Simultaneous product-mix planning, lot sizing and scheduling at bottleneck facilities

Planning and scheduling of bottleneck operations is a fundamental problem in production management because bottleneck facilities control the output and profitability of the entire system. The authors develop optimal solutions for the product-mix planning, lot sizing, and scheduling of such bottleneck facilities. The integrated product-mix planning, lot sizing and scheduling problem yields a nonconvex, mixed-integer nonlinear program which is difficult to solve for global optimality. The present strategy is to characterize the optimal solution and reduce the overall problem to a series of smaller, single variable, constrained optimization problems which can be solved relatively easily. The authors provide results for the two-product case for both the single-stage and two-stage production systems and for two types of production environments. Optimal solutions are also provided for the single-stage multiproduct case when all products are produced under a common-cycle restriction. The present work represents an extension of classical product-mix models to include the economic lot sizing and scheduling model.