A perfect information lower bound for robust lot-sizing problems

Abstract

Robust multi-stage linear optimization is hard computationally and only small problems can be solved exactly. Hence, robust multi-stage linear problems are typically addressed heuristically through decision rules, which provide upper bounds for the optimal solution costs of the problems. We investigate in this paper lower bounds inspired by the perfect information relaxation used in stochastic programming. Specifically, we study the uncapacitated robust lot-sizing problem, showing that different versions of the problem become tractable whenever the non-anticipativity constraints are relaxed. Hence, we can solve the resulting problem efficiently, obtaining a lower bound for the optimal solution cost of the original problem. We compare numerically the solution time and the quality of the new lower bound with the dual affine decision rules that have been proposed by Kuhn et al. (2011).

Comparison of different approaches to multistage lot sizing with uncertain demand

“…Under seasonality trends, reoptimization capabilities pay off in significantly better objective values. Upper and lower bounds for robust lot sizing are derived by Santos et al (2018). In particular, a lower bounding technique is set up analogous to the perfect information relaxation from stochastic programming through relaxing nonanticipativity.…”