A New Approach in Decision of Pareto Efficient Concept in Probabilistic Vendor - Buyer Supply - Chain Problem for Imperfect Quality with Lead - Free Demand

Abstract

In this paper, the mathematical analysis of optimal solution or Economic Order Quantity (EOQ) of probabilistic vendor-buyer systems has been analyzed using Pareto optimal concept. It's assumed that lead time length is limited. The quality of the product from vendor is not always 100% perfect, so imperfect quality product always exist due to specific probability rate. Pareto optimal concept has been used to find the weighted sum of the players' objectives. Karush - Kuhn - Tucker (KKT) criteria is applied to determine the optimum value of decision variables and also minimum value of total cost as objectives function. Numerical example of appropriate simulation data is provided to compare the analytical result and to find how the effectiveness the Pareto Optimal concept to minimize the inventory cost in probabilistic assumptions rather than integrated scheme.