Reducing production costs has become one of the most important concerns, due to the economic development and increasing competitiveness in industries. To achieve this goal, considering real conditions is important. On the other side, the main goal of the most companies is trying to fulfill the needs of their customers without spending a lot of time. Optimization models have been used to support decision making in production planning. However, several of those models are deterministic and do not address the variability that is present in some of the data. Robust Optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible scenarios of the data within a given uncertainty set. Simultaneous Lot-sizing Scheduling is an important problem in production planning environments. In this thesis a model similar to traveling salesman problem with uncertain demand is presented. The problem objective is to determine the production lot sizes and their schedules in order to minimize the sum of the total setup cost, total holding cost, and total backorder cost. Two robust optimization criterions are applied to formulate a robust linear programming model. The first model, considering deviation from optimal and shortage cost. The second model is based on worst-case criterion that can adjust different risks for decision makers. Finally, we provide a set of numerical examples for 1000 small scaleproblem to verify the effectiveness of the approaches. Since the model could not solve the NP-hard large size problems, two heuristic Fix Relax algorithms, are used to solve this group of problems. Then the efficiency of these algorithms in different groups of problems evaluated. Experimental results, that among 900 large scaleproblems, show that the first method is better in averagetime and the second method has lower average error.The average errors of these two algorithms are 4.89 and 3.12 for the first robust model and 2.35 and 1.55 for the second robust model, respectively.
