Production planning and scheduling are the most important issues of the production industries, which have a considerable influence on the productivity of the production systems. On the other hand, Nowadays, many companies outsource their jobs to a third party instead of managing them directly. The outsourcing of non-critical activities to subcontractors allows firms to focus more on high value operations. A proper plan for outsourcing can improve lead times, reduce total costs, and make a company more competitive. While a manufacturer can benefit from outsourcing, the potential maximum benefit cannot be achieved unless there is an efficient production plan that can cope with the complexity of outsourcing. To achieve this benefit, management needs to decide what quantities of each product to be manufactured and what quantities to be outsourced to external subcontractors. For this purpose, a joint scheme between production and outsourcing plans is necessary in an efficient scheduling scheme. In this thesis, we investigate a simultaneous Lot-sizing Scheduling problem i capacitated flow sho environment with outsourcing in each stage of production with the objective of minimizing sum of total production,set up, outsourcing,inventory and backlogging cost. Assumptions such as capacity constraint, sequence-dependent setup costs and times, and the possibility of setup carryover at successive periods have been considered in the problem. In this paper, two mathematical models are developed for the problem, and the efficiency of them is evaluated in different problem sets. These two models are different in the method of lot-sizing. Most lot sizing problems are hard to solve, especially in medium and large scale.In recent years, to deal with the complexity and find optimal or near-optimal results in reasonable computational time, a growing number of researchers have employed metaheuristic approaches to lot sizing and scheduling problems. We have developed a discrete version of the Cuckoo Optimization Algorithm(COA) to solve this model. In addition, Two mixed integer programming-based approaches with rolling horizon framework have been used to solve this model. Also, a hybrid meta-heuristic based on a combination of cuckoo optimization algorithm and proposed heuristic(rolling horizon) is developed to solve the problem.To test the accuracy of algorithms, a lower bound is developed and compared against proposed algorithms. To evaluate the performance of the proposed model and also solution methods, some problems have been studied. Finally computational result demonstrated the effectiveness of rolling horizon algorithms against both meta-heuristic and hybrid approach
