On Capacity Modeling for Production Planning with Alternative Machine Types

Analyzing the capacity of production facilities in which manufacturing operations may be performed by alternative machine types presents a seemingly complicated task. In typical enterprise-level production planning models, capacity limitations of alternative machine types are approximated in terms of some single artificial capacitated resource. In this paper we propose procedures for generating compact models that accurately characterize capacity limitations of alternative machine types. Assuming that processing times among alternative machine types are identical or proportional across operations they can perform, capacity limitations of the alternative machine types can be precisely expressed using a formulation that is typically not much larger than the basic linear programming formulation that does not admit alternative resource types. These results have important implications for industrial practice, suggesting that in the case that processing times are nearly proportional among alternatives, the prevalent approximation that involves using a single, capacitated, artificial resource may be dropped in favor of our formulation incorporating the approximation that processing times among the alternatives are proportional. Another advantage is that the set of capacity constraints we formulate can be used to check the feasibility of suggested production schedules or demands simply by plugging them into the constraints, without need to develop values for allocation variables