On the integrated production, inventory, and distribution routing problem

The integrated Production, Inventory, and Distribution Routing Problem (PIDRP) is concerned with coordinating production, inventory, and delivery operations to meet customer demand with the objective of minimizing the cost. The PIDRP considered in this paper also involves heterogeneous transporters with noninstantaneous traveling times and multiple customer demand centers each with its own inventory capacity. Optimally solving such an integrated problem is in general difficult due to its combinatorial nature, especially when transporter routing is involved. We propose a two-phase solution approach to this problem. Phase I solves a mixed-integer program which includes all the constraints in the original model but with the transporter routings being restricted to direct shipments between facilities and customer demand centers. The resulting optimal solution to phase I 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 heuristically. Unlike the classical decoupled approach, this two-phase approach does not separate the optimization for the production lot sizes and the transportation schedules. Its main advantage lies in its ability to simultaneously coordinate the production, inventory, and transportation operations of the entire planning horizon, without the need to aggregate the demand or relax the constraints on transportation capacities. This enables us to quickly identify a quality suboptimal solution to the original complex problem. The suboptimality is, however, due to the simplified assumption that in phase I only direct shipment is deployed, which is then partially corrected for by the effort of phase II. We evaluate the performance of this proposed two-phase approach and report on its application to a real-life supply network.