Myopic heuristics for the random yield problem

We consider a single item periodic review inventory problem with random yield and stochastic demand. The yield is proportional to the quantity ordered, with the multiplicative factor being a random variable. The demands are stochastic and are independent across the periods, but they need not be stationary. The holding, penalty, and ordering costs are linear. Any unsatisfied demands are backlogged. Two cases for the ordering cost are considered: The ordering cost can be proportional to either the quantity ordered (e.g., in-house production) or the quantity received (e.g., delivery by an external supplier). Random yield problems have been addressed previously in the literature, but no constructive solutions or algorithms are presented except for simple heuristics that are far from optimal. In this paper, we present a novel analysis of the problem in terms of the inventory position at the end of a period. This analysis provides interesting insights into the problem and leads to easily implementable and highly accurate myopic heuristics. A detailed computational study is done to evaluate the heuristics. The study is done for the infinite horizon case, with stationary yields and demands and for the finite horizon case with a 26-period seasonal demand pattern. The best of our heuristics has worst-case errors of 3.0% and 5.0% and average errors of 0.6% and 1.2% for the infinite and finite horizon cases, respectively.