Using Penalty in Mathematical Decomposition for Production-Planning to Accommodate Clearing Function Constraints of Capacity

The idea of using clearing functions in Linear Programming models for production planning to represent the nonlinear dependence between workload and lead times in productive systems may result in a large nonlinear convex model. Nevertheless, this convex programming model is not considered directly, but approximated by using linear programming models which sometimes results in a large linear programming problem, requiring mathematical decomposition for efficient solution. The classic method of decomposition, however, does not function properly in the presence of the restriction of capacity provided by the clearing function, frustrating the efforts to introduce lead times into the models. In this chapter we provide a strategy to modify the classical decomposition approach using a penalty function for the subproblems, which circumvents the pointed drawbacks.