Analytical results and algorithms for vehicle routing problems with bin-packing features: Bramel, Julien Dana, Ph.D. Columbia University, 1993. 120 pp. adviser:David Simchi-Levi

Abstract

Due to the increased importance of the service sector of the economy, there is a need for a better analytical understanding of service and distribution systems. In such systems, servers based at a single warehouse provide delivery, customer pick-up or repair and maintenance services to customers geographically dispersed in a given region. Such distribution systems integrate problems involving inventory and routing issues, as well as vehicle capacity and time constraints. At the core of these distribution problems is the Capacitated Vehicle Routing Problem (CVRP). Here, a fleet of vehicles of limited capacity must be dispatched and routed so that each customer receives a certain load. A thorough analysis of the CVRP entails an understanding of a sub-problem, called the bin-packing problem. Here, a set of items of different sizes must be packed into equal size bins in such a way that the total size assigned to any one bin is at most the capacity of the bin and the number of bins used is as small as possible. We show that as the number of customers increases the capacitated vehicle routing problem can be solved using results from the bin-packing literature. We then look at some of the classical heuristics designed for the CVRP and show that a class of these are provably inefficient. That is, as the number of customers increases, the solutions produced by heuristics in this class tend to be far from the optimal solution. These results are in agreement with the empirical performance reported in the literature for heuristics of this class. We next discuss practical algorithms for the CVRP and the problem of integrating inventory issues with transportation cost. We develop a general framework to solve these problems that involves a traditional location model commonly called the Capacitated Concentrator Location Problem. In the next chapter, we consider a vehicle routing problem where each customer requests service and provides a time window in which service is desired. The objective is to serve each customer in its time window in such a way that the total distance traveled is as small as possible. We show that the problem can be solved using similar techniques to the capacitated vehicle routing problem. Finally, we study the bin-packing problem with a different cost structure. We consider the problem when the cost of a bin is a function of the number of items in the bin. We derive results that bound the relative difference between the heuristics solution and the optimal solution. As a result of this analysis, we also derive some new results for the classical bin-packing problem.