مدل سازی زنجیره تامین تصادفی چندهدفه برای ارزیابی مبادلات پایاپای بین سود و کیفیت

Many companies struggle with justifying the cost of quality within their supply chain. Outsourcing suppliers to countries such as China has become popular in recent years due to the fact it appears to be more profitable. These outsource decisions do not effectively determine the impacts of quality defects. In this paper we demonstrate a method for evaluating the systemic supply chain risk of poor quality. We introduce a multi-objective stochastic model that uses Six Sigma measures to evaluate financial risk. Results from modeling suggest quality, profit, and customer satisfaction can be evaluated.

Many companies struggle with justifying the cost of quality within their supply chain. Outsourcing suppliers to countries such as China has become popular in recent years due to the fact it appears to be more profitable. However, what many companies fail to see is the cost associated with varying quality levels from their suppliers. In order to create a quality product, the company must address all aspects of the supply chain, including individual processes and supplier selection. A supply chain (SC) can be expressed as the sum of parts involved in fulfilling a customer request (Chopra and Meindl, 2007). By this definition, a supply chain consists of suppliers, manufacturers, warehouses, retailers, transporters, and customers. The purpose of a supply chain analysis is to maximize an organization's profit in the process of generating value for the customer, namely maximizing the difference between the final product worth and the total cost expended by the supply chain to provide the product to the customer. Many organizations emphasize quality as a means to stay competitive in the marketplace over the long run. They view having a reputation of high quality as representing future market share for new customers and maintaining market share for existing customers over their lifetime. Further, improving quality can provide long term financial savings, such as scrap and rework reduction. We associate these quality savings as long term savings that are difficult to quantify. One method to quantify quality is the initiative known as Six Sigma. The label “Six Sigma” originates from statistical terminology, wherein sigma (σ) represents standard deviation. The probability of falling within plus or minus six sigma on a normal curve is 0.9999966, which is more commonly represented as a defect rate of 3.4 parts per million ( Yang and El-Haik, 2003). This level of quality is seen as the goal in most Six Sigma initiatives, but the terminology is also used to evaluate current levels below that, such as 4 Sigma representing a plant that has 6210 defects per million. The corresponding defective rates for each Sigma level are shown in Table 1 below. Table 1. Sigma levels for parts per million defective. Sigma level Parts per million defective 1 691,462 2 308,538 3 66,807 4 6210 5 233 6 3.4 Table options In order for a supply chain to remain profitable, quality from suppliers must be considered on the decision making process. Competing strategies of increasing profit as opposed to increasing quality will require many tradeoffs. The purpose of this article is to model the tradeoffs and to identify situations that a decision maker can use to optimize the benefits of both.

Modeling a supply chain can be a challenging process due to the fact that there are a large number of factors that need to be translated into the model. The use of multi-objective stochastic optimization partially overcomes those problems since more information is used when building the model. Uncertainty on parameters and multiple objectives are ways to give more flexibility and robustness to the decision making process since the process can take into account much more information. Profit or cost is usually the classic choice when optimizing a supply chain. The problem with this formulation is that other important factors, such as quality and supplier selection, are not taken into account in the model. In this paper we proposed a formulation with a comprehensive approach that considers the aforementioned factors. A stochastic optimization model was proposed to optimize the profit and the quality function of the supply chain. This model defines typical strategic and tactical decisions regarding the supply chain. A set of Pareto efficient solutions is generated and the strategic binary variables take into account the randomness of the demand. This provides a useful tool for decision making since this process rarely is done based on only one objective or without considering the risks of randomness. Numerical experiments showed the tradeoffs of the profit and quality function considered in the objectives and gave important insight to assist decision making process. We generated a set of scenarios in order to approximate a continuous distribution for the stochastic demand. The example illustrated how the model could be used in a real situation. It demonstrates the tradeoffs and the financial risk by a numeric application, thus supporting the need for the multi-objective and the stochastic approach. Finally, there is the possibility of extending the model by analyzing the production lines and determining how the raw material interacts with the process to generate imperfect products. This formulation will require several assumptions and may be difficult to solve to proven optimality. The result is a multi-objective nonlinear stochastic programming model.