Inventory Routing Problem with Route Duration Limits and Stochastic Inventory Capacity Constraints

This paper studies the inventory management and routing problem in a two-level supply chain in which a single plant serves a set of warehouses, which in turn serve a set of customers with stochastic demands. A nonlinear integer program based on set partitioning and probabilistic chance constraint is proposed. The program accounts for the probabilities of inventory capacity violation, order quantity capacity, service levels, vehicle capacity restrictions, and route duration limits in the combined continuous inventory control and multidepot vehicle routing problem. Two tabu search heuristics differing in the way in which initial solutions were generated were applied to solve the problem. Computational tests on standard test networks revealed that the integration of the inventory management and routing decisions by solution of the combined inventory management and routing problem might yield cost savings of up to 14% over the cost of the sequential approach in which both problems were solved separately. The best objective function value obtained by the tabu search heuristic was found to increase with an increase in customer demand variance but decrease with an increase in order quantity capacity and route duration limit. Variance of the customer demand was found to have a significant impact on the quality of the solution.