Optimization in production planning faces serious difficulties, most important of them is that the market data is typically uncertain.in case the demand uncertainty is neglected during production planning process, the obtained production plan may become extremely costly or even infeasible. Failures or delays in delivery to customers are highly undesirable and may cause penalties; demands that are unsatisfied in time can cause the loos of costumers. Robust optimization is a methodology which can deal with the uncertainty or variability in optimization problem by computing a solution which is feasible for all possible scenarios of data within a given uncertainty set. Simultaneous lot sizing and scheduling is an important problem in production planning environments. In this thesis, simultaneous lot-sizing scheduling in capacitated flow shop environment with uncertain demand has been considered. At first we proposed three robust models that are based on worst-case criterion. By solving the worst case, the upper bound on total costs for any demand scenario can be guaranteed. The first model is based on an iterative approach but the second model is based on the construction of robust counterpart. The third model is an extension of the second model where in some decision variables are allowed to get numerical values already after some part of uncertain data are known. Then we provide a set of numerical examples to verify the effectiveness of these models. Since solving medium and large size instance exactly is impossible, due to complexity of problem, two heuristics based on rolling horizon and a metaheuristic are provided. Then the efficiency of these algorithms in different group of problems evaluated. Experimental results show that the third algorithm has lower average error and the other two algorithms have almost the same results.
