78 European Journal of Operational Research 40 (1989) 78-84 North-Holland Theory and Methodology Modeling learning effects linear programming via successive Terry P. HARRISON Management Science Department, The Pennsylvania State University, University Park, PA 16802, USA J. Edward KETZ Department of Accounting and MIS, The Pennsylvania State University, University Park, PA 16802, USA Abstract: A learning effect occurs when the amount of labor required per unit of production decreases as cumulative production increases. Learning effects occur in many situations, and this effect can be especially significant in the startup of a new process. However, from a modeling viewpoint, the inclusion of learning effects can result in a problem that is considerably more difficult to solve than when these effects are ignored. A number of mathematical programming solution methods have been proposed for modeling a learning effect. Unfortunately, these methods frequently require the implementation of sophisticated algorithms. In this paper we develop an alternate solution strategy for modeling a learning effect based upon the use of Successive Linear Programming (SLP). This approach is particularly attractive in that it can be easily implemented, and only requires access to a linear programming package. Keywords: Learning, mathematical programming, nonlinear programming Introduction Suppose that an enterprise can manufacture a number of products. One goal of management is to maximize the contribution margin (revenues less variable costs), however the production process faces a variety of resource constraints. When all of the underlying mathematical relationships are linear, then linear programming is one of several techniques that may be used to address this optimization problem. However, one of the assumptions of linear programming is that the coefficients describing the technology of production are constant. On the other hand, if learning effects exist this assumption is invalid. Learning effects imply that the technological coefficients are declining and that the contribution margins per unit are increasing as cumulative output increases. Therefore, to obtain a better approxima- tion to reality a mathematical programming model should incorporate these effects if learning is present. The direct labour hours needed to produce a unit of output may decline as more units are produced, which is precisely the learning effect. Learning processes are well-documented and occur with labor efficiency, production technology, product redesign, product standardization, and scale effects. Two comprehensive reviews are Nanda and Alder (1977) and Yelle (1979). Received October 1987; revised April 1988 0377-2217/89/$3.50 © 1989, Elsevier Science Publishers B.V. (North-Holland)