Product-Mix Models When Learning Effects are Present

An important problem confronting decision makers in modern organizations is the determination of an optimal product-mix (or service-mix) in situations where learning effects are present. Learning has been observed to exist in a variety of production and service situations in which the amount of input required per unit of output decreases as total output increases. Little research has appeared, however, on the incorporation of learning effects into resource allocation models that attempt to determine good or optimal allocations of scarce resources to competing activities via mathematical programming. Enriching a traditional linear programming product-mix model to include learning effects results in a nonlinear model which may be more realistic, but is also likely to be more difficult to solve. In this paper, nonlinear product-mix models which incorporate learning effects are formulated and a procedure is developed for their solution. A key feature of the procedure is that decision makers are presented with good feasible solutions to a more realistic model early in the overall solution process together with bounds on the value of the best possible solution. Good feasible solutions and bounds are obtained with relatively little computational expense and effort through the use of linear approximation techniques. Feasible solutions serve as base points in a branch and bound process to refine solutions and bounds. Decision makers are able to terminate the solution procedure at any point prior to completion once a satisfactory, near optimal solution is identified. Alternatively, if allowed to run to completion, the solution procedure is capable of identifying and verifying a global optimal solution.