: Lot-sizing and scheduling are two important issues in production planning which are considered simultaneously in researchers studies recently. In this study, simultaneous lot-sizing and scheduling problem in capacitated flow shop environment with outsourcing has been considered. At first we proposed an exact formulation for the problem of simultaneous lot-sizing and scheduling in flow shop with sequence dependent setups as a mixed integer program. Efficiency of proposed model is demonstrated in comparison to the former model, by comparing the number of continuous and binary variables, number of constraint and solving CPU times. Then outsourcing is also taken into account and extended model has been proposed. Since solving medium and large size instances exactly is impossible, due to complexity of problem, five MIP-based heuristics based on rolling horizon are provided. The first three heuristics are based on original model which are appropriate for small problem sizes. Two other heuristics are based on permutation flow shop which is a restricted model. To test the accuracy of heuristics, a lower bound is developed and compared against optimal solutions. Finally computational results demonstrated the effectiveness of heuristic algorithms which offered solutions in less than 10% -15% GAP of developed lower bound.
