An efficient column-generation algorithm for a new fleet size and mix pickup and delivery problem with Time windows

Abstract

In this paper, a new variant of the pickup and delivery problem with time windows (PDPTW) named the Fleet Size and Mix Pickup and Delivery Problem with Time Windows (FSMPDPTW) is addressed. This work is motivated by fleet sizing for a daily route planning arising at a Hospital center. In fact, a fleet of heterogeneous rented vehicles is used every day to pick up goods to locations and to deliver it to other locations. The heterogeneous aspect of the fleet is in term of capacity, fixed cost and fuel mileage. The objective function is the minimization of the total fixed cost of vehicles used and the minimization of the total routing cost. A set partitioning model is proposed to model the problem, and an efficient column-generation algorithm is used to solve it. In order to test our method, we propose a new set of benchmarks based on Li and Lim’s benchmark (altered Solomon’s benchmark) for demands and from Lui and Shen’s benchmark for types of vehicles. In the propounded column-generation algorithm, the pricing problem is divided in sub-problems such that each vehicle type have its own pricing problem. A mixed integer linear program is proposed to model and solve the pricing sub-problems. Regret heuristics are proposed to speed-up the resolution of pricing sub-problems. Computational experiments are done on 56 (with up to 100 customers) new proposed instances.