Management of co-products with different shelf-lives

In reality, some firms can use one kinds of raw material to produce many kinds of products which are called co-products, and the production quantity of each kind of product will affect the ordering policy of the raw material. So it is important to find out an effective ordering policy for the firm. In this paper, we take a food production firm as an example to study the optimal ordering policy for a raw material to produce two types of products for the multi-period horizon. For these demands are uncertain, the company should determine the procurement of the raw material to minimize the cost of procurement, production, holding, shortage, and outdating cost for these two kinds of products. Dynamic programming is used to analyze the structure and propositions of the optimal ordering policy, and we give the upper and lower bound for this policy. In numerical studies, we discuss the influence of the production fraction, the relative market volatility and the relative cost of two kinds of products on the minimum expected cost. Finally, we propose and compare three widely used heuristic policies with the optimal one.