Probabilistic Analysis of Multi-Item Capacitated Lot Sizing Problems

This paper conducts a probabilistic analysis of an important class of heuristics for multiitem capacitated lot sizing problems. We characterize the asymptotic performance of so-called progressive interval heuristics as T, the length of the planning horizon, goes to infinity, assuming the data are realizations of a stochastic process of the following type: the vector of cost parameters follows an arbitrary process with bounded support, while the sequence of aggregate demand and capacity pairs is generated as an independent sequence with a common general bivariate distribution, which may be of unbounded support. We show that important subclasses of the class of progressive interval heuristics can be designed to be asymptotically optimal with probability one, while running with a complexity bound which grows linearly with the number of items N and slightly faster than quadratically with T. We generalize our results for the case where the items' shelf life is uniformly bounded, e.g. because of perishability considerations.