Abstract

Integrating location and routing into a unified decision-making framework offers a more comprehensive re-flection 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 likecustomer waiting times. In this paper, we address the latency location routing problem with opening costsand split deliveries (LLRP-OCSD). This complex problem involves optimizing the design of a supply chainnetwork by determining depot locations, assigning vehicles and demand nodes to these depots, and designingroutes. This must be done while accommodating split deliveries and prioritizing minimizing waiting times fordemand nodes. We formulate a mathematical model and propose an iterated local search (ILS) algorithm tosolve the problem. To validate the performance of our approach, we adapted a set of benchmark instancespreviously used for LLRP-OC without considering split deliveries. Computational results demonstrate thatthe 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 lesscomputational 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 splitdeliveries enhance vehicle utilization, enabling the use of smaller vehicles and creating balanced routes withminimal increases in latency costs.