LEARNING IN SETUPS - ANALYSIS, MINIMAL FORECAST HORIZONS, AND ALGORITHMS

We analyze the dynamic lot-sizing model in which the cost of a setup d epends on the number of setups that have occurred prior to it. This ar ises, for example, when there exist learning effects in setups. Our mo del is more general than most learning models in the literature since it allows the total setup cost to be a general nondecreasing (but not necessarily concave) function of the number of setups. We explore tigh t relationships between our model and special cases of the classical d ynamic lot-sizing model. On the basis of these we find minimal forecas t and planning horizons for our model, which determine the first decis ion when the model is solved on a rolling horizon basis. When a foreca st horizon cannot be found, we provide guidelines regarding the optima l first decision. We also provide an algorithm to solve the finite hor izon problem, which uses as subproblems variations of the classical dy namic lot-sizing problem. The advantage of this approach is the abilit y to use the extensive literature available on the latter, to generali ze the results of this paper. As many of our results are qualitative i n nature, they provide insights which can be useful for other models w ith a similar setup cost behavior.