Separating setup and quantity decisions in stochastic lot sizing models

Description

When dealing with optimization problems that include uncertain input parameters, two popular modelling approaches are available in the literature. Stochastic programming approximates the distribution of the uncertain parameters by discrete scenarios aiming at minimizing the expected costs over these scenarios. Robust optimization serves as a worst-case approach hedging solutions against unfavorable realizations of the stochastic parameters. We investigate two-stage stochastic programming and robust optimization for multi-item multi-stage capacitated lot sizing under demand uncertainty. The objective is to minimize the overall costs consisting of production-, setup-, holding- and backlog costs. For the stochastic model the flow of information needs to be specified by deciding on which variables are fixed before the uncertain parameters are realized and which can still be adapted afterwards. In the context of lot sizing usually setup and production quantity decisions are fixed, while inventory and backlog variables act as the recourse variables. We investigate the case of only fixing setup decisions in the first stage, while shifting quantity decisions to the second stage, representing a more flexible approach of planning. For the stochastic programming approach this formulation leads to significantly larger and therefore more complex models. Since solving the compact model of this formulation is already challenging for small instances we tailored a Benders decomposition approach to the problem. We compare this formulation to the stochastic version where setup and quantity decisions are made in the first stage, as well as to a static budget-uncertainty robust approach. We analyze the obtained production plans and investigate the impact of being more flexible in planning.

Period	07 Sept 2022
Event title	International Conference on Operations Research - OR 2022
Event type	Conference
Location	GermanyShow on map