A Multi‐Trip Vehicle Routing Problem With Release Dates and Interrelated Periods

Abstract

This article proposes a new multi‐trip vehicle routing problem variant, originally motivated by a practical application, namely a car components distribution to repair centers (warehouses). The problem is named the multi‐trip vehicle routing with release dates and interrelated periods (MTVRP‐RDIP). The routes may start at different pre‐defined periods, called departure periods, and may have different durations. Thus, two routes that start at different periods may be active at the same period, leading to the so‐called interrelated periods. Moreover, a route may only start at a period if a vehicle is available, and the availability of the vehicle depends not only on the existing vehicles but also on the active routes at that time period. The clients are classified according to their importance and represent warehouses that require car components that are made available throughout the time horizon, thus leading to the consideration of release dates. Delays in satisfying client orders and not serving orders in the time horizon result in penalty costs that must be minimized. The objective to minimize also includes routing costs and vehicle utilization costs. Two metrics are defined to compute an order's delay, each leading to a different mixed integer linear model. Computational results showed that one model clearly outperforms the other and even this one is only suited to address the smallest instances. A matheuristic based on a rolling‐horizon process that iteratively solves the better‐performing model with fewer periods was designed to tackle the largest instances. The matheuristic can provide feasible solutions for all test instances in an efficient manner that are, on average, better than the ones provided by the model in most of the compared key performance indicators.