Multi product inventory location routing problem

The Multi-Product Inventory-Location-Routing Problem (MILRP) with heterogeneous fleet considers a supply chain, which consists of multiple producers, potential distribution centers (DCs) with opening capacity levels and geographically scattered retailers each of which has deterministic demand over a discrete planning horizon. The goal is determining a set of DCs with their capacity levels to open, assigning retailers to the opened DCs and for all periods finding product quantities to be ordered by and distributed from opened DCs and determining the routes to satisfy the demands of retailers with minimum cost. A mixed-integer linear programming model is proposed to describe the problem, which is strengthened by two valid inequalities. Since the commercial solver can solve only the very small-sized instances within a reasonable time, two heuristic methods (sequential and hybrid) are developed. The sequential heuristic comprises a greedy algorithm for location-allocation, an exact approach for inventory management and tabu search for vehicle routing decisions. The hybrid heuristic creates the initial solution and calls intensification and diversification steps for a pre-determined times to find the best solution. Results show that the proposed valid inequalities are effective and both methods provide important savings in acceptable run times compared to the commercial solver