A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand

Abstract

An order-level inventory problem is discussed with the demand rate being represented by a continuous, quadratic function of time. It is assumed that a constant fraction of the on-hand inventory deteriorates per unit of time. The solution of the model is discussed both for infinite and finite time-horizon. A numerical example is taken up to illustrate the solution procedure and sensitivity analysis is also carried out. The rationale for the time-dependent quadratic demand is discussed. Scope and purpose The purpose of the present paper is to give a new dimension to the inventory literature on time-varying demand patterns. Researchers have extensively discussed various types of inventory models with linear trend (positive or negative) in demand. The main limitation in linear time-varying demand rate is that it implies a uniform change in the demand rate per unit time. This rarely happens in the case of any commodity in the market. In recent years, some models have been developed with a demand rate that changes exponentially with time. Demands for spare parts of new aeroplanes, computer chips of advanced computer machines, etc. increase very rapidly while the demands for spares of the obsolete aeroplanes, computers etc. decrease very rapidly with time. Some modellers suggest that this type of rapid change in demand can be represented by an exponential function of time. The present authors feel that an exponential rate of change in demand is extraordinarily high and the demand fluctuation of any commodity in the real market cannot be so high. A realistic approach is to think of accelerated growth (or decline) in the demand rate in the situations cited above and it can be best represented by a quadratic function of time. Thus, this paper has the scope of direct application in the very practical situations noted above.