delay correlation (h) — 2.4183* — 2.0754* — 0.6848*** Log likelihood –639 –596 –1496 –1,412 –1,383 –1,333 No. respondents 174 174 377 377 347 347 No. observations 1,380 1,380 2,970 2,970 2,750 2,750 Average tons per shipment 16.1 16.1 15.1 15.1 14.4 14.4 ($/shipment-hour) 103.2 25.3 94.6 25.1 44.7 14.3 ($/ton-hour) 6.4 1.6 6.3 1.7 3.1 1.0 ($/shipment-hour) 68.0 66.2 183.4 192.7 293.3 260.8 ($/ton-hour) 4.2 4.1 12.2 12.8 20.3 18.1 *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. VOT VOT VOR VORϕ ϕ Table 4-6. Models by shipment distance ranges.

34 Estimating the Value of Truck Travel Time Reliability 1–4 Employees 5–100 Employees More than 100 Employees Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A constant –0.2064*** –0.3173*** –0.2582*** 0.7254*** –0.8536*** –2.2209*** Cost ($000) –0.5163*** –3.1464*** –3.0809*** –38.667*** –1.9432*** –9.4939** Time (h) –0.126*** –0.5322*** –0.0884*** –0.0622*** –0.0553*** –0.1391 95th percentile delay (h) –0.3149*** –0.6017*** –0.4057*** –4.2627*** –0.3631*** –1.5815*** SD time (h) — 1.2814*** — –3.1996*** — –0.8165*** SD 95th percentile delay (h) — 0.3494*** — 2.03*** — –0.007 Time: 95th percentile delay correlation (h) — –0.349*** — 3.7222*** — 1.6239*** Log likelihood –1,765 –1,664 –1,200 –1,127 –479 –431 No. respondents 429 429 334 334 135 135 No. observations 3,385 3,385 2,646 2,646 1,069 1,069 Average tons per shipment 18.4 18.4 15.1 15.1 14.5 14.5 ($/shipment-hour) 244.0 169.1 28.7 1.6 28.5 –– ($/ton-hour) 13.3 9.2 1.9 0.1 2.0 –– ($/shipment-hour) 609.9 191.2 131.7 110.2 186.9 166.6 ($/ton-hour) 33.2 10.4 8.7 7.3 12.9 11.5 *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. VOT VOT VOR VOR ϕ ϕ Table 4-7. Models by company size. Contained Perishable Commodity Delivery Window Less than 5 Minutes JIT Supply Chain Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A constant –0.2978*** –0.4807*** –0.3295*** –0.5500*** –0.4449*** –0.8918*** Cost ($000) 0.0543 1.2543 0.4245 2.7000** –0.6481*** –0.1506 Time (h) –0.1133*** –0.6888*** –0.1491*** –0.4034*** –0.0889*** –0.4868* 95th percentile delay (h) –0.4169*** –1.4151*** –0.2036*** –0.4899*** –0.2843*** –0.8848*** SD time (h) — 1.2503*** — 0.6814* — –1.3149*** SD 95th percentile delay (h) — 1.0295*** — 0.4669* — 0.5591 Time: 95th percentile delay correlation (h) — –0.2765* — –0.6800** — 0.9447*** Log likelihood –597 –554 –440 –424 –554 –528 No. respondents 165 165 93 93 133 133 No. observations 1,312 1,312 741 741 1,047 1,047 Average tons per shipment 14.2 14.2 16.4 16.4 16.8 16.8 ($/shipment-hour) –– — — –149.4 137.2 — ($/ton-hour) — — — –9.1 8.2 — ($/shipment-hour) — — — –181.4 438.7 — ($/ton-hour) — — — –11.1 26.2 — *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. VOT VOT VOR VOR ϕ ϕ Table 4-8. Models by shipment characteristics.

Modeling 35 Own Company Customer Intermodal Transfer Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A specific constant –0.5755*** –1.059*** –0.2342*** –0.3265*** –0.2331*** 0.0218 Cost ($000) –3.2976*** –16.967*** –0.9578*** –9.7676*** –2.0926*** –10.509*** Time (h) –0.0676*** –0.4439*** –0.0871*** –0.0855* –0.0942*** –0.4554*** 95th percentile delay (h) –0.5046*** –1.2791*** –0.3315*** –1.5027*** –0.4035*** –1.0199*** SD time (h) — 1.2513*** — –1.1654*** — –1.3021*** SD 95th percentile delay (h) — 0.7474*** — 0.78005*** — 0.5149*** Time: 95th percentile delay correlation (h) — –0.381*** — 1.35091*** — 0.7325*** Log likelihood –597 –559 –2,359 –2,228 –160 –143 No. respondents 206 206 981 981 43 43 No. observations 1,619 1,619 4,600 4,600 343 343 Average tons per shipment 16.7 16.7 15.7 15.7 22.9 22.9 ($/shipment-hour) 20.5 26.2 90.9 33.3 115.2 182.0 ($/ton-hour) 1.2 1.6 5.8 2.1 5.0 7.9 ($/shipment-hour) 153.0 75.4 346.1 183.6 101.8 82.8 ($/ton-hour) 9.1 4.5 22.0 11.7 4.4 3.6 *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. VOT VOT VOR VOR ϕ ϕ Table 4-10. Models by shipment receiver. High-Value Commodities Intermodal Transfer Less than Truckload Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A constant –0.2965*** –0.4197*** –0.4143*** –0.9479*** –0.2097*** –0.3295*** Cost ($000) –1.9236*** –5.0589*** –3.7145*** –8.9503*** –1.1882*** –4.5225*** Time (h) –0.0756*** –0.3258*** –0.3364*** –1.4745*** –0.0396*** 0.0445 95th percentile delay (h) –0.4195*** –0.6431*** –0.3498*** –0.6777*** –0.2551*** –0.9251*** SD time (h) — 0.5787*** — 2.5238*** — –0.4883*** SD 95th percentile delay (h) — 0.3276 — 0.2562 — 0.2621 Time: 95th percentile delay correlation (h) — –0.2551*** — –0.0457 — 1.2833*** Log likelihood –707 –667 –238 –215 –1,342 –1,311 No. respondents 196 196 62 62 301 301 No. observations 1,551 1,551 495 495 2,380 2,380 Average tons per shipment 14.7 14.7 21.8 21.8 6.8 6.8 ($/shipment-hour) 39.3 64.4 90.6 164.7 33.3 — ($/ton-hour) 2.7 4.4 4.2 7.6 4.9 –– ($/shipment-hour) 218.1 127.1 94.2 75.7 214.7 204.6 ($/ton-hour) 14.8 8.6 4.3 3.5 31.4 29.9 *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. VOT VOT VOR VOR ϕ ϕ Table 4-9. Models by shipment characteristics.

36 Estimating the Value of Truck Travel Time Reliability 4.3.6 Question Order The order of the questions presented to respondents could influence the results. On the one hand, respondents could take the first questions more seriously because they were less fatigued. On the other hand, some respondents could take time to warm up and learn how to respond to the hypothetical questions. As can be seen in Table 4-11, the VOR estimated for just the first three questions was higher than for the last three, although from this information alone it is impossible to know which set of answers to trust more. Respondents were given fewer choice questions than previous studies, which typically presented respondents two to three times more questions (Jin and Shams 2016, for example). This could also explain why previous studies estimated lower VORs if the trends identified in Table 4-11 extend to longer surveys. 4.4 VOT and VOR Estimates The modeling results recommended for planning analysis are summarized in Table 4-12. Values are only shown for ML models with parameter correlation because this was the most flexible and robust model estimated. These models reweighted the sample by commodity and distance shares in the United States to improve the representativeness of the results. Valuations are shown both by shipment and by tonnage. The latter measure is useful because many of the costs of unreliability increase with shipment size. The average VOR was estimated to be $159.9/shipment-hour, or, equivalently, $9.4/ton-hour. This is the value recommended for general planning analysis. In this sample, the VOR was found to have a standard deviation of $87.9/shipment-hour, indicating that 50 percent of respon- dents had a value between $100.1/shipment-hour and $219.6/shipment-hour. The VOT was not found to be statistically significant in the overall model; however, more-detailed models *Statistically significant at 95% level; **statistically significant at 99% level; ***statistically significant at 99.9% level. First 3 Questions All Questions Last 3 Questions Parameter MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting MNL + Com. & Dist. Weighting ML Correlation + Com. & Dist. Weighting Alternative A specific constant –0.451*** –0.5504*** –0.3100*** –0.3242*** –0.2331*** 0.0218 Cost ($000) –1.0001*** –3.3579*** –1.5441*** –9.1721*** –2.0926*** –10.509*** Time (h) –0.0713*** –0.0895 –0.0903*** –0.0856 –0.0942*** –0.4554*** 95th percentile delay (h) –0.3352*** –0.8255*** –0.3537*** –1.4665*** –0.4035*** –1.0199*** SD time (h) — 0.4195*** — –1.0587*** — –1.3021*** SD 95th percentile delay (h) — 0.5239*** — 0.8059*** — 0.5149*** Time: 95th percentile delay correlation (h) — –0.5977*** — 1.2888*** — 0.7325*** Log likelihood –1,304 –1,251 –3,474 –3,268 –1,241 –1,168 No. respondents 898 898 898 898 898 898 No. observations 2,662 2,662 7,100 7,100 2,662 2,662 Average tons per shipment 16.3 16.3 16.4 16.4 16.6 16.6 ($/shipment-hour) 71.3 — 58.5 — 45.0 43.3 ($/ton-hour) 4.4 — 3.6 — 2.7 2.6 ($/shipment-hour) 335.2 245.8 229.0 159.9 192.8 97.0 ($/ton-hour) 20.6 15.1 14.0 9.8 11.6 5.8 VOT VOT VOR VOR ϕ ϕ Table 4-11. Models by question order.

Modeling 37 estimated VOT values ranging from $14.5/hour to $411.6/hour. Overall, there was a weaker effect for VOT than VOR, suggesting that respondents were most concerned about whether they could predict arrival times. It is recommended that freight planners use the marginal cost estimate published by the American Transportation Research Institute, which for 2017 was $66.7 per hour of travel time. The results in Table 4-12 point strongly toward the value of reliability being determined by the ability of respondents to react to unreliability and implement contingencies. Small companies with four or fewer employees had VORs 15 to 75 percent greater than larger companies. Small motor carriers (and particularly owner–operators) are more vulnerable to unreliability because they do not have spare vehicles and drivers to help when operations fall behind schedule. More- over, a delayed shipment could represent the loss of a key customer, which is critical for small companies. The analysis showed that truck operators had a higher VOR when the receiver of Segment No. Respondents ($/shipment- hour) ($/shipment- hour) ($/ton-hour) ($/ton-hour) All 898 — 159.9 — 9.4 Respondent type Motor carriers 505 411.6 851.5 20.7 42.8 Shippers w/ transportation 106 14.5 186.4 1.8 13.2 Shippers w/o transportation 287 15.3 84.7 1.2 6.6 Shipment distance 75 miles or less 174 25.3 66.2 1.6 4.1 75 to 500 miles 334 — 192.7 — 12.8 500 miles or more 347 14.3 260.8 1.0 18.1 Company size 1–4 employees 429 169.1 191.2 9.2 10.4 5–100 employees 334 1.6 110.2 0.1 7.3 More than 100 employees 135 — 166.6 — 11.5 Shipment characteristics Contained perishable commodity 165 — — — — Delivery window less than 5 minutes 93 — — — — JIT supply chain 133 — — — — High-value commodities 196 64.4 127.1 4.4 8.6 Intermodal transfer 62 164.7 75.7 7.6 3.5 Less-than-truckload 301 — 204.6 — 29.9 Shipment Receiver Own company 206 26.2 75.4 1.6 4.5 Customer 981 33.3 183.6 2.1 11.7 Intermodal transfer 43 182.0 82.8 7.9 3.6 Question order First 3 questions 898 — 245.8 — 15.1 Last 3 questions 898 43.3 97.0 2.6 5.8 Note: VOT and VOR estimated with ML models with normal parameters and correlation between time and reliability coefficients. Sample reweighted to match shares of U.S. truck shipments by commodity and distance per Freight Analysis Framework v. 4.4. All values shown calculated with parameters significant at the 95% level. VOT VOR VOT VORϕ ϕ Table 4-12. VOT and VOR estimates.

38 Estimating the Value of Truck Travel Time Reliability the shipment was a customer—2.4 times higher than if the shipment was internal. Small ship- pers are also more sensitive toward lateness, in part because shipments are less frequent and any delay could have a larger negative impact on operations. Large truck fleets pool risks and can redeploy resources quickly to reduce the costs of delays. In summary, the study found that VOR is sensitive to the economies of scale that give companies a better ability to mitigate and react to unreliability. Contingencies are also easier to implement for shorter shipments that are late than for longer ones. Shorter shipments typically occur in urban areas and often involve the restocking of com- mercial establishments, sometimes many times a week. These shipments also tend to be smaller. VOR estimates are lower for these shipments because there is less at stake with any individual shipment arriving late. The origin is relatively close to the destination, providing shippers more options for addressing delays. Moreover, companies that operate in urban areas, particularly densely populated ones, are well aware of how congestion affects their operations and have built slack into their system. Given this, it is unsurprising that longer trips had a much higher VOR than shorter trips. Shipments of 500 miles or more had a VOR 3.9 times greater than shipments of 75 miles or less. The other factor that had a strong influence on reliability valuation, not surprisingly, was the content being moved. Shipments carrying agricultural products and fish had the highest VORs, probably because of perishability, and less-than-truckload shipments had higher VOR than average, particularly in terms of tonnage. These results suggest that respondent type has a strong effect on valuation. Motor carriers were found to have a VOR that was many times higher than that of shippers. This was caused in part by the high response rate of owner–operators and small motor carriers, who are more susceptible to unreliability costs. Additionally, it is possible that many motor carriers internal- ized the costs of shippers when responding to the stated-preference questions. For these reasons, the differences between respondent type are deemphasized in this study’s recommendations. The results of the overall model provide more accurate valuations because they consider a wider range of firm sizes and contexts. Additional research is needed to break down these valuations by type of respondent while considering how respondents operate and interact on a daily basis. The interaction between variables was not explored in the statistical modeling. Future research should estimate models that better capture these types of interactions, to isolate the preferences of more specific subgroups of the sample, such as motor carriers with more than 100 employees providing short-haul service of 75 miles or less.