Learning in setups: Analysis, minimal forecast horizons, and algorithms

We analyze the dynamic lot-sizing model in which the cost of a setup depends on the number of setups that have occurred prior to it. This arises, for example, when there exist learning effects in setups. Our model is more general than most learning models in the literature as it allows the total setup cost to be a general nondecreasing (but not necessarily concave) function of the number of setups. We explore tight relationships between our model and special cases of the classical dynamic lot-sizing model. On the basis of these we find minimal forecast and planning horizons for our model, which determine the first decision when the model is solved on a rolling horizon basis. When a forecast horizon cannot be found, we provide guidelines regarding the optimal first decision. We also provide an algorithm to solve the finite horizon problem, which uses as sub-problems variations of the classical dynamic lot-sizing problem. The advantage of this approach is the ability to use the extensive literature available on the latter, to generalize the results of this paper. As many of our results are qualitative in nature, they provide insights which can be useful for other models with a similar setup cost behavior.