Establishing relation between production rate and product quality in a single-vendor multi-buyer supply chain model

This paper develops a single-vendor multi-buyer supply chain model with variable production cost, imperfect quality of products and environmental factors. A unit production cost is considered as a function of the production rate. Costs that vary depending on the production rate of a company is variable production cost. Increase in production rate deteriorates the product quality, resulting in imperfect quality of products. High production rate also produces significant carbon emission in the environment. In order to reduce the environmental pollution, industries must invest an amount. The cost associated with the environmental impact of one's company's business operations is environmental cost. In order to obtain the global optimum solution, a classical optimisation technique is employed. An illustrative algorithm is established to obtain the numerical results. Numerical examples are given to illustrate the model. Numerical study proves the effects of variable production rate on the total cost of supply chain model.