A Generalized Lagrange Multiplier Algorithm for Optimum or Near Optimum Production Scheduling

In this paper we apply the concept of generalized Lagrange multipliers, introduced by Everett [Everett, H. 1963. Generalized lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. XI 399-417.], to the development of an algorithm for a one-period multi-product production model, where the objective is to maximize profit subject to constraints on aggregate regular time and overtime production. We assume no difference between the cost of idle time and regular time labor, so that the regular time cost is fixed. Overtime cost is variable. The price for each product is constant (independent of quantity sold), and everything produced can be sold. The optimum production schedule (maximum profit) will depend upon revenues, overtime costs, setup times, and productivities.