A Node-based Mathematical Model towards the Location Routing Problem with Intermediate Replenishment Facilities under Capacity Constraint

In this paper, we study the location routing problem with replenishment facilities (LRPRF), an extension of the location routing problem (LRP) where the vehicles can replenish at some replenishment facilities. Vehicles leave the depot with load on-board, serve customers until out of load, and then either return to a replenishment facility to reload or return to the depot, completing their route. For this problem, we initiate a mathematical node-based mixed integer programming model. The objective of the problem is to find routes for vehicles to serve all the customers at a minimal cost in terms of number of routes (vehicles) and total travel cost, without violating the capacity constraint of the vehicles. The solution to the LRPRF is obtained through commercial software GAMS 23.5.1 and Genetic Algorithm (GA) in this paper. Computational results are obtained on a set of randomly generated instances and indicate the effectiveness of the proposed algorithm.