Quadratic Approximation of the Newsvendor Problem with Imperfect Quality

Abstract

The paper presents a newsvendor problem in a fuzzy environment by introducing product quality as a fuzzy variable, and product demand as a probability distribution in an economic and supply chain management environment. In order to determine the optimal order quantity, a methodology is developed where the solution is achieved using a fuzzy ranking method combined with a quadratic programming problem approximation. Numerical examples are provided and compared in both situations, namely fuzzy and crisp. The results of these numerical examples show that the decision maker has to order a higher quantity when product quality is a fuzzy variable. The model can be useful for real world problems when historical data are not available.

A Constructive Methodology to Solving the Capacitated Newsvendor Problem: an Approximate Approach

“…Traditional cases and distribution-free cases are compared when the mean and the variance of the demand are the only available data to the decision-maker. Areerakulkan [22] introduces the product quality as a fuzzy variable into the newsvendor problem. Quadratic approximation and iterative solution finding steps using KKT's conditions are utilized to achieve the optimum.…”