Combinatorial optimization and vehicle fleet planning: Perspectives and prospects

Abstract

As a well‐structured and costly activity that pervades industries in both the public and private sector, vehicle fleet management would appear to be a splendid candidate for model‐based planning and optimization. And yet, until recently the combinatorial intricacies of vehicle routing and of vehicle scheduling have precluded the widespread use of optimization (exact) methods for this problem class. Our discussion in this paper identifies the extent and nature of these problem complexities and draws contrasts with other applications of combinatorial optimization. It also summarizes a number of successful uses of optimization for vehicle fleet planning and highlights potentially fruitful avenues for algorithmic development. In particular, we describe several alternative models and novel algorithms for the vehicle routing problem, show how various modeling approaches for this problem are intimately related, and illustrate the interplay between model formulations and the algorithms that they suggest. This discussion shows that prospects for applying exact methods, possibly in conjunction with heuristics, are far from fully realized and points to vehicle fleet planning as a tempting target of opportunity for further investigation.

An exact algorithm for the full truckload pick-up and delivery problem with time windows: concept and implementation details

“…The formulation was first introduced in vehicle routing by Balinski and Quandt (1964). Magnanti (1981) has shown that the vehicle flow formulation of the classical one depot vehicle routing problem may be rewritten into a formulation similar to the set partitioning problem. In the classical VRP a feasible solution should satisfy a number of constraints like: (1) a vehicle is used at most once; (2) if a vehicle arrives at a customer, it must also depart from there; (3) the load of the vehicle should not exceed its capacity; (4) subtour elimination constraints and (5) integrality of the decision variables.…”

Demand Point Aggregation Analaysis for Location Models

“…Using the classification of Magnanti (1981), Laporte (1988) puts the integer programming algorithms into the following four categories:…”

Heuristics for Solving Problem of Evacuating Non-Ambulatory People in a Short-Notice Disaster

“…In the literature, Laporte and Nobert (1987) presented an extensive survey that was entirely devoted to exact methods for the VRP, where they gave a complete and detailed analysis of the state-of-the-art up to the late 1980s. Other surveys also cover exact methods, but are often more devoted to heuristic and metaheuristic methods, including those by Christofides, Mingozzi, and Toth (1979), Magnanti (1981), Bodin et al (1983), Christofides (1985), Laporte (1992), Fisher (1995, Toth and Vigo (1998), and Golden et al (1998). Bibliographies were presented by Laporte and Osman (1995) and Laporte (1997), while books include those by Golden and Assad (1988) and Toth and Vigo (2002).…”