


Awi Federgruen, Joern Meissner


Abstract 

This paper conducts a probabilistic analysis of an important class of heuristics for multiitem capacitated lot
sizing problems.
We characterize the asymptotic performance of socalled 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.


Keywords 

probabilistic analysis, supply chain management, inventory models, lot sizing, time partitioning


Status 

Working Paper 

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