Karen Smilowitz

Last Mile Distribution in Humanitarian Relief

Last mile distribution is the final stage of a humanitarian relief chain; it refers to delivery of relief supplies from local distribution centers (LDCs) to beneficiaries affected by disasters. In this study, we consider a vehicle-based last mile distribution system, in which an LDC stores and distributes emergency relief supplies to a number of demand locations. The main decisions are allocating the relief supplies at the LDCs among the demand locations and determining the delivery schedules/routes for each vehicle throughout the planning horizon. We propose a mixed integer programming model that determines delivery schedules for vehicles and equitably allocates resources, based on supply, vehicle capacity, and delivery time restrictions, with the objectives of minimizing transportation costs and maximizing benefits to aid recipients. We show how the proposed model optimizes resource allocation and routing decisions and discuss the tradeoffs between these decisions on a number of test problems. Finally, we identify opportunities for the use of intelligent transportation systems in last mile distribution.

The Period Vehicle Routing Problem and its Extensions

This chapter presents an overview of the Period Vehicle Routing Problem, a generalization of the classic vehicle routing problem in which driver routes are constructed over a period of time. We survey the evolution of the PVRP and present a synopsis of modeling and solution methods, including classical heuristics, metaheuristics, and mathematical programming based methods. We review three important variants of the problem: the PVRP with Time Windows, the Multi-Depot PVRP, and the PVRP with Service Choice. We present case studies and highlight related implementation issues, including metrics that quantify the operational complexity of implementing periodic delivery routes. Finally, we discuss potential directions for future work in the area.

The Period Vehicle Routing Problem with Service Choice

The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). In this paper, we consider a variation of the PVRP in which service frequency is a decision of the model. We refer to this problem as the PVRP with service choice (PVRP-SC). We explore modeling issues that arise when service choice is introduced, and suggest efficient solution methods. Contributions are made both in modeling this new variation of the PVRP and in introducing an exact solution method for the PVRP-SC. In addition, we propose a heuristic variation of the exact method to be used for larger problem instances. Computational tests show that adding service choice can improve system efficiency and customer service. We also present general insights on the impact of node distribution on the value of service choice.

OPTIMAL INSPECTION AND MAINTENANCE POLICIES FOR INFRASTRUCTURE NETWORKS

State-of-the-art infrastructure management systems use Markov decision processes (MDPs) as a methodology for maintenance and rehabilitation (M&R) decisionmaking. The underlying assumption in this methodology is that inspections are performed at pre-set and fixed time intervals and that they reveal the true condition of the facility, with no measurement error. As a result, after an inspection, the decisionmaker can apply the activity prescribed by the optimal policy for that condition state of the facility. In prior research, the second author of this paper has applied a methodology for M&R activity selection accounting for the presence of both forecasting and measurement uncertainty--the latent Markov decision process (LMDP), an extension of the traditional MDP that relaxes the assumptions of error-free annual facility inspections. In this paper, the authors extend this methodology to include network-level constraints. This can be achieved by extending the LMDP model to the network-level problem through the use of randomized policies. Both finite- and infinite-horizon formulations of the network-level LMDP are presented. A case study application demonstrates the expected savings in life cycle costs that result from increasing the measurement accuracy used in facility inspections and from optimal scheduling of inspections.

Multi-resource routing with flexible tasks: an application in drayage operations

This paper introduces an application of a Multi-Resource Routing Problem (MRRP) in drayage operations. Drayage involves the movement of loaded and empty equipment between rail yards, shippers, consignees, and equipment yards. The problem of routing and scheduling drayage movements is modeled as an MRRP with flexible tasks, since the origins and destinations of some movements can be chosen from a set of possible nodes. The complexities added by routing choice are studied, along with the impact of these complexities on problem formulation. The solution approach developed to solve this problem includes column generation embedded in a branch-and-bound framework. Using this approach, efficient operating plans are designed to coordinate independent drayage operations in the Chicago region.

Deferred item and vehicle routing within integrated networks

This paper studies the possible integration of long-haul operations by transportation mode and service level (defined by guaranteed delivery time) for package delivery carriers. Specifically, we consider the allocation of deferred items to excess capacity on alternative modes in ways that allow all transportation modes to be utilized better. Model formulation and solution techniques are discussed. The solution techniques presented produce efficient solutions for large-scale problem instances. Allowing deferred items to travel by air reduces long-haul transportation costs. These savings increase with the amount of excess air capacity.

Community-based operations research

“Community-based operations research” is defined as the collection of analytical methods applied to problem domains in which interests of underrepresented, underserved or vulnerable populations in localized jurisdictions, formal or informal, receive special emphasis, and for which solutions to problems of core concern for daily living must be identified and implemented so as to jointly optimize economic efficiency, social equity and administrative burdens. As such, it represents a specific domain within public-sector operations research. Community-based OR problems tend to be “messy” and highly dependent on political and social considerations. Nevertheless, solution of these problems is essential to the continued health and well-being of individuals, families, communities and entire regions.

Workforce Management in Periodic Delivery Operations

Service quality and driver efficiency in the delivery industry may be enhanced by increasing the regularity with which a driver visits the same set of customers. However, effectively managing a workforce of drivers may increase travel distance, a traditional metric of the vehicle routing problem VRP. This paper evaluates the effect that workforce management has on routing costs, providing insight for managerial decision making. The analysis is presented in the context of the period vehicle routing problem PVRP, an extension of the VRP with vehicle routes constructed to service customers according to preset visit frequencies over an established period of time. We develop models to apply workforce management principles. Through a computational study with standard PVRP test cases and real-world delivery data, we show that multiobjective PVRP models can achieve a balance between workforce management and travel distance goals. With the proper parameters in place, workforce management principles may be successfully applied without sacrificing other operational objectives.

Some observations of highway traffic in long queues

The arrival times of vehicles traveling southbound along a two-lane, bidirectional highway were recorded at eight neighboring locations upstream of a bottleneck caused by an oversaturated traffic signal. Cumulative curves constructed from these observations describe completely and in great detail the evolution of the resulting long queues. These queues formed directly upstream of the signal when the signal’s service rate fell below the southbound arrival rates, and never formed away from the bottleneck. The predictability of bottlenecks like the one studied here can be exploited to manage traffic more effectively. The behavior of vehicles within the queue, however, was rather interesting. Although the flow oscillations generated by the traffic signal were damped out within 0.8 km (0.5 mi) of the bottleneck, it was found that other oscillations arose within the queue farther upstream, at varied locations, and then grew in amplitude as they propagated in the upstream direction. Thus, the queue appeared to be stable close to the bottleneck and unstable far away. Oscillations never propagated beyond the upstream end of the queue, however; that is, the unusual phenomena always arose after the onset of queueing and remained confined within the queue. Some of these findings run contrary to current theories of traffic flow. Because the data set collected in this study is unprecedented in scope and detail and so that it may be of use to other researchers, it has been posted on the Internet and is fully described here.

Improved modeling and solution methods for the multi-resource routing problem

This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies. 2006 Elsevier B.V. All rights reserved.