Control of a production system with variable yield and random demand

This paper considers a dynamic production/inventory problem where the yield (or quantity supplied) is not exactly equal to quantity ordered. It is assumed that demand in each period is random with a given distribution. Assuming quadratic costs, order quantity for the unconstrained order quantity case is calculated using dynamic programming and is found as a linear function of the entering inventory. The more realistic case of constrained (nonnegative) order quantity is also analyzed using a heuristic. Two cases, (1) pay-for-input and (2) pay-for-output are separately discussed but found to be closely related. It is found that the heuristic proposed performs well in majority of the 8000 simulated test cases. A nonlinear regression model is also provided which can be used to estimate the performance of the heuristic for the given values of the six parameters of 50 period problems. Several numerical examples illustrate the results.