Robust optimization approach to production planning problem and an application

The variability of the environmental conditions in which businesses are included, have been increased, recently. This variability has also brought with it uncertainty. While making decisions and plans on future, taking the uncertainty account has been become as a rule. For this reason, number of the papers' that is used stochastic programming, fuzzy logic, simulation and robust optimization has been increased. Robust optimization, is an operations research technique that produces results which are less affected from data uncertainty by considering possible situations that may come up in the future while modelling of the problem. Lot sizing, that is one of the main sub-processes of the production planning, is to decide from which product, when and how much will be produced, with a most basic definition. Modelling and solution of the lot sizing problems changes depending on structure of the production processes, parameters and variables. In this thesis, it is aimed to generate and apply scenario based robust optimization model for capacitated two-stage multi-product lot sizing problem under parameter and demand uncertainty. With this purpose, production planning problem of a textile company that operate in İzmir has been modelled and solved, then deterministic scenarios' and robust method's results have been compared. Robust method has provided a production plan that has higher cost but, will result close to feasible and optimal for most of the different scenarios in the future. The reason of the higher cost of the robust model has been explained with addition of the deviations from optimal cost values and the penalty costs of the deviations from feasibility on total expected cost. As a result of sensitivity analysis of the robust model parameters, it has been shown that low-cost, less robust plans could be obtain by sacrificing model robustness. This thesis is the first study in Turkey on application of robust optimization in production planning and it constitutes example and resource for the studies in future. Keywords: Production Planning, Lot Sizing, Robust Optimization, Solution Robustness, Model Robustness.