Time-partitioning heuristic algorithm for optimal production, inventory, and transportation planning with direct shipment

We developed a mixed integer linear programming model for an integrated decision problem of production, inventory, and transportation planning. Our model combines the direct shipment into the production, inventory, and distribution planning. The objective was to minimize the total operation cost which is comprised of production setup cost, inventory holding cost, transportation cost, and reorder cost. The model is solved to optimality using the leading optimization software, IBM ILOG CPLEX (CPLEX), but the software shows a limited capability to solve large size problems. A time-partitioning heuristic algorithm is proposed to efficiently solve the problem. Numerical experiments are extensively conducted to test the proposed algorithm. In our numerical experiments, the proposed algorithm can solve many large size problems, whereas CPLEX fails to solve them. The numerical experiment shows that a company can gain a significant saving by optimally incorporating the direct shipment. The proposed heuristic algorithm performs well in most cases in terms of a total cost and the computation time.