Co-production models with random functionality yields

Production systems with random functionality yields and downward substitutable demand are modeled and investigated. Such systems arise frequently in the electronics and petrochemical industries. We analyze two single-period models. The first models a single production process in which the total yield of usable products is uncertain; furthermore the realized usable products are of two grades, higher and lower, and the portions of each grade products are also uncertain. Demand for lower-grade products can be met, if necessary, by higher-grade units. The second model we analyze has two parallel production processes: one is as in the previous model; the other is attempting to produce lower-grade products only, but their yield is random. In both single-process and two-process scenarios the relative magnitudes of the salvage values of the two product grades lead to somewhat different models that need to be analyzed separately. We prove that all the expected profit functions are concave (jointly concave), and derive the optimality conditions. Some related modeling and managerial issues are discussed.