Capacity and production decisions in stochastic manufacturing systems: An asymptotic optimal hierarchical approach

The authors present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. They show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions. The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the purchase. The objective is to minimize the discounted costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting problem in which the random capacity is replaced by its mean. The authors develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. They obtain error estimates for these constructed decisions.