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are general quite different from problems commonly treated in the literature. Problems that arise in practice typically involve a wide variety of constraints that are disregarded in the standard optimization literature. To remedy this shortcoming of previous research, we will focus on two of the more complex and realistic forms of vehicle routing and scheduling problems which involve time windows constraints and stochastic demands and clients. Empirically investigations have confirmed that the time-windows version of the VRP
(VRPTW) is more difficult to solve than the VRP (Solomon 1987). Beyond this, stochastic VRPs differ from their deterministic counterparts in crucial respects that likewise render them much harder to solve. At the current time, in spite of the fact that most real world applications involve important aspects of uncertainty and hence fall in the domain of the stochastic models, very little has been done to address this challenging problems. Naturally, vehicle routing and scheduling problems are central in transportation, distribution, and logistics. However, a large number of other problems not directly related to vehicle routing can be solved using the same model and algorithms. For example, vehicle routing and scheduling models have been shown to provide a basis for solving manpower planning problems (Bohoris and Thomas 1995, Bailey and Field 1985, Brusco and Jacobs 1998), timetabling problems (Ismail and Johnson 1998), stochastic facilities-equipment planning (Averbakh, Berman, and Simchi-levi 1994), communication networks (klincewicz et al. 1998, Amiri and Pirkul 1997) and production scheduling (Brusco and Jacobs 1993). One again, the stochastic element is pervasive in real world instances of such problems, yet is largely neglected in the design of solution procedures. In addition, it should be noted that heuristic techniques used for solving vehicle routing and scheduling models may likewise be used for a number of other network problems that have been applied to optimize different Navy operations. The relevance of these models for personnel planning has been particularly emphasized in the work of Krass, Pinar, Thompson, and Zenios (1994). |
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