A Two-Phase Hybrid Heuristic Method for a Multi-Depot Inventory-Routing Problem

Document Type: Research Paper


1 MSc. Student, School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

2 Assistant Professor, School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

3 Ph.D. Candidate, School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


In this study, a two phase hybrid heuristic approach was proposed to solve the multi-depot multi-vehicle inventory routing problem (MDMVIRP). Inventory routing problem (IRP) is one of the major issues in the supply chain networks that arise in the context of vendor managed systems (VMI) The MDMVIRP combines inventory management and routing decision. We are given on input a fleet of homogeneous vehicles, in which any of these vehicles have a capacity and a fixed cost. Also, a set of distribution centers with restricted capacities are responsible to serve the customer’s demands, which are known for distributer at beginning of each period. The problem consists of determining the delivery quantity to the customers at each period and the routes to be performed to satisfy the demand of the customers. The objective function of this problem is to minimize sum of the holding cost at distributer centers and the customers, and of the transportation costs associated to the preformed routes. In the proposed hybrid heuristic method, after a Construction phase (first phase) a modified variable neighborhood search algorithm (VNS), with distinct neighborhood structures, is used during the improvement phase (second phase). Moreover, we use simulated annealing (SA) concept to avoid that the solution remains in a local optimum for a given number of iterations. Computational results on benchmark instances that adopt from the literature of IRP indicate that the proposed algorithm is capable to find, within reasonable computing time, several solutions gained by the approaches that applied in the previous published studies.


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