Effects of variable production rate on quality of products in a single-vendor multi-buyer supply chain management

A supply chain with multiple buyers leads to a hike in demand and for satisfying them, a high standard production manufacturing system is required. A predetermined production rate in a supply chain model with economic production lot size is quite inappropriate for this type of situation as production rate can be changed in some cases to fulfill demand of customers. Rate of production has an impact in maintaining process quality. Manufacturing quality deteriorates with an increasing rate of production. In this context, this paper develops a single-vendor multi-buyer supply chain model with variable production rate and imperfect quality of products. The unit production cost is considered as a function of the production rate. Three different production functions are established to relate process quality and production rate. Due to huge demand by multi-buyer, the lead time demand is considered as random variable and it follows a normal distribution. The objective of this study is to analyze how the flexibility of the production rate affects the product quality as well as entire supply chain cost under a single-setup multiple-delivery policy. A classical optimization technique is employed to obtain the global optimum solution. An illustrative algorithm is established to obtain the numerical results. Numerical examples and graphical interpretations, and sensitivity analysis are given to illustrate the model. Numerical study proves that the variable production rate effects a lot on the total cost of supply chain model.