Title: Modelling the newsvendor problem with a random fraction of defective items in the lot

Authors: Mohammad J. Alkhedher; Abdulrahman Alenezi; Mehmet Savsar

Addresses: Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait ' Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait ' Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

Abstract: An important assumption in deriving a formula for the optimal lot size newsvendor problem is that 100% of items in an ordered lot are assumed conforming to specifications. In real-life situations, however, this assumption may not hold for many production processes because of process deterioration and other factors. This paper develops a model for the newsvendor problem under the assumption that each ordered lot contains a random fraction of defective items which follows a beta distribution. The concavity of the expected total profit is established and the global optimal solution is determined by an algorithm based on Karush-Kuhn-Tucker conditions. Also, the effects of model's key parameters on the optimal solution are investigated using several case examples.

Keywords: imperfect quality; defective items; sampling inspection; rework; inspection policies; fraction defective.

DOI: 10.1504/IJPM.2017.085039

International Journal of Procurement Management, 2017 Vol.10 No.4, pp.495 - 513

Received: 31 Mar 2016
Accepted: 25 Jun 2016
Published online: 10 Jul 2017 *

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