Browsing by Author "Rich, Jennifer L."
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Item A Computational Study of Vehicle Routing Applications(1999-05) Rich, Jennifer L.This thesis examines three specific routing applications. In the first model, the scheduling of home health care providers from their homes, to a set of patients, and then back to their respective homes, is performed both heuristically and optimally for very small instances. The problem is complicated by the presence of multiple depots, time windows, and the scheduling of lunch breaks. It is shown that the problem can be formulated as a mixed integer programming problem and, in very small instances, solved to optimality with a branch-and-cut procedure. To obtain solutions for larger instances, though, a heuristic is shown to have more success. The second application considers the vehicle routing problem with time windows, or VRPTW. The vehicle routing problem involves finding a set of routes starting and ending at a single depot that together visit a set of customers. In the VRPTW there is an additional constraint requiring that each customer must be visited within a given time window. The best known solution procedures for solving the VRPTW use a set partitioning model with column generation. Within this framework, we present a new approach for generating valid inequalities, specifically k-path cuts, to improve the linear programming relaxation. Computational results are given for the standard library of test instances. In particular, the results include solutions for ten previously unsolved instances. The final application concerns the less-than-truckload, or LTL, trucking industry. An LTL carrier primarily handles shipments that are significantly smaller than the size of a tractor-trailer. Savings are achieved by consolidating shipments into loads at regional terminals and transporting these loads from terminal to terminal. The strategic load plan determines how to route the flow of consolidated loads from origin terminals to destination terminals cost effectively and allowing for certain service standards. To find good solutions to this problem, we apply a dual-ascent procedure to a related uncapacitated network design problem to obtain wcomputational results for three different companies.Item A Parallel Cutting-Plane Algorithm for the Vehicle Routing Problem with Time Windows(1999-05) Cook, William; Rich, Jennifer L.In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cutting-plane approach followed by a branch-and-bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimum-cut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making use of parallel processing in both the cutting-plane generation and the branch-and-bound search, we solve 80 of these examples, including 10 that were previously unsolved in the literature. Our parallel implementation utilizes the Tread Marks distributed shared memory system.