Selection, acquisition, and allocation of manufacturing technology in a multi-period environment

This paper addresses a multi-period investment problem for selection, acquisition, and allocation of alternative technology choices to meet the demand of a number of product families over a long-range planning horizon. The problem captures the essential features of many existing models for analyzing long-term trade-offs between dedicated and flexible technologies in the chemical, manufacturing, telecommunications, and service industries. We show that the general problem is NPNP-hard and present a solution strategy based upon perturbing the linear programming (LP) relaxation solution of a multi-period mixed-integer linear programming formulation for the problem. The key feature of the proposed strategy is a temporal capacity shifting heuristic, whereby capacity expansions are shifted to earlier time periods from amongst those periods chosen for capacity expansion by the LP relaxation solution. With mild assumptions on the problem parameters, we carry a probabilistic analysis which proves that the proposed solution approach is asymptotically optimal almost surely. Our analysis provides a sound theoretical basis for incorporating capacity shifting in existing LP relaxation-based heuristics for long-term technology planning problems in a variety of industries.