Stochastic supply chain model with imperfect production and controllable defective rate

Abstract

This paper investigates the impact of ordering cost reduction and process quality improvement on an integrated vendor–buyer inventory system with variable lead time in just-in-time (JIT) manufacturing environment. We assume that the vendor invests money in order to improve the production process quality and reduce the number of defectives, and buyer invests money to reduce the ordering cost. Each lot received by the buyer contains a certain percentage of defective items and it is assumed that there is an inspection activity on the part of the buyer with a fixed screening rate greater than the demand rate. Shortages are partially backlogged with a certain limit of backorder price discount. The objective of this study is to obtain the optimal decisions and the best investment policy to minimise the joint total cost incurred by the buyer and the vendor. An efficient algorithm is developed to determine the optimal policy. The model is illustrated through a numerical example. From the numerical results, it is observed that significant savings can be achieved through the reductions of lead time, ordering cost and defective rate. Some managerial insights also obtained from the numerical study.

Keywords:

• Supply chain management
• defective items
• investment
• backorder price discount
• stochastic lead time demand

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

S. Sarkar

S. Sarkar is a Ph.D. scholar in the Department of Mathematics, Jadavpur University, Kolkata, India. He received his B.S. degree in Mathematics from the University of Calcutta, India, and M.S. degree in Applied Mathematics from Vidyasagar University, India. His research interests include inventory/supply chain management, production planning and scheduling, and his research papers have appeared in Journal of Manufacturing System, Applied Mathematics and Computation, Economic Modelling, Journal of Industrial and Management Optimization, International Journal of Machine Learning and Cybernetics, Operational Research: An Intentional Journal, Scientia Iranica E, and others.

B. C. Giri

B. C. Giri is a Professor in the Department of Mathematics, Jadavpur University, Kolkata, India. He did his M.S. in Mathematics and Ph.D. in Operations Research both from Jadavpur University, Kolkata, India. His research interests include inventory/supply chain management, production planning and scheduling, reliability and maintenance, and his research papers have appeared in Naval Research Logistics, International Journal of Production Research, OMEGA, Journal of the Operational Research Society, European Journal of Operational Research, International Journal of Production Economics, Journal of Cleaner Production, and other journals. He was a JSPS Research Fellow at Hiroshima University, Japan, during the period 2002–2004, Humboldt Research Fellow at Mannheim University, Germany, during the period 2007–2008 and a Fulbright-Nehru Senior Research Fellow at Louisiana State University, USA, in 2012.