An inventory system of non-instantaneous deteriorating items with backlogging and time discounting

ABSTRACT

In this paper, an economic order quantity inventory model is analysed, considering the effect of inflation on a multivariate demand function and inventory control for non-instantaneous deteriorating items. The demand rate is a linear function of price and decreases negative exponentially with time. Shortages are allowed and partially backlogged. The objective is to find the optimal selling price, the optimal replenishment cycles and the optimal lot size simultaneously such that the present value of total profit in a finite time horizon is maximised. An algorithm has been presented to find the replenishment number and then the optimal solution for the proposed model. Finally, numerical examples are used to illustrate the theoretical results and the sensitivity analysis with respect to major parameters on the optimal solutions is also performed.

Keywords:

• Inventory
• deterioration
• backlogging
• inflation
• finite planning

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

R. Sundararajan

R. Sundararajan is working as an Assistant Professor, Department of Mathematics, PSNA College of Engineering and Technology, Dindigul. His current research interests include optimisation and inventory control.

M. Palanivel

M. Palanivel is working as an Assistant Professor, Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi. He has published about 20 papers in international and national journals. His research interests are in the field of inventory management and control, optimisation techniques and their applications.

R. Uthayakumar

R. Uthayakumar is currently a Professor & Head, Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, India. He received his MSc in Mathematics from American College, Madurai, India in 1989 and PhD in Mathematics from The Gandhigram Rural Institute – Deemed University, Gandhigram, India in 2000. He has published about 170 papers in international and national journals. His research interests include the following fields: Operations Research, Industrial Engineering and Fractal Analysis, Fuzzy spaces and Inventory models.