Anticipation of Future Demand Changes in Capacity Planning : The Inverse Capacity Boost

Many production systems cannot produce to stock and utilize capacity management to cope with variability in demand, for example Make-to-order (MTO) systems. Often, regular capacity can be increased through a flexible workforce, but the decision about the additional capacity must be made before receiving the actual orders.This work analyzes how future expected demand changes are anticipated by optimized production capacities in manufacturing systems that cannot preproduce but have to cope with stochastic and time-dependent effects. To optimize the time-dependent aggregated production capacity, we integrate approaches for time-dependent performance evaluation into an optimization model. The objective considers a reward for finished orders, backlog costs, and capacity costs. When investigating the structure of time-dependent capacities, one might expect that a demand decrease (increase) would lead to decreasing (increasing) production capacities in the period of the demand change or later. We verify this expectation analytically under general assumptions when using a piecewise-stationary or fluid approach for the performance evaluation. The optimal capacities can be determined periodwise in isolation and do not anticipate future demand changes.Contrary to these analytical results, optimized production capacities may increase several periods before an expected demand decrease when considering both the interdependencies between periods and stochastic effects, for example, when using a stationary backlog-carryover approach for time-dependent performance evaluation. The intuition for this inverse capacity boost is that an increase in the capacity in any period accelerates clearing orders from the system. Furthermore, a marginal increase in capacity just before a demand decrease allows the use of additional capacity more effectively than after a demand decrease. We show the impact of different demand patterns and cost structures on the magnitude of this effect. The numerical analyses demonstrate significant benefits of the inverse capacity boost for single demand shocks as well as for smoothly changing demand