Order crossover problem with variable lead time

Optimal order quantity at each period is an important issue in supply chain management. To avoid backorder or inventory holding costs, inventory models play key role in finding the optimal values at every time period. However, the inventory models fail to obtain the optimal solution when the sequence of ordering and receiving is different, which is called order crossover. Many factors bring to the order crossover problem. In this paper, we formulate a dynamic programming model for order crossover problem with lead time variation and propose a solution approach. The model provides the strategy to find the optimal solution when occurring the order crossover.