Joint economic production allocation and ordering policies in a supply chain consisting of multiple plants and a single retailer

This article discusses the production and ordering policies in a supply chain consisting of a single manufacturer and a single retailer. The retailer places orders based on the EOQ-like policy, and the manufacturer purchases raw materials and allocates them to the multiple plants in parallel to produce demand requirement from the retailer. The model is mathematically formulated, and the solution procedure is developed to determine the production cycle length, ordering quantity and frequency, and production allocation ratios for multiple plants. The closed forms of the production cycle length, ordering quantity, and frequency in terms of the production allocation ratios are obtained. It is also shown that the production allocation problem is NP-hard. An efficient and effective heuristic algorithm is proposed to determine the near-optimal production allocation ratios. A numerical experiment demonstrates that the proposed algorithm performs quite satisfactorily.