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Procedures for generating compact models that accurately characterize capacity limitations of alternative machine types are presented. 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 suggest 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 the formulation incorporating the approximation that processing times among the alternatives are proportional. The set of capacity constraints formulated can be used to check the feasibility of suggested production schedules or demands simply by plugging them into the constraints, without developing values for allocation variables.
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