On the Integrated Production, Inventory, and Distribution Routing Problem

The integrated production, inventory and distribution routing problem (PDRP) is concerned with coordinating the production, inventory and delivery operations to meet customer demand with an objective to minimize the cost. The particular PDRP that we consider in this study also involves heterogeneous transporters with non-instantaneous traveling times and many customer demand centers each with its own inventory capacities. Optimally solving such an integrated problem is in general not easy due to its combinatorial nature, especially when transporter routing is involved. In this paper, we propose a two-phase solution approach to this problem. Phase I solves a mixed integer programming model which includes all the constraints in the original model except the transporter routings are restricted to direct shipment between facilities and customer demand centers. The resulting optimal solution to the Phase I problem is always feasible to the original model. Phase II solves an associated consolidation problem to handle the potential inefficiency of direct shipment. The delivery consolidation problem is formulated as a capacitated transportation problem with additional constraints and is solved by an efficient heuristic routing algorithm. The main advantage of this proposed approach, over the classical decoupled approach, is its ability to simultaneously optimize the production, inventory and transportation operations (subject to restricted routing/direct shipments) without the needs for aggregating the demand and relaxing the constraints on transportation capacities. We evaluate the performance of this proposed two-phase approach and report its application to a real-life supply network which motivated this study. ( Integrated production, inventory and distribution routing problem; Mixed integer programming; Direct shipment; Heterogeneous transporters; Heuristic routing algorithm) Acknowledgements: The jointed sponsored by Rutgers Business School and ROTCOR is gratefully acknowledged.