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Dynamic Decision Making for Commercial Fleet Operations Using Real-Time Information AMELIA C. REGAN, HANI S. MAHMASSANI, AND PATRICK JAILLET The application of intelligent transportation system technologies to freight mobility requires dynamic decision-making techniques for commercial fleet operations, using real-time information. Recognizing the productivity-enhancing operational changes possible using real-time information about vehicle locations and demands coupled with constant communication between dispatchers and drivers, a general carrier fleet management system is described. The system features dynamic dispatching, load acceptance, and pricing strategies. A simulation framework is developed to evaluate the performance of alternative load acceptance and assignment strategies using real-time information. Real-time decision making for fleet operations involves balancing a complicated set of often conflicting objectives. The simulation framework provides a means for exploring the trade-offs between these objectives. Results suggest that reductions in cost and improvements in service quality should result from the use of dynamic dispatching (assignment) strategies in addition to traditional planning tools. These results and the overall simulation framework are discussed.

The availability and declining costs of telecommunications and information technologies afford opportunities for using real-time information to enhance the productivity and performance of fleet operations. These opportunities have created a significant need for the development of tools for real-time decision making. Dynamic fleet management tools can improve the efficiency of fleet operations by taking into account current and predicted supplies of vehicles and demands for service, as well as conflicting multiple objectives with respect to cost, customer service, and driver and dispatcher job satisfaction. In addition, these tools should provide fleet managers with the ability to react to and in some cases take advantage of changes in the system as they occur. When either the level or the timing of demands for service cannot be accurately predicted and when high-priority or time-sensitive demands arise, the ability to make decisions dynamically as demands unfold, network conditions fluctuate, and driver or equipment availability status changes is a key to providing reliable, responsive service at a reasonable cost. A demand-responsive fleet management system should ideally include an approach for generating a set of initial vehicle assignments that would take known and predicted future demands into account and incorporate strategies for reacting to changes as they occur. A diagram of such a system is presented in Figure 1. Initial assignments could be generated by some a priori optimization method, such as the stochastic programming approaches used by Powell (1–3) to produce solutions for the dynamic vehicle allocaDepartment of Civil Engineering and Department of Management Science and Information Systems, The University of Texas at Austin, Austin, Tex. 78712.

tion problem. These approaches explicitly incorporate the stochastic nature of both future supplies of vehicles and demands for service. Methods for solving variations of the probabilistic traveling salesman problem (PTSP) are also candidates for generating initial vehicle and load assignment solutions. In the standard PTSP the goal is to produce a robust solution to a problem in which one cannot predict future demands with certainty. Typically, the set of potential demand locations is known, but the probability that a particular location will require a visit is nonzero but not certain. Bertsimas et al. (4) and Jaillet (5) have addressed the PTSP, as well as the probabilistic vehicle routing problem (PVRP) and other probabilistic combinatorial optimization problems. Solutions to the PTSP or PVRP are sequences in which the potential demand locations will be visited. Then, when demands become known the a priori order is maintained, but locations without demands are dropped from the route. The goal is to produce a priori the sequence (or sequences if more than one vehicle is involved) that is minimal in the expected sense. Although these approaches to solving fleet management problems may well be adaptable to operations under real-time information availability, they are at present unable to take full advantage of such information because their underlying formulations do not recognize possible decisions that are only meaningful under realtime information. Several technologies are available to provide real-time information on vehicle locations and demands to support fleet operations decisions. Mirroring industry trends, it is assumed that all vehicles are equipped with some kind of continuous automatic vehicle location system, typically a global positioning system or a geosyncronous satellite-based system; that all vehicles are equipped with continuous two-way communications devices; and that driver-todispatcher communication takes place within a short period of time (6 ). It is further assumed that the dispatch center has a means of displaying the current locations of all vehicles, either on a map with a geographic information system interface or with text messages, and that agents making load acceptance and load acquisition decisions have available at all times more or less accurate estimates of the revenue potential of requested loads, either from a list of representative values or by entering the requested loads into a computer program. It is also assumed that dispatchers have available to them tools that can be used to assign vehicles to loads and that in the best case these tools would include a static assignment generator that produces an initial operating plan taking both known (but partial) and predicted demands into account and a dynamic assignment generator that generates assignments as changes in the system occur. The methodologies underlying the load acceptance rules and the

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place at discrete instances only, typically at a load pickup or delivery point. Cost-Sensitive Empty Repositioning Strategies Companies that can make accurate predictions about the timing and locations of new demands for service can use this information to make profitable decisions about empty repositioning movements. One possibility is that instead of empty movements being routed over least-distance paths, drivers could be routed through regions of high demand in the hope that demands for service will materialize along the way. The paths that drivers follow through the network could be determined by using a least-cost path algorithm in which the costs on links through certain regions reflect the likelihood that a revenuegenerating demand for service will be generated in the near future. Dynamic Pricing and Load Acquisition

FIGURE 1 Overview of dynamic carrier fleet operations.

dynamic assignment and reassignment capabilities presented in Figure 1 form the focus of this work.

POTENTIAL OPERATIONAL CHANGES Real-time information can increase the flexibility of carrier operations. Potential changes include the following: (a) assignments may be considered flexible until service by a particular driver to a particular customer has begun; (b) empty repositioning moves may be directed through historically high-demand areas in the hope that a new load will be picked up along the way; (c) prices, both internal (revenue predictions) and those charged to shippers, may be updated on the basis of the current and near-term predicted state of the system; and (d) aggressive, cost-based load acquisition strategies may be used to reduce some empty movements. This work has explored both conceptually and through simulation some of the benefits of increased flexibility with respect to vehicle-to-load assignments and of cost-based load acceptance policies. Each of these changes is addressed in the following section.

Diversion Strategies Because empty moves made to pick up loads may be long, new information on demands to be served may arrive while a driver is en route to a pickup. Assuming that time windows for movements are flexible, this new demand information may be used to order demands to reduce empty miles driven. Quasi-continuous dispatcher-to-driver communication makes it possible to divert to an alternative load a driver who is en route to a pickup location, thereby inducing a resequencing or reassignment of the original load. Such diversion strategies are not generally feasible under current operations because dispatcher-driver communication takes

The revenue realized for each loaded movement is highly dependent on driver proximity and availability at the time that the load is moved. In addition, each movement affects the ability of individual drivers or a fleet of drivers to respond to near-term demands for service. Although many companies make an effort to predict where and when excess vehicles and drivers will be available and use load acquisition strategies that discount services in regions that would otherwise require excessive empty movements, an overall pricing and load acquisition strategy that takes the current and predicted nearterm state of the system into account could increase productivity. This can be accomplished in several ways. Demands for services could be forecast over time; on the basis of these forecasts the surpluses and deficits in each region or traffic lane could be estimated. These surpluses and deficits can be used to calculate the estimated return on each load, adjusted by predictions about whether vehicles moving loaded in a particular lane will be needed at their destination locations or repositioned empty to other locations. These revenue projections can be used internally to identify regions or traffic lanes that should be targeted for aggressive load acquisition and can be used to calculate the price incentives to be offered to shippers. As demands unfold over time these can be compared with forecast demands, and dispatchers and managers can be made aware of any unexpected fluctuations that require attention. Powell and Frantzeskakis (7–9) have suggested several ways to forecast demands and have used these forecasts both to solve a rolling horizon stochastic programming formulation of the problem and to estimate the marginal cost (and hence expected return) for movements. Powell (7 ) explored marginal cost estimation, which relies on solving either a deterministic or a stochastic formulation of the vehicle allocation problem, and found that although the output from the stochastic (and nonlinear) version of the model provided potentially useful insights, these were difficult to extract from the model without reoptimizing under many different scenarios. Although this and related approaches may indeed lead to the development of planning tools for carriers, it will likely not lead to an approach that can take full advantage of the opportunities afforded by real-time information.

SIMULATION MOTIVATION AND RESULTS The development of solutions for static vehicle routing and scheduling problems has typically involved simplifying operational prob-

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lems to the extent that they can be solved by using exact methods. Because time constraints and operational realism often made such methods infeasible or impractical, heuristic methods that are faster or that can solve problems with increased complexity have been used. In many cases exact methods have been used to generate lower bounds and to lend insight into heuristic methods. In other cases assignments produced by approximate methods that rely on forecasts of future demands, for example, have been compared with assignments generated with the benefit of hindsight. It is important to be able to test operational strategies in various ways before and after applying them in practice. One challenge is to construct such tests of dynamic dispatching strategies. Although it is possible to derive analytically some insights into the performance of certain strategies (diversion strategies, for example), the dependence of each move on the moves that preceded it makes such derivations unwieldy under all but the simplest assumptions. For this reason a simulation program to test assignment, load acceptance, and dynamic pricing strategies has been developed (10). Simulation also makes it possible to explore a wide spectrum of scenarios with respect to the geographic regions covered, realizations of demands for services, travel delays, information availability, and communication capabilities. Although the simulation program developed at this time may lack realism in certain respects, it provides a framework for exploring important questions and a test bed for defining and investigating new operational strategies for fleet management under real-time information.

Simulation Framework The simulation framework considers demands arising over time and space, according to a specified pattern, in a given study area. Travel in this area takes place according to a specified metric. A set of vehicles is available to respond to the loads. The simulation allows tests of alternative load acceptance rules and assignment-reassignment rules under different scenarios regarding the demand patterns and

FIGURE 2

Record of vehicle states.

information availability. The principal elements of the simulation are as follows: • Geographic region: circular, rectangular, actual; • Demand arrival pattern: continuous or discrete (zones) demand locations and various distributions of arrivals over time and space; • Travel metric: Euclidean, Manhattan, or realistic, static, or time dependent; • Number of vehicles; • Load acceptance rules; and • Assignment-reassignment rules. Demands are randomly generated according to a specified spacetime stochastic process (or according to a preset schedule) and are characterized by the following attributes: time of request, an origin location (x?y or latitude-2 longitude coordinates), a destination location, and a service time window (we and wl, for earliest and latest pickup times, respectively). In the truckload application these two parameters are sufficient to specify the service time window. However, in a less-than-truckload application these would be extended to include the earliest and latest delivery times as well as pickup times. At each instant in time vehicles have an associated status, and there are four mutually exclusive possibilities: moving loaded, moving empty, idle and available to accept assignments, or idle and unavailable to accept assignments. Figure 2 provides a possible record of vehicle states over time. Such a diagram may also be constructed for the future on the basis of current assignments made to each vehicle. The simulation breaks planning of carrier fleet operations into two steps: load acceptance and load assignment. Load acceptance is concerned with making a decision about whether or not a candidate load will be admitted into a pool of committed demands; load assignment is concerned with assigning committed demands to individual vehicles for service. Load acceptance decisions are made once, whereas assignment decisions may be made several times for the same load.

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Assignment of loads to vehicles takes place in the following way. After a request arrives a decision is made about whether or not it will be served. This decision may be made immediately or within a short time after the request is received. Then, either the load is immediately assigned to a particular vehicle or it is sent to a pool of accepted but unassigned demands for future assignment. The question of how best to handle the trade-offs between immediate assignment to a vehicle and assignment to a pool is of significant importance to this research. Similar issues arise in scheduling and assignment decisions in many different fleet management contexts as well as in other scheduling and queuing systems. Two scenarios are described in Figure 3: one in which loads are held in a large common pool of accepted demands until assignment to a particular vehicle close to the time at which service is scheduled to begin and another in which most accepted demands are assigned to a particular vehicle’s queue. Between these two extreme assignment strategies (keep all accepted loads in the pool until a vehicle is available versus assign the load immediately upon acceptance to an individual vehicle queue), a spectrum of hybrid strategies can be defined. These differ in the number of loads assigned to individual vehicle queues, the size of the common pool, the timing of acceptance decisions, the timing of assignment decisions, and the extent of reassignment. The purpose of the simulation framework is to investigate systematically the performance of such strategies.

FIGURE 3 strategies.

Pooled versus individual vehicle queue assignment

The standard queuing literature strongly advocates systems in which a single pooled queue supplies several (identical) servers with customers rather than separate queues for each server. However, the geographically dispersed nature of the dynamic vehicle allocation problem and the dependence of service times on the order in which loads are served (because the associated empty movements to pick up the loads are different, depending on the service order) do not conform to the assumptions under which this result is typically derived. Thus, the superiority of a pooled queue strategy may or may not be applicable in this case. Figure 4 illustrates the potential efficiencies gained by reordering even a few loads as opposed to serving them in the order of arrival (or in the order of assignment to an individual vehicle). It shows the average ratio of empty to loaded distances traveled to serve a series of loads. The origin and destination points for each load served are uniformly and independently generated over a circular work area. The demands are examined in the order of arrival, but n of them are sequenced in an optimal way. So if n is equal to 3, the first three demands are sequenced optimally, and then the first demand in the optimal sequence is served. Another demand (the first unsequenced demand) is added to the first two demands and these are optimally sequenced. The first demand is served and another is added and so on until all demands are served. The dramatic decrease in the empty-to-loaded ratio of the tour (and the associated increase in efficiency) suggests that building small routes for each vehicle may be helpful in determining service order in conjunction with overall assignment strategies. Naturally, good preprocessing heuristics, for example, assigning cluster loads to a subset of vehicles, will reduce the magnitude of the benefits gained from reordering loads. Nevertheless, the potential benefits may be significant and should be leveraged if time window flexibility allows. This insight, derived in the context of trucking operations, may be even more important for the routing and assignment of local fleet operations (10). In the simulation program all the described strategies involve the same representation of individual queues. Under the pooled service strategy, in which all loads remain in a pool until a vehicle is ready for its next assignment, the queue contains at most one load: the vehicle’s next assignment. Each vehicle has an associated queue

FIGURE 4 Changes in empty-to-loaded ratio of sequence of loads as queue of optimally sequenced loads increases.

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Qk(t) of committed assignments. A queue for a particular vehicle is represented in Figure 5. If the slack time associated with a particular load in the queue is nonzero it may be possible to shift the load further back in the queue as other loads are assigned to this vehicle.

Load Acceptance Strategies In truckload trucking operations carriers have the ability to accept or decline requests for service. Naturally, in times of low demand almost all requests are accepted. However, for some companies and in times of high demand, or in times when the variability of demand results in peak periods in which not all requests can be accommodated, decision-making strategies should be used to make the best acceptance decisions. Many different load acceptance strategies can be used. In the extreme, a global optimization problem could be solved each time a new request or a set of requests is made, and the expected cost to serve the requested loads could be calculated. Loads could be accepted or rejected on the basis of the cost estimate. However, this is unlikely to be a feasible approach when customers are waiting for a prompt answer about a carrier’s ability to handle a particular load. In addition, solving a global optimization problem on current demands would require extensive computational effort (if indeed the problem could be solved) to be expended on a static approximation of a problem that is stochastic and dynamic in nature. The problem would need to be re-solved repeatedly as changes in the demand pool occurred. More practical load acceptance decision-making strategies use simple rules based on historical information, the revenue associated with a particular load (typically tied to the length of the loaded movement), or simple heuristics for testing how a load will fit with the existing committed loads. Various strategies have been explored in the singlevehicle case and are discussed in the next section. The simulation framework described here allows the performance evaluation of strategies with various degrees of restrictiveness.

FIGURE 5

Representation of individual vehicle queue.

Real-Time Assignment A central focus of this research is to identify and test ways in which operations should change to take full advantage of real-time information on vehicle locations and demands. One strategy introduced in previous work (6) is that of diverting a vehicle en route to a particular location to make a pickup of a more time-sensitive load or a load that when sequenced first will improve the efficiency of the vehicle’s travel route. Referring back to Figure 2, the difference between a strategy that allows diversion and a base case that does not can be illustrated. If it is assumed that a new load has been accepted at the time marked by the first of the two vertical lines, in the diversion case three of the vehicles shown would be considered candidates for immediate acceptance of the load. However, in the intelligent base case, only Vehicle 3 in Figure 2 would be a candidate, because the other vehicles are moving toward pickup points or are moving loaded. The question of whether this strategy, which requires additional flexibility on the part of dispatchers, drivers, and in some cases customers, will increase the efficiency and profitability of carrier operations is central to this work. In the next section insights gained from the simulation of a single vehicle are discussed.

INSIGHTS AND SELECTED RESULTS GAINED FROM SINGLE-VEHICLE SIMULATION EXPERIMENTS Extensive investigation of the performance of load acceptance and assignment strategies in the case of a single-vehicle operation was conducted under somewhat idealized conditions to gain insight into more general multivehicle cases. Some of the issues addressed with respect to diversion strategies have been the following. If, while a driver is en route to a load origin, information about another load to be moved becomes available, what is the probability, given various diversion decision rules, that the driver will be diverted to serve the new load first? What is the probability that following such diversion decision rules will result in a reduction of overall distance traveled? And, what is the associated expected reduction in travel? With respect to overall operations some of the issues under examination are the following: How much can be gained by waiting to decide whether to accept or reject a load for service for some time after a customer calls with a request? How beneficial are stricter load acceptance policies? What are the benefits of more or less flexibility with respect to committed time windows for service? Even within a simulation framework an important methodological question arises regarding the design of tests to evaluate the performance of certain strategies compared with those of benchmark or base cases. The relative improvement possible under strategies that allow a driver to be diverted to serve a new load while that driver is en route to another load origin depends on the relative locations of the alternative pickup and delivery points. The load that the driver is diverted to may be a load that has just arrived or a previously committed demand if the addition of the new load to a queue of committed demand makes this attractive. Under some distribution assumptions about the locations of these points, we are interested in the probability that diverting the driver to a new demand (or a queued demand) while en route to a previously assigned pickup will be beneficial. This probability and various other performance measures are evaluated through simulation of such strategies over service horizons of various lengths, under different arrival stream dis-

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tributions, and under load acceptance rules that either require all loads to be served or allow less profitable loads to be rejected. Initial exploration through simulation of single-vehicle diversion strategies compared the diversion scenario with one in which demands are served in the order that they arrive (base case) and revealed that diversion outperforms the base case by as much as 15 percent of the overall distance traveled (6). A more efficient “intelligent” base case, against which real-time diversion can be tested, is defined for this evaluation. It is described next, in conjunction with the scenarios and assumptions investigated in the simulation experiments. Assume a circular service region with demands generated uniformly over space and from a Poisson arrival stream over time. Travel takes place over straight-line distances (with no loss of generality). At time t a vehicle k has associated with it a queue of committed demands to be served of length Qk(t), in which for both operational and computationally practical reasons the maximum queue length is quite short, five in the present test case. Assume that the demands in the queue are optimally sequenced to minimize travel time, within any associated service time constraints. A vehicle also has an associated status, which is loaded, empty (and moving), or idle. If a demand arrives while a vehicle is moving loaded, the (simulated) dispatching system must wait until completion of the service to add a new load and resequence the queue. If a vehicle is moving empty, in the intelligent base case the vehicle must complete service to the first load in the queue before accepting a new load into the queue. However, under the diversion strategy, the load is evaluated for acceptance and resequenced as soon as it arrives, provided there is at least one available slot in the queue. The acceptance decision is based on the cost of serving the new load along with other loads already accepted for service (see below). If the queue is full, the load will not be evaluated for acceptance; if a load is not evaluated within a certain time after a request is made the opportunity to serve it is lost. Loads are evaluated for acceptance on the basis of an emptyto-loaded ratio of a tour that includes demands already committed for service and the candidate load. When a load is evaluated for acceptance the ratio of empty-to-loaded distances in the optimal tour that includes the candidate load and the already accepted demands is compared against a threshold value. If this empty-to-loaded ratio exceeds the acceptable threshold the load is rejected. The derivation of the threshold values for load acceptance decisions and load assignment decisions (in the multivehicle case) merits explanation. In a compact work area the empty-to-loaded ratio of a tour that includes n 1 1 loads will in general be less than the empty-to-loaded ratio of a tour that contains n loads. If the same threshold value for acceptance were applied to tours that had queues of different lengths, the tours with the longest queues would be favored. If empty-to-loaded ratio was the only figure of merit, that would not be problematic. However, if the queue of demands waiting to be served is always at or near its maximum length, the average time that an accepted load must wait for service is high. Therefore, threshold values that allow the addition of loads to the queue but that take into account the average empty-to-loaded ratio of queues of a particular length are used. The graph in Figure 4 shows the average empty-to-loaded ratio of tours in which it is assumed that the queue always holds the maximum number of loads, that the loads in the queue are sequenced optimally, and that loads are added to the queue in the order in which they arrive (from a Poisson arrival stream over time). Figure 6 highlights the comparison of diversion to base under four different load acceptance rules. The comparison was based on

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FIGURE 6 Effect of load acceptance rule on empty-to-loaded ratio and wait times.

a simulation performed on the same set of service requests and continued until 50 demands had been served. When the thresholds were applied, it was desirable to favor slightly longer queues (these led to better results with only a slight extension of service times) by using the values (from Figure 4) for a queue size of n 2 1 when in fact a queue of length n was being evaluated. The rationale for this choice of threshold values is that the resulting empty-to-loaded ratio of the tour was not more than it would have been, on average, without the addition of the load. A multiplier is applied to these threshold values. The multiplier makes acceptance into the queue more restrictive than the baseline described earlier, moderate (equal to the baseline with the n to n 2 1 shift), or unrestricted (all loads accepted unless acceptance time windows are violated). In the cases presented in Figure 3 the multipliers were 0.8, 1.0, 1.4, and 1.8 in the restrictive, moderate, less restrictive, and unrestrictive cases, respectively. The demand arrival rate used in each of the simulations is slightly faster than the average service rate, but the effective arrival rate is less than the average service rate because up to 60 percent of the arriving service requests are not accepted because they do not meet the threshold criteria. The results suggest that less restrictive threshold values are more effective than restrictive ones and highlight the fact that diversion strategies perform well against the base case, resulting in a 5 to 7 percent reduction in the empty-to-loaded ratio. Although the empty-to-loaded ratio of unrestricted cases (all demands served) is almost as low as that of the less restrictive case, in which less than 10 percent of the demands are turned away, the unrestricted case leads to longer average times in the queue. The change in average wait times for service under more or less restrictive load acceptance policies is provided in Figure 6. When these two criteria are used to evaluate acceptance strategies, the one in which the worst loads are rejected but most loads are accepted appears to fare the best. The advantage of real-time information on vehicle locations and demands is that decisions can be made earlier and with more complete information on the state of the system. Real-time (continuous) dispatching methods perform best relative to decision processes that

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FIGURE 7 Effect of time windows for acceptance.

can be applied at discrete instances only when opportunities for reacting as new information becomes available exist. One operational rule or constraint that has been explored is the addition (or lack) of time windows for acceptance of service requests. It is assumed that customers can wait for some period of time after a service request for an answer about whether a particular carrier can carry a given load. Scenarios with short, medium, and no acceptance windows have been simulated. As in the previous simulations the demand arrival rate is assumed to be approximately equal to the service rate. In the case in which time windows are short, when 50 demands are served, 26 service requests are rejected for time window violations in the base case, whereas on average only 8 are rejected in the diversion case. In the medium time window case five loads are rejected (no average) in the base case, whereas only one load is rejected in the diversion case. The results in Figure 7 demonstrate that, as can be expected, diversion performs much better than the base case when time windows for acceptance are short. It is of particular interest that diversion outperforms the base case even when customers are willing to wait indefinitely for an answer (surely not a realistic scenario).

CONCLUSION Integrated systems for dispatching, load acceptance, and dynamic pricing for fleet operations can play an important role in helping fleet managers take full advantage of intelligent transportation system technologies. Simulation results suggest that reductions in cost and improvements in service quality should result from the use of dynamic dispatching (assignment) strategies in addition to tradi-

tional planning tools. Historical demand and revenue data—which will be much more readily accessible when fleets are equipped with automatic vehicle location devices, two-way communication devices, and onboard computers—can be used with real-time information on the locations and status of vehicles and committed demands to estimate the cost (and hence revenue potential) of serving requested loads. This information can be used to make load acceptance decisions as well as to trigger load acquisition activities. The ability to react quickly to time-sensitive demands is extremely important, but results indicate that operational efficiency can be improved by reacting early to the existence of demands that are not as time sensitive. The encouraging performance of simple load assignment and acceptance strategies under idealized conditions has motivated the extension of a single-vehicle simulation framework to a multivehicle simulation capable of evaluating a variety of assignment strategies under various conditions. Simulation results and associated analytic evaluation of real-time assignment and acceptance strategies are the subject of ongoing work.

REFERENCES 1. Powell, W. B. A Stochastic Formulation of the Dynamic Vehicle Allocation Problem. Transportation Science, Vol. 20, pp. 117–129, 1986. 2. Powell, W. B. An Operational Planning Model for the Dynamic Vehicle Allocation Problem with Uncertain Demands. Transportation Research, Part B, Vol. 21, No. 3, 1987, pp. 217–232. 3. Powell, W. B. A Comparative Review of Alternative Algorithms for the Dynamic Vehicle Allocation Problem. In Vehicle Routing: Methods and Studies (B. L. Golden and A. A. Assad, eds.), North-Holland, Amsterdam, 1988, pp. 249–291. 4. Bertsimas, D. J., P. Jaillet, and A. R. Odoni. A Priori Optimization. Operations Research, Vol. 36, No. 6, 1990, pp. 1019–1033. 5. Jaillet, P. A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers are Visited. Operations Research, Vol. 36, No. 6, 1988, pp. 929–936. 6. Regan, A. C., H. S. Mahmassani, and P. Jaillet. Real-Time Information for the Improved Efficiency of Commercial Vehicle Operations. In Transportation Research Record 1495, TRB, National Research Council, Washington, D.C., 1995, pp. 188–198. 7. Powell, W. B. Marginal Cost Pricing of Truckload Services. Transportation Research, Part B, Vol. 19, No. 5, 1985, pp. 433–445. 8. Powell, W. B., and L. Frantzeskakis. Restricted Recourse Strategies for Dynamic Networks with Random Arc Capacities. Transportation Science, Vol. 28, No. 1, 1994, pp. 3–23. 9. Frantzeskakis, L. F., and W. B. Powell. A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems. Transportation Science, Vol. 24, No. 1, 1989, pp. 40–57. 10. Regan, A. C., H. S. Mahmassani, and P. Jaillet. Dynamic Vehicle Allocation for Fleet Management: Operational Changes for Improved Efficiency. Proc., 2nd World Congress on Applications of Transport Telematics & Intelligent Vehicle-Highway Systems, Nov. 1995.

Publication of this paper sponsored by Committee on Transportation Supply Analysis.