Optimal procurement and production planning for multi-product multi-stage production under yield uncertainty

Many products with several types are produced in more than one production stage subject to various potential complications, yield uncertainty being a very costly one. This study investigates the input procurement and semi-processed item allocation decisions of a producer in a multi-product-type and two-stage production system subject to yield uncertainty. A make-to-order production environment with deterministic production leadtimes is considered. For the problem, a discrete stochastic optimization model with binomial yield at each production stage is proposed. Optimal solution is determined with a novel solution algorithm developed by showing the convexity of the problem. The model is applicable not only to production in industries such as chemical, electronic, and mechanical manufacturing, but also to process types such as transportation and remanufacturing. As result of a comprehensive sensitivity analysis, it is found that improving yield in a single stage may not be effective in ensuring cost savings, improvements in different stages should be considered together. More interestingly, higher demand does not always lead to higher production, in contrast it may even reduce production amounts under yield uncertainty.