Capacity acquisition and subcontracting

The fundamental question encountered in acquiring capacity to meet nonstationary demand over a multi-period horizon is how to balance the tradeoff between having insufficient capacity in some periods and excess capacity in others. In the former situation part of the demand is subcontracted, while in the latter capacity that has been paid for is rendered idle. Capacity and subcontracting decisions arise in many economic activities ranging from production capacity planning in semiconductor fabs to leasing communication networks, from transportation contracts to staffing of call centers. In this paper, we investigate the tradeoffs between acquiring capacity, subcontracting, production, and holding inventory to satisfy nonstationary demand over a finite horizon. We present capacity acquisition models with holding and without holding inventory and identify forecast-robust properties of the models that restrict the dependence of optimal capacity decisions on the demand forecasts. We develop algorithms for numerous practical cost structures involving variable and fixed charges and prove that they all have polynomial time complexity. For models with inventory, we solve a sequence of constant capacity lot-sizing and subcontracting subproblems, which is also of independent interest. Supported by NSF grants DMI-9908705 and DMI-0070127. Supported by NSF grants DMI-9713482 and DMI-9908705.