Abstract: Owning to the traditional capacity extending method of product-based coarse-grained pattern, a conservative plan is made according to the product mix solution under the outsourcing or self-manufacturing mode, often resulting in loss of profit. To improve the situation, a new capacity extending method of process-based fine-grained pattern under the outside processing manufacturing mode is introduced which discriminatively identifies and exploits capacity constrained resources (CCR) and non-CCR to increase overall equipment utilization efficiency, maximize system throughput, and satisfy the demands for the finished products to the maximum extent. First, from the very different but inter-related viewpoints of the manufacturer and contractor, the throughput of each party is defined and their interrelations are analyzed. In addition, a comparison of throughput is drawn between the outside processing mode and product outsourcing mode and their relationships are deduced. Second, two mathematical models are presented based respectively on integrated optimization strategy of the traditional theory of constraints (TOC) operational logic and individual optimization strategy the new logic. Third, the two models are analyzed and their optimal throughputs are compared. Furthermore, if the expenses of aggregate outside processing for every product are equal to its expenses of outsourcing, then some relevant theorems are proved, which state that, the integrated optimization strategy performs as well as or better than the individual optimization strategy under the same manufacturing mode, either it is outside processing or product outsourcing mode, and that the TOC product mix optimization solution considering outside processing mode is more outstanding than the one considering outsourcing mode under the same optimization strategy, either it is integrated or individual optimization strategy. But it is not sure that the solution considering the outside processing mode using individual optimization strategy would be superior to the one considering the outsourcing mode using integrated optimization strategy. These conclusions lay the foundation not only for further algorithms to be established in follow-up research, but also help production planners make scientific decisions when dealing with product mix problems. Finally, some single bottleneck and multi-bottleneck examples show the validity of these models and theorems.

Key words: product mix optimization, theory of constraints, outside processing, integrated optimization strategy, throughput, modeling