Separable programming for aggregate production planning: A high-order cost case

Many production managers are faced with the problem of planning production, inventory and work-force under the constraint of limited resources to meet a seasonal demand. Considerable research has been done on this planning problem and various planning models have been introduced. In those cases where linearity of the cost functions of an undertaking may reasonably be assumed, an ordinary linear programming model suffices. In many cases, however, this simple linear approach to certain essentially non-linear cost functions is unacceptable owing to the gross approximation made.Separable programming (SEP) is introduced as a solution methodology to this aggregate production planning problem in a complex, high-order cost structure case. The cost structure was used by Goodman for the application of goal programming (GP) in this field. The Goodman GP model makes provision for positive or negative slack for the production level, work-force level and inventory level with penalty costs for these slack-deviations. Goodman also made use of a 'sectioning search' model for this high-order cost case to serve as a measure for his GP model. A comparison is made between the results of these three approaches. SEP offered an improvement of more than 4% in total cost in comparison with the sectioning search model, and performs 26% better than the GP model.