Optimal Production Planning by a Gradient Technique I. First Variations

A gradient technique baaed on the first variations is used to solve a production scheduling problem with known sales forecasting. The function to be minimized is the sum of the costs derived from holding inventories, stockouts, and the deviation of the production rate from the optimal rate for the plant. This technique has the advantage of being able to investigate problems with a large number of state variables and can also be extended to multiproduct, multifacility operations with complex interconnections.