Pricing strategies and advance payment-based inventory model with partially backlogged shortages under interval uncertainty

Abstract

In the current market situation, uncertainty in the market economy plays a significant role for proper controlling of inventory. In this situation, during an analysis of an inventory system with more realistic assumptions, it becomes a necessity to consider the imprecise behaviour of various inventory parameters. This work demonstrates a partially backlogged inventory model with interval uncertainty in which products during stock-in situation deteriorate at a certain rate. Two distinct cases are considered based on the advance payment and availability of discount. In the first case, the retailer makes full payment in advance to the corresponding supplier, and for this regard, supplier offers some price discount on the total purchasing cost. In the second case, the retailer makes partial payment in advance to the supplier but no discount facility is available. However, the retailer needs to make the rest of the payment at the time of receiving a lot from the supplier. As the inventory parameters are considered interval-valued, the objective function of the corresponding optimisation problem is converted into interval-valued, and to solve the same problem, the c-r optimisation technique is used. Two numerical examples are considered and solved using three distinct variants of QPSO to check the feasibility of the proposed model.

KEYWORDS:

• Interval-valued demand
• interval-valued deterioration
• interval-valued backlogging
• advance payment policy
• c-r optimisation technique

Acknowledgement

First of all, we convey our sincere thanks to the editor for considering our work for review and the anonymous reviewers for their valuable comments/suggestions to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors declared that they don't use any publish data inside this manuscript.

Additional information

Funding

The first author greatly acknowledges the financial support given by Council of Scientific & Industrial Research (CSIR) (New Delhi) under CSIR-SRF Fellowship (Sr.No.1061741522, Ref.No:18/06/2017(i)EU-V). The last two authors would like to acknowledge the Department of Science and Technology, Government of India for FIST support (SR/FST/MSII/2017/10 (C)).

Notes on contributors

Rajan Mondal

Rajan Mondal completed his M.sc degree in the stream of applied mathematics in 2016 from The University of Burdwan, West Bengal, India. Presently, he is working as a Senior research fellow at the department of Mathematics, University of Burdwan, West Bengal, India. Mr. Mondal has published six research articles. His interest of research area is inventory control, Interval analysis, Soft-computing, etc.

Subhajit Das

Subhajit Das received MSc degree in Mathematics from The University of Burdwan in India. He joined the Department of Mathematics at The University of Burdwan in 2019 as a Junior Research Fellow. His research interests include optimal control theory, industrial engineering, and interval mathematics. He has published nine research articles in different reputed journals including Journal of the Franklin Institute, Soft Computing, Alexandria Engineering Journal etc.

Subhash Chandra Das

Subhash Chandra Das is an Assistant Professor of Mathematics at Chandrapur College, West Bengal, India. He obtained his M.Sc. and PhD in Mathematics from The University of Burdwan, India. He has published four research papers in different international journals of repute. His research interests include inventory control, interval optimisation, and particle swarm optimisation.

Ali Akbar Shaikh

Ali Akbar Shaikh is an Assistant Professor of Mathematics at The University of Burdwan, West Bengal, India. Earlier, he was a Postdoctoral Fellow at the School of Engineering and Sciences of Tecnológico de Monterrey, México. He has obtained the award SNI of level 1 (out of 0–3) presented by the National System of Researchers of México from Government of México, in 2017. He obtained his PhD and MPhil in Mathematics from The University of Burdwan, and MSc in Applied Mathematics from University of Kalyani, India. He has published more than 90 research papers in different international journals of repute. His research interests include inventory control, interval optimisation, and particle swarm optimisation.

Asoke Kumar Bhunia

Asoke Kumar Bhunia is a Professor at the Department of Mathematics, The University of Burdwan, West Bengal, India. He obtained his PhD in Mathematics and MSc in Applied Mathematics from Vidyasagar University, India. His research interests include computational optimisation, soft computing, interval mathematics, and interval ranking. He has published over 140 research papers in various national and international journals of repute. He is a reviewer of several SCI journals. He has guided 13 PhD and two MPhil students. He is an author of four research monographs and six book chapters. He has written two text/reference level books in the area of optimization and Operations Research. He is an INSA Visiting Fellow and former Associate Editor of the Springer's journal, OPSEARCH.