Shipment planning and safety stock placement in maritime supply chains with stochastic demand and transportation times

This paper introduces and studies shipment planning and safety stock placement in bulk and semi-bulk maritime supply chains. This problem jointly optimizes the assignment of destinations to origins, shipment quantities of multiple products by determining the share of the contract by sea transport options, sailing speed, and multi-echelon safety stocks with the objective to minimize the expected total transportation and inventory cost. In the case of a serial system supplying a single product, we analytically characterize the effect of sailing speed and different time and cost parameters on optimal safety stock placement. For the general case, the integrated problem can be solved in four different ways. We present a mixed integer nonlinear program (MINLP) and the superior reformulation of the mixed integer conic quadratic integer program (MICQP) that can be solved using state-of-the-art solvers. Then, we propose two exact solution procedures that iteratively approximate the nonlinear terms in the objective function and constraints. Our numerical experiments illustrate the interdependence between safety stock placement, assignment decisions, and sailing speed. Results also show that it is important to adopt multi-stage inventory optimization and there is an added value in integrating shipment planning and safety stock placement. Furthermore, computational experiments demonstrate that all the solution approaches are alternatives to solving small instance sizes. For medium and large instances, the solvers are unable to provide quality solutions within one hour while the iterative procedures find optimal or near-optimal solutions in reasonable CPU times.