Decomposition approach for a problem of lot-sizing and sequencing under uncertainties

The paper addresses a problem of optimal lot-sizing and sequencing of manufacturing items for production lines. The following factors are taken into account: processing times, set-up times, random machine breakdowns and rejects. The goal is to maximize the probability of a desired output for a given period. A mathematical model of the problem and an optimization approach are discussed. This approach is based on the decomposition of the initial problem in three sub-problems: an enumeration, a travelling salesman problem and a knapsack problem. An iterative optimization procedure is proposed, based on this decomposition.