یک مدل بهینه سازی برای انتخاب همزمان تلرانس و تامین کنندگان

The quality loss function incorporates the quality cost for design of tolerances, however, it does not consider the manufacturing cost and design constraints. In this paper, a stochastic integer programming (SIP) approach is presented for simultaneous selection of tolerances and suppliers based on the quality loss function and process capability indices. A direct link between the minimum manufacturing cost and the required level of manufacturing yield is established through the process capability index. The optimization model is illustrated with examples for concurrent selection of mechanical and electrical tolerances and the suppliers.

Why is concurrent selection of tolerances and suppliers important? In today's manufacturing environment, every firm purchases various portions of components or subassemblies for its final product assembly. An internationally established firm in Reading, Pennsylvania used to purchase 80% of materials by volume and 50% by dollars. A recent corporate decision has called for the total elimination of its machining operations. Therefore, this plant is switching to 100% purchasing of its components. Based on the first author's consulting experience with this firm in quality and supplier management, most quality experts now agree that a majority of the problems and related costs associated with a firm's product quality is caused by the quality and variability of incoming materials used in the manufacturing process. This fact coupled with the additional fact that the cost to find and repair a quality problem escalates tremendously as an item progresses through the chain of production activities, bringing the issue into sharp focus. Consider the following cost data developed by General Electric shown in Table 1(Cali, 1993). It is well known as the GE 10-times rule in quality management. While it is important to develop tools to assist concurrent design of tolerances and their manufacturing processes, the same is true for concurrent selection of tolerances and suppliers. Table 1. Estimated cost to find and fix a quality problem (Cali, 1993) Process Cost ($) Incoming material inspection 0.03 Fabrication inspection 0.30 Subassembly inspection and test 3.00 Final assembly inspection and test 30.00 Field service 300.00 Table options This paper addresses the issue of achieving quality by concurrent tolerance design and supplier selection. It features the following contributions. First, the stochastic integer programming approach is used to model the relationship between manufacturing cost, quality loss cost, assembly yield, and discrete tolerances. The SIP model follows the philosophy of concurrent engineering as it considers assemblibility, cost, and quality at the product design stage. Second, process capability index and quality loss coefficient A proposed by Taguchi in the SIP model can be used in one optimization model to achieve the required quality level and the minimum total of manufacturing and quality loss cost. The paper is organized as follows. The remainder of this section introduces the assumptions used in this paper. Section 2 briefly reviews the Taguchi quality loss functions used in tolerance synthesis. The SIP approach is presented in Section 3. Section 4 illustrates the proposed approach with a numerical example, and Section 5 concludes the paper.

In this paper, a constrained statistical tolerance optimization problem with the quality loss cost is presented. The constrained quality loss model is shown to be easy to use. It eliminates the regression errors, considers the process shift, and defines a relationship between component tolerances, manufacturing cost, and manufacturing yield through the process capability Cp for centered processes or Cpk for off-centered processes. The constrained quality loss model relates tolerances and manufacturing processes, as well as follows the philosophy of achieving the quality by robust engineering design advocated by Taguchi, 1986 and Taguchi et al., 1989. It has demonstrated how the model applies to concurrent selection of tolerances and suppliers and how it relates to traditional tolerance optimization models. It allows for analysis of the producibility, cost, and quality at the product design stage. Future research is directed to the incorporation of the inventory cost, scrap and rework cost, and inspection cost into concurrent selection of tolerances and suppliers ( Feng & Wang, 1997).