A hybrid inventory policy for non-stationary lot-sizing problem with lateral transshipment

This paper addresses the two-stocking locations single item non-stationary stochastic lot-sizing problem. The inventory level at each location is reviewed periodically. Items can be reordered and received from a common central warehouse and can also be transshipped laterally from the other location. Lateral transshipment is assumed to be proactive to re-distribute the stock between two stocking locations. Therefore, the order of action in each period is: transshipping (if necessary), reordering (if necessary) and satisfying the demand at each location and each installation. The costs are imposed on transshipping, ordering, holding, and back-ordering. The key issue in such systems is to determine the quantity of the lateral transshipment between depots and the order quantities from the warehouse to both locations. We formulate the problem via stochastic dynamic programming to minimise the expected total cost. Since the number of actions increases exponentially as the feasible quantities of transshipment and replenishment grow, we develop two-stage dynamic programming to improve the computation efficiency. A near-optimal policy against this two-stage formulation is introduced based on a mixed integer linear programming and receding-horizon approach. numerical experiments are implemented to demonstrate the performance of the two-stage model and the heuristic algorithm.