Production to order on a two machine line with random yields and rigid demand

Random yields may necessitate multiple production runs whenever demand is ‘rigid’; i.e., whenever shortages are not permitted. In this paper, we extend the analysis of problems with rigid demand to a two machine system which has an intermediate inventory of inspected units. For such systems, the production policy must specify, as a function of the intermediate inventory level and the remaining demand, which machine to run next and its lot size. After showing that the optimal policy can be calculated through a series of linear programs, we use the dual formulation to demonstrate that a straightforward policy improvement algorithm will yield the optimal policy. Finally, some empirically observed properties of both the optimal policy and its cost function are used to develop a simpler heuristic algorithm which performs within 1 or 2% of the optimal over a test bed of 180 problems.