Robust demand service achievement for the co-production newsvendor

The co-production newsvendor problem is motivated by two-stage production processes that simultaneously yield a set of output products of different grades from the same input stocks. Co-production is a characteristic feature of processes such as semiconductor manufacturing and crude oil distillation. In the first stage, the newsvendor executes the order quantities for the input stocks prior to learning the actual demands and grading fractions of the products. In the second stage, the available production is allocated to satisfy the realized demands. Downward substitution is allowed in the allocation; i.e., demands for lower grades can always be filled by higher grades but not vice versa. The co-production newsvendor seeks to achieve maximum demand service level, subject to resource or budget constraints. This article proposes the use of the aspiration level approach to model the decision problem. Furthermore, it is assumed that only the means and supports of the uncertain demands and grading fractions are available, and the model is extended using robust optimization techniques. The resulting model is a linear program and can be solved very efficiently. Computational tests show that the proposed model performs favorably compared to other stochastic optimization approaches for the same problem.