考虑工序外协的TOC产品组合优化研究

 针对 “粗粒度”产品外包或自制模式进行能力拓展时造成的产品规划保守和接单损失问题,采用“细粒度”工序外协模式对瓶颈、非瓶颈有区别地进行产能提升,使企业设备平均利用率最高、整体有效产出最优、市场需求满意度最好。从自制商和外协商两种角度定义了有效产出,并推导了工序外协和产品外包两种不同制造模式下有效产出的关系。基于传统和新型两种约束理论（TOC）运作逻辑,根据独立优化和集成优化两种优化策略,构建了考虑工序外协的两种TOC产品组合优化数学模型。分析了工序外协和自制/外包模型间的关系,并进行了数学证明。若单位产品的外包成本等于所有工序外协的累加成本,则同一制造模式下集成优化策略不差于独立优化策略,同一优化策略下工序外协制造模式不差于产品外包制造模式。最后通过单瓶颈、多瓶颈算例分析验证了模型以及定理的有效性。

TOC Product Mix Optimization with Elevated Capacity of Outside Processing

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.