an algorithm based on theory of constraints and branch and bound for solving integrated product-mix-outsourcing problem

One of the most important decision making problems in many production systems is identification and determination of products and their quantities according to available resources. this problem is called product-mix. however, in the real-world situations, for existing constrained resources, many companies try to provide some products from external resources to achieve more profits. in this paper, an integrated product-mix-outsourcing problem (ipmo) is considered to answer how many products should be produced inside of the system or purchased from external resources. for this purpose, an algorithm based on theory of constraints (toc) and branch and bound (b&b) algorithm is proposed. for investigation of the proposed algorithm, a numerical example is presented. the obtained results show the optimal result by the new algorithm is as same as the results of integer linear programming.