Managing flexibility in stochastic multi-level lot sizing problem with service level constraints

Abstract

We investigate the stochastic multi-level lot sizing problem with a service level and in a general setting in which it is possible to have independent demand for the components as well. In this work, we present a systematic approach to evaluate the value of adding flexibility in such context. To this end,the problem with uncertain demand is modeled as a two-stage stochastic program considering different demand scenarios. We first consider at all levels a static strategy in which both the setup decisions and the production quantities are determined in the first stage before the demand is realized. We also model a more adaptive strategy to be more responsive to the realized demand when production quantity decisions of some items can be treated as recourse decisions. We investigate the value of applying such an adaptive strategy and adding more flexibility in the system under different settings. Three different bill of material (BOM) structures (serial, assembly, and general) are considered. We numerically show that adding flexibility to the system results in a cost savings depending on where we add the flexibility in the BOM. While controlling the variation in the plans is very important in the multi-level system, this research shows that even having a small degree of flexibility may result in a reasonable amount of cost savings.