| We study a two-stage multi-product manufacturing facility from the perspective of determining good stocking policies for raw materials inventory, work-in-process and finished goods inventory, which take into account the effects of one decision upon the other. This involves determining an external purchasing policy, as well as the production policies at each stage of the system.; For the external purchasing subsystem, we consider the problem of setting order quantities for purchased components, subject to uncertainty in the delivery amounts. Assuming the periodic production volumes (demands) to be known and constant, we model this as a random yield problem with the objective of minimizing average inventory cost subject to a service level constraint over the infinite horizon. Since conventional definitions of service can be inappropriate under conditions of random yield, we refine the definition of service and use it to formulate an optimization model. Exact solution of this model proves to be computationally impractical and, as we show, the common heuristic of inflating demands by a constant proportion is not robustly accurate. Therefore, we develop a new heuristic, which we term the linear inflation policy, that specifies a linear function for the inflation factors. Numerical tests indicate that this heuristic can substantially outperform the traditional constant inflation policy and works well relative to a lower bound on the optimal solution for a range of examples.; For the production subsystem, we consider the problem of simultaneously determining optimal base stock levels at both stages of production (work-in-process and finished goods inventory), where the schedule for inventory replenishment of different products follows a predetermined cycle. Under the assumptions of constant setup and production times, and random demand, we first model each stage separately as a stochastic economic lot size problem (ELSP), with the objective of minimizing total expected holding plus penalty cost. For each of these models, we then develop an optimization algorithm, based upon the combination of stochastic approximation and a simulation based gradient estimation technique, which is shown to converge to the optimal solution. The two algorithms are then used within an iterative scheme to determine the optimal base stock levels in the joint two-stage problem. Numerical testing shows that the iterative scheme converges to the optimal solution quickly and reliably. |
