A Robust Design Model for Quality Control in Supply Chains with Quality Prevention Uncertainty

This paper investigates strategy and supply chain quality control problems in order to address uncertainty in quality control and ensure the effectiveness of supply chain operation. A multi-product,multi-stage supply chain consists of one manufacturer and one buyer. The manufacturer can choose a certain level of quality prevention to produce and sell products to the buyer. The buyer may choose its quality level to evaluate items and make three kinds of decisions after evaluation:( 1) accept good products,( 2) accept defective products,and( 3) accept potentially defective products. Internal failure happens to the buyer in the case of defective products and a penalty is placed on the manufacturer. External failure happens to the buyer in the case of potentially defective products and a big penalty is then given to the manufacturer. In the process of supply chain operation,the buyer optimizes its quality requirements and order quantity in order to maximize its own objective profit. The manufacturer decides how to deliver products to the buyer in order to maximize profit.We proposed a research model to achieve three objectives. The first objective is to improve supply chain cooperation between the manufacturer and the buyer so that the delivery quantity from the manufacturer equals to the order quantity of the buyer. The second one is to maximize the manufacturer's profit. The third objective is to maximize the buyer's profit. A basic programming model was developed to describe three operational objectives accordingly. The manufacturer makes profits from selling quality products and defective ones after subtracting production costs,material procurements,holding costs,and penalties from the buyer for both internal and external quality failures. On the other hand,the buyer benefits from selling quality products,defective ones,and potentially defective ones after subtracting procurement costs,holding costs,and penalties from the buyer for internal and external quality failures.Interval analysis method is used to describe the uncertainty of quality prevention levels. When mass production process is under good control,the manufacturer's quality prevention level is assumed to be a random variable in the form of normal distribution. The practical value of quality prevention level deviates near the expected standard value. For convenience,it is proposed to describe the uncertainty in quality prevention level by symmetric bounded intervals. Furthermore,analysis is made to understand the effect of uncertainty on the profit objectives of manufacturers and buyers. The effect is then quantified and added to the objective functions of the manufacturer and the buyer. Bertsimas' s robust linear method can be used to deal with the fluctuation model. The manufacturer and buyer's objective functions with uncertainty in quality prevention level can be turned into several constraints for the problem. At the same time,the manufacturer and buyer's operation objectives are rewritten in the form of a new objective programming model for supply chains.The manufacturer's operation depends on the buyer's order quantity even though the manufacturer's operation influences the buyer's order quantity. In the research,the buyer's objective precedes the manufacturer's one. Supply chains operate under the condition that the delivery can meet the order requirements from the buyer. Three priority factors are defined for these three objectives in supply chain operations. The whole supply chain is considered as an integrated one and an objective programming model is developed after integrating these three objectives: maximization of the manufacturer's operation profit,maximization of the buyer's operation profit,and the delivery volume equaling to order quantity. The buyer's capacity constraints on stock volume,production volume,and actual sales are included in the model in addition to the manufacturer's stock capacity constraint. Thus,the optimization problem is turned into a linear one and the model is easily optimized. The three objectives in supply chain operations can be satisfied at the same time,and the objective programming model is robust when quality prevention level fluctuates within some extent.In addition,a numerical example is given. Linprog tools in the Matlab 7. 0 Optimizer software are used to solve the objective programming model. Computation is done for two cases when the manufacturer's quality prevention level is certain and uncertain,respectively. The operation strategy is derived through optimization which includes manufacturer's production volume,delivery volume,stock volume,the buyer's order quantity,stock volume,and sales volume. Comparison results show that the manufacturer's decision on operations is the same as the buyer's when the manufacturer's quality prevention level fluctuates within 0. 1 units. The only difference is that their profits are reduced by 3. 86% and 10. 78 %,respectively. Moreover,a computation is done after considering that the manufacturer's quality prevention level fluctuates from 0. 1 units to 2. 6 units. Results indicate that the uncertainty of quality prevention level within certain limits weakens the performance of supply chain when operation strategy is still working. That is,the model and its solution are both robust.Finally,a method and a technique for modeling and optimizing supply chain quality control are proposed with the objectives of coordinating quality control and strengthening its ability to deal with uncertainty in supply chain operations.