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 intermediate replenishment facilities (LRPIRF), an extension of the location routing problem (LRP), where the vehicles can replenish at some intermediate facilities. Vehicles leave the depot with load on-board, serve customers until out of load, may return to an intermediate facility to replenish, and finally return to the depot, completing their route. In this paper, we initiate a mathematical mixed integer programming model with new kind of subtour elimination constraints for this problem. Moreover, the facility location phase is considered besides vehicle routing phase in our problem. The objective of the problem is to find routes for vehicles to serve all customers at a minimal cost in terms of total travel cost and total facility location cost, without violating the capacity constraint of the vehicles. The solution to the LRPIRF is obtained through CPLEX solver in commercial software GAMS 23.5.1, Genetic Algorithm and Tabu Search algorithm. Computational results are obtained on a set of randomly generated instances and indicate the effectiveness of the proposed algorithms in terms of solution time and quality.