A Two Stage Supply Chain Model with Selling Price Dependent Demand and Investment for Quality Improvement

This paper presents the problem of a vendor-buyer integrated production inventory model for two stage supply chain under investment for quality improvement. The buyer faces as a linear demand, which is assumed to be function of its unit selling price. Total profit is the supply chain performance measure and it is computed as the difference between revenue from sales and total cost, where the latter is sum of the vendor’s and buyer’s setup/order and inventory holding costs, and opportunity investment cost . Moreover, a capital investment, which is necessary to improve the quality of the product, is also considered in the total profit function. Main focus for this paper is the investment for quality improvement for joint optimization. In this paper we can use logarithmic function to obtain the investment in quality improvement. The model is based on the integrated total profits of both buyer and vendor which find out the optimal value of order quantity, opportunity investment cost for quality improvement.In this study first, we developed mathematical model and procedure of finding the optimal solution is developed. Also the solution procedure is developed in order to find the total profit of the vendor and the buyer which is to be maximized. Some numerical examples are also used to analyze the effect of the price-sensitivity of demand on the improvements in total profit. A computer code using the software Matlab is developed to derive the optimal solution and numerical example is presented to illustrate the proposed models. The result are illustrate with the help of numerical example. Graphical representation is also presented to illustrate the proposed model. 2010 Mathematics Subject Classification. 90B05.