Unreliable EPQ model with variable demand under two-tier credit financing

ABSTRACT

This article deals with an unreliable production-inventory model with varying demand under two-level trade credit policies. We consider that the supplier offers a fixed period to the manufacturer to repay the due amount whereas the manufacturer also provides a credit period to the customers for a payout of the buying price. In this model, the demand for the produced items depends on the selling price, frequency of advertisement, and the manufacturer's offered credit period. Here, the production system is unreliable, and after a certain period, the system goes into the “out-of-control” state and starts simultaneously to produce complete and defective items, where the random time variable follows two parameters “Weibull” distribution. Our prime purpose is to determine the optimal average integrated profit for the decision variables selling price, frequency of advertisement, offered credit period, and size of ordering raw material. Numerical examples are given to illustrate the model.

KEYWORDS:

• EPQ
• reliability
• trade credit
• variable demand pattern

Acknowledgments

The authors would like to express their gratitude to the editors and referees for their valuable suggestions and corrections to enhance the clarity of the present article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Anindya Mandal

Anindya Mandal is an Assistant Professor in the Department of Mathematics, Tehatta Sadananda Mahavidyalaya, Purba Bardhaman, West Bengal, India. He obtained his M.Sc. degree in Applied Mathematics from The University of Burdwan, India. His research interests include inventory control and supply chain management.

Brojeswar Pal

Brojeswar Pal is an Assistant Professor in the Department of Mathematics, The University of Burdwan, West Bengal, India. He received his Ph.D. degree from the Jadavpur University, India. He has published several research papers in international journals of repute in the areas of production planning, inventory control, and supply chain management.

Kripasindhu Chaudhuri

Kripasindhu Chaudhuri was a senior professor since 1983–2008 in the Department of Mathematics, Jadavpur University, India. He is now an UGC emeritus fellow in Jadavpur University. He received his B.Sc. degree in Mathematics, an M.Sc. degree in Applied Mathematics and a Ph.D. in fluid mechanics at Visva-Bharati, Santiniketan, India. He was a visiting mathematician to International Centre for Theoretical Physics (ICTP), Trieste, Italy, in 1986; a fulbright scholar to the North Carolina State University, Raleigh, USA, in 1989; fellow of the National Academy of Sciences (FNASc), India, in 1996; fellow of the Institute of Mathematics and its Applications (FIMA), UK, in 1999. He has so far guided 42 research scholars and has published 220 papers in international journals of repute in the areas of fluid mechanics, solid mechanics, computer science, atmospheric science, operations research, mathematical ecology, history of mathematics, and marketing science.