On The Robust Lot Sizing with Spoiled Goods

This work addresses the problem of lot sizing for perishable products under uncertainty in demand, using robust optimization. The model considers a finite planning horizon with no limit on production capacity and with production costs, storage, delay and deterioration, in addition to a limited useful life for the products and FIFO policy. The resolution adopts a decomposition into master problem and separation subproblem, with iterative generation of adverse scenarios. The subproblem is solved by two approaches: an exact mixed integer formulation and a heuristic based on dynamic programming (PD), whose state records the period, the number of deviations used, and the accumulated deviation. It is shown that this state does not satisfy the principle of optimality, since the perishing under FIFO depends on the temporal distribution of the deviations, and not just of its total. Experiments on 324 instances indicate that PD separation has consistently lower execution times than the exact model, with increasing advantage in larger instances without the loop termination being certified.