Optimal time-based consolidation policy with price sensitive demand

We consider a single-item inventory system where shipments are consolidated to reduce the transportation cost using a time-based consolidation policy and develop a mathematical model to obtain the optimal price, replenishment quantity and dispatch cycle to maximize the total profit. The long-run average profit is computed and the optimality properties are obtained. Using the optimality properties, we develop an efficient algorithm to obtain the optimal values of price, replenishment quantity and dispatch cycle for the proposed policy. We then extend our results to consider quantity discount of unit dispatch cost. In order to compare the performances of the proposed policy with the optimal quantity-based policy, extensive numerical experiments are conducted, and the total profit and the customer waiting time that represents quality of service are compared. We also propose the quantity-time-based policy, which is a hybrid approach, and the numerical results show that additional profit can be obtained without sacrificing quality of service.