Production allocation and shipment policies in a multiple-manufacturer-single-retailer supply chain

This paper investigates purchasing and production allocation policies in a supply chain consisting of multiple manufacturers and a single retailer. Demand at the retailer is known and constant over time. The retailer places orders based on the EOQ policy and allocates them to the multiple manufacturers to minimize the average total cost incurred in the whole supply chain. The problem is modelled and the solution procedure is presented to determine the purchasing cycle length, the shipment frequencies, and the production allocation ratios for multiple manufacturers. The closed form solutions of the purchasing cycle length and the shipment frequencies are derived in terms of the production allocation ratios. However, the production allocation problem has the structure of a concave minimization problem, which is known as an NP-hard problem. We develop an efficient heuristic algorithm to obtain the near-optimal solution, and show that the proposed heuristic algorithm performs quite satisfactorily through a numerical experiment.