Sequential-analysis based randomized-regret-methods for lot-sizing and scheduling

Lot-sizing and scheduling comprises activities that have to be done repeatedly within MRP-systems. This paper considers the proportional multi-item, capacitated, dynamic lot-sizing and scheduling problem that is more general than the discrete lot-sizing and scheduling problem, as well as the continuous set-up lot-sizing problem. A greedy randomized algorithm with regret-based biased sampling is presented. The paper partitions the parameter space of the stochastic algorithm and chooses subspaces via sequential analysis based on hypothesis testing. The new methods provided in this paper, i.e. the randomized-regret-based backward algorithm, as well as the controlled search via sequential analysis, have three important properties: they are simple, effective and rather general. Computational results are also presented.