A fuzzy periodic review integrated inventory model involving stochastic demand, imperfect production process and inspection errors

In this study, we investigate an integrated production-inventory system consisting of a single-vendor and single-buyer. The buyer manages its inventory level periodically at a certain period of time. We consider a fuzzy annual demand, imperfect production, inspection errors, partial backordering, and adjustable production rate in the proposed model. Additionally, it is assumed that the protection interval demand follows a normal distribution. The model contributes to the current literature by allowing the inclusion of fuzzy annual demand, adjustable production rate and imperfect production and inspection processes. Our objective is to optimize the number of deliveries from vendor to buyer, the buyer’s review period, and the vendor’s production rate, so that the joint expected total annual cost incurred has the minimum value. Furthermore, an iterative procedure is proposed to find the optimal solutions of the model. We also provide a numerical example and conduct a simple sensitivity analysis to illustrate the model’s behaviour and feasibility. The results from the sensitivity analysis show that the defective rate, type I inspection *Corresponding author: Wakhid Ahmad Jauhari, Production System Laboratory, Industrial Engineering Department, Sebelas Maret University, Surakarta, Indonesia E-mail: [email protected] Reviewing editor: Ping Lou, Wuhan University of Technology, China Additional information is available at the end of the article ABOUT THE AUTHORS Wakhid Ahmad Jauhari is currently a Lecturer in Sebelas Maret University. He obtained Bachelor and Master degrees, both in Industrial Engineering, from Sepuluh Nopember Institute of Technology (ITS) in Surabaya. His research’s interests include modelling inventory, supply chain management and manufacturing design. Selvia Mayangsari is a researcher in Production System Laboratory, Sebelas Maret University. Her research interests are inventory management, production management and operations research. Nughthoh Arfawi Kurdhi received his BS degree from Sebelas Maret University (2007), Indonesia, and MS degree from Gadjah Mada University (2010), Indonesia, both in Applied Mathematics. He is working as a lecturer in the Mathematics Department at Sebelas Maret University. His research interests include operations research, supply chain management and combinatorics. Kuan Yew Wong holds a PhD from the University of Birmingham, United Kingdom. He is a Professor and the Head of the Industrial and Systems Engineering Research Group in Universiti Teknologi Malaysia (UTM), Skudai, Malaysia. He is also a Chartered Engineer and Fellow of the British Computer Society. PUBLIC INTEREST STATEMENT The proposed model is interesting for the practitioners working in a supply chain consisting of a vendor and a buyer. The model can help the practitioners to keep the inventories more efficiently by deciding the optimum review period, production rate and number of deliveries. The model considers a situation where demand is formulated using fuzzy and production rate is assumed to be adjusted flexibly. The vendor’s production process is imperfect and the buyer’s inspection process is not 100% error-free. The buyer uses periodic review to manage his inventory level. An algorithm is proposed to find the decision variables. Received: 10 November 2016 Accepted: 13 March 2017 First Published: 21 March 2017 Page 1 of 24 © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.