An Order-Level Inventory Model for a Deteriorating Item with Time-Quadratic Demand and Time-Dependent Partial Backlogging with Shortages in All Cycles

SYNOPTIC ABSTRACT

The purpose of this work is to study an inventory model for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. The sufficient condition of the optimal solution is also studied. It is then illustrated with the help of numerical examples.

Key Words and Phrases::

• inventory
• deterioration
• time-quadratic demand
• partial backlogging
• shortage
• variable replenishment.

Acknowledgments

The authors express their heartfelt thanks to anonymous referees for their most valuable comments and suggestions that have led to a significant improvement on an earlier version of this paper.