The purpose of the paper is to present an integrated model for the location of warehouse, the allocation of retailers to warehouses, and finding the number of vehicles to deliver the demand and the required vehicle routing in order to minimize total transportation costs, fixed and operating costs, and routing costs.
The model assumes that the number of plants has already been determined and answers the following questions: what is the number of warehouses to open? How warehouse are allocated to plants? How retailers are allocated to warehouses? Who are the retailers that will be visited and in what order? How many vehicles are required for each route? What are the total minimum costs?
The model was formulated as a mixed integer linear programming model and solved using Lagrange relaxation and sub‐gradient search for the location/allocation module and a traveling salesman heuristic for the routing module. The results for the randomly selected problems show that the deviation in objective function value ranges between 0.29 and 2.05 percent from the optimum value. Also, from the CPU time point of view, the performance was very good.
An attempt is made to integrate location, allocation, and routing decisions in the design of a supply chain network.
