A joint production and transportation planning problem with heterogeneous vehicles

We consider a manufacturer's planning problem to schedule order production and transportation to respective destinations. The manufacturer in this setting can use two vehicle types for outbound shipments. The first type is available in unlimited numbers. The availability of the second type, which is less expensive, changes over time. Motivated by some industry practices, we present formulations for three different solution approaches: the myopic solution, the hierarchical solution and the coordinated solution. These approaches vary in how the underlying production and transportation subproblems are solved, that is, sequentially versus jointly or heuristically versus optimally. We provide intractability proofs or polynomial-time exact solution procedures for the sub-problems and their special cases. We also compare the three solution approaches over a numerical study to quantify the savings from integration and explicit consideration of transportation availabilities. Our analytical and numerical results set a foundation and a need for a heuristic to solve the integrated problem. We thus propose a tabu search heuristic, which quickly generates near-optimal solutions.