Abstract
AbstractWe present a solution approach for a multi‐trip vehicle routing problem with time windows in which the locations of a prescribed number of depots and the fleet sizes must also be optimized. Given the complexity of the task, we divide the problem into subproblems that are solved sequentially. First, we address strategic decisions, which are solved once and remain constant thereafter. Depots are allocated by solving a p‐median problem and fleet sizes are determined by identifying the vehicle requirements of several worst‐case demand instances. Then, we address the operational planning aspect: optimizing the vehicle routes on a daily basis to satisfy the fluctuating customer demand. We assign customers to depots based on distance and “routing effort,” and for the routing problem we combine a tailor‐made branch‐and‐cut algorithm with a heuristic consisting of a route construction phase and packing of routes into vehicle trips. Our strategic decision models are robust in the sense that when applied to unseen data, all customers could be visited with the allocated fleet sizes and depot locations. Our operational routing methods are both time and cost‐effective. The exact method yields acceptable optimality gaps in 20 min and the heuristic runs in less than 2 min, finding optimal or near‐optimal solutions for small instances. Finally, we explore the trade‐off between depot and fleet costs, and routing costs to make recommendations on the optimal number of depots. Our solution approach was entered into the 12th AIMMS‐MOPTA Optimization Modeling Competition and was awarded the first prize.
Highlights
The vehicle routing problem (VRP) is among the most studied problems in the field of combinatorial optimization
In an effort to improve the efficiency of the exact method implemented by CPLEX, we propose a VRP-specific branch-and-cut approach
We propose a variation of the first fit decreasing (FFD) heuristic in which the items are sorted in decreasing order by their size and they are assigned to the first vehicle in which they fit, at the earliest possible start time, such that the time windows are not violated
Summary
The vehicle routing problem (VRP) is among the most studied problems in the field of combinatorial optimization It is a generalization of the well-known traveling salesman problem (TSP) where instead of a single salesman there is a fixed number of identical vehicles leaving from and returning to a given depot. (ii) In this problem, there is not a single depot; a fixed number of depots is given as a problem parameter; the locations of these depots must be determined These are well studied problems and they are referred to in the literature as the multi-depot VRP and the location routing problem, respectively. We propose a method that efficiently determines the location of a given number of depots, optimizes the fleet size and produces a sensible routing strategy in a reasonable time.
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