The fragility-constrained vehicle routing problem with time windows

TL;DR

This paper introduces a new variant of the Vehicle Routing Problem with Time Windows that incorporates fragility constraints, develops an efficient exact algorithm to solve it, and analyzes how these constraints impact routing costs under various conditions.

Contribution

The paper formulates the fragility-constrained VRPTW, characterizes route feasibility, and develops a specialized branch-price-and-cut algorithm for its solution.

Findings

The proposed BPC algorithm outperforms the alternative in computational efficiency.

Fragility constraints significantly increase routing costs under certain conditions.

Cost impact of fragility constraints grows with decreased vehicle capacity and increased stack height.

Abstract

We study a new variant of the well-studied Vehicle Routing Problem with Time Windows (VRPTW), called the fragility-constrained VRPTW, which assumes that 1) the capacity of a vehicle is organized in multiple identical stacks; 2) all items picked up at a customer are either "fragile" or not; 3) no non-fragile items can be put on top of a fragile item (the fragility constraint) ; and 4) no en-route load rearrangement is possible. We first characterize the feasibility of a route with respect to this fragility constraint. Then, to solve this new problem, we develop an exact branch-price-and-cut (BPC) algorithm that includes a labeling algorithm exploiting this feasibility characterization to efficiently generate feasible routes. This algorithm is benchmarked against another BPC algorithm that deals with the fragility constraint in the column generation master problem through infeasible path cuts. Our computational results show that the former BPC algorithm clearly outperforms the latter in terms of computational time and that the fragility constraint has a greater impact on the optimal solution cost (compared to that of the VRPTW) when vehicle capacity decreases, stack height increases and for a more balance mix of customers with fragile and non-fragile items.