Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

Abstract

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.

Keywords:

• Inventory model
• finite time horizon
• non-instantaneous deteriorating items
• optimal schedule
• permissible delay in payment
• mixed integer nonlinear programming
• submodular function

Acknowledgments

The authors would like to thank the reviewers for their valuable comments on the original version of the paper

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed.

Disclosure statement

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

Additional information

Notes on contributors

Rashid. M. Aladwani

Rashid M. Aladwani was a Master student at the Department of Statistics and Operations Research (Kuwait University) until August 2022. The subject of the present paper is part of his MSc dissertation.

Lakdere Benkherouf

Lakdere Benkherouf is a Professor in the Department of Statistics and Operations Research, Kuwait University. He obtained a BSc in Mathematics from the University of Science and Technology (Algiers) in 1983, an MSc. in Management Science in 1985 and a PhD in 1988 in Statistics both from Imperial College (London). His research interests cover broadly Stochastic Modeling and Inventory Control. He has over 100 publications in various international journals.

Fatmah Almathkour

Fatmah Almathkour is an Associate Professor in the Department of Statistics and Operations Research, Kuwait University. She undertook her BSc in Industrial Engineering at Kuwait University in 2001, MSc. of Science in Operations Research in 2009 from Northeastern University, and a PhD in 2014 in Industrial Engineering from Clemson University. Her research interests focus on Optimization, Integer Programming, and Inventory Control.