A deteriorating inventory model with displayed stock-level-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimisation

Abstract

The goal of this research is to develop a price break inventory model for a single deteriorating item with imprecise inventory costs by considering all unit discount policy and variable demand rate dependent on displayed stock level. Shortages are partially backlogged with a variable rate dependent on the length of the waiting time up to the arrival of fresh lot. Analysing the relative size of the displayed stock-level-dependency parameters of demand and the storage capacity of the showroom/shop, different scenarios have been considered. Then, for each scenario, the model has been formulated as a constrained optimisation problem with interval objective and solved with the help of different versions of particle swarm optimisation (PSO) and interval order relations. To illustrate the model, three numerical examples have been solved by different versions of PSO and the results have been compared. Finally, to study the effect of changes of different parameters on optimal policies, sensitivity analyses have been presented numerically.

Keywords:

• inventory model
• deterioration
• displayed stock-level-dependent demand
• partially backlogging
• particle swarm optimisation

Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments regarding the acceptance of the paper.

Additional information

Notes on contributors

A.K. Bhunia

Asoke Kumar Bhunia is an associate professor in the Department of Mathematics, The University of Burdwan, India. His research interests include computational optimisation, soft computing, interval mathematics, interval ranking, etc. He has published more than 100 research papers in various international SCI journals. He is a reviewer of several Elsevier Science, Springer, Taylor & Francis and other SCI journals. Nine Ph.D. and two M.Phil students have received their degrees under his supervision. He has also written three book chapters, two research monographs and a book entitled ‘Advanced Operations Research’. He is an INSA visiting fellow and also an associate editor of the Springer journal ‘OPSEARCH’.

S.K. Mahato

Sanat Kumar Mahato is an assistant professor of mathematics, Durgapur Govt. College, West Bengal, India. He has received the master degree in applied mathematics from The University of Burdwan and submitted his PhD thesis in November 2013. Mr Mahato has published five research papers in different peer reviewed international journals. His area of research work includes applications of genetic algorithm in inventory control and reliability optimisation, interval optimisation and its applications, particle swarm optimisation, etc.

Ali Akbar Shaikh

Ali Akbar Shaikh is a faculty member of Krishnagar Government College, Krishnagar, Nadia, India. He obtained MSc degree in applied mathematics from the University of Kalyani, India and MPhil degree in mathematics from The University of Burdwan, India. Mr Shaikh has published five research papers in different peer reviewed international journals. His research interests include inventory control theory, interval optimisation and particle swarm optimisation.

Chandra K. Jaggi

Chandra K. Jaggi, professor and head, Department of Operational Research, University of Delhi, India. He is a fellow member of International Science Congress Association since 2012 and in 2009 was awarded certificate for his significant contributions in operation management by SREQOM, New Delhi. A recipient of Shiksha Rattan Puraskar (for Meritorious Services, Outstanding Performance and Remarkable Role) in 2007 by India International Friendship Society. He is a life member of ORSI, ISCA, CSI, ISPS, fellow member of International Science Congress Association, The Society of Mathematical Sciences, University of Delhi, India, Society for Reliability Engineering, Quality and Operations Management. He is a reviewer of more than 25 international/national journals. His research interest lies in the field of supply chain and inventory management. He has published five book chapters and more than 94 papers in various international/national journals. He has guided seven PhD and 20 MPhil in operations research. He is an editor-in-chief of IJICM and an associate editor of IJSAEM, Springer, co-editor/reviewer-in-charge of The Gstf JMSOR and on the Editorial Board of the IJSOI, AJOR, IJECBS, JASR, AJBAS. He has travelled to Canada, Philippines, Macau, Iran and different parts of India delivered Key Note Address, invited talks.