A generalized assignment heuristic for vehicle routing

TLDR

The study focuses on a vehicle routing variant where a fleet delivers depot‑stored products to customer orders, with each vehicle having a fixed capacity and each order consuming a fixed portion of that capacity. The authors propose a heuristic that assigns customers to vehicles by solving a generalized assignment problem that approximates delivery cost. The heuristic determines vehicle assignments and routes to minimize delivery cost, solves a generalized assignment problem, and can vary fleet size parametrically to find the minimal feasible fleet. The heuristic outperforms existing methods on standard tests, always finds a feasible solution when one exists, offers many attractive features, and can be adapted to additional complexities.

Abstract

Abstract We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.