The latency location routing problem with split deliveries: mathematical formulation and metaheuristic algorithm

Integrating location and routing into a unified decision-making framework offers a more comprehensive reflection of real-world scenarios where different facility layouts directly influence routing plans. Consequently, addressing the issue holistically becomes imperative, especially when considering service level metrics like customer waiting times. In this paper, we address the latency location routing problem with opening costs and split deliveries (LLRP-OCSD). This complex problem involves optimizing the design of a supply chain network by determining depot locations, assigning vehicles and demand nodes to these depots, and designing routes. This must be done while accommodating split deliveries and prioritizing minimizing waiting times for demand nodes. We formulate a mathematical model and propose an iterated local search (ILS) algorithm to solve the problem. To validate the performance of our approach, we adapted a set of benchmark instances previously used for LLRP-OC without considering split deliveries. Computational results demonstrate that the proposed model is able to optimally solve only 2 out of the 38 tested instances within a 2-hour timeframe. On the other hand, the proposed ILS algorithm is able to find good-quality solutions in significantly less computational time for the LLRP-OCSD. Extensive experimentation on larger instances (up to 200 nodes) yields consistent results within reasonable computational limits. In summary, our findings highlight how split deliveries enhance vehicle utilization, enabling the use of smaller vehicles and creating balanced routes with minimal increases in latency costs.