Optimal policies for finite horizon model with time-varying demand rate, non-instantaneous deterioration and backlogging

Abstract

This paper is concerned with the problem of finding an optimal replenishment policy for a finite planning horizon inventory model with time-varying demand, non-instantaneous deteriorating items and backlogging. This is formulated as a problem of solving some mixed integer non-linear program whose optimal solution delivers the frequency of orders as well as the timing of orders. The phenomena of non-instantaneous deterioration introduce a non-smoothness in the objective function which makes direct application of existing results, in the literature, not possible to the present model. A complete mathematical analysis of the problem is undertaken to overcome the non-smoothness of the objective and derive the optimal inventory policy. Uniqueness of the policy is shown under some technical conditions. Numerical results are presented for illustration.

Keywords:

• Inventory model
• finite time horizon
• optimal schedule
• mixed integer nonlinear programming
• submodular function

AMS CLASSIFICATION:

• 90B05

Disclosure statement

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

Data availability statement

The authors can confirm that the data for tables are provided with the paper and no data from the literature was used.

Additional information

Notes on contributors

Fatmah Almathkour

Fatmah Almathkour is an Assistant 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.

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.