An Inventory Model for Non-Instantaneous Deteriorating Items Under Two-Phase Demand and Two-Level Trade Credit

Abstract

Trade credit is widely used in modern business transactions as it provides alternative to
price reduction, encourage retailer’s demand and minimizes holding cost. In this study, an
inventory model for non-instantaneously deteriorating items under trade credit is developed.
The demand is in two–phase, in the first phase, when there is no deterioration, the demand
is stock dependent due to freshness of the stocked items whereas in the second phase, when
deterioration sets in, the demand is assumed to be price dependent as a result of reduction in
quality of the product. Profit functions of the model was obtained. The necessary and sufficient
conditions for the existence and uniqueness of the optimal solutions to the profit functions was
established. The Newton-Raphson iterative method was employed to find the solutions to the
numerical examples using MATLAB. Sensitivity analysis was carried out to test the sensitivity
of the model’s parameters on the model. The major findings reveal that the holding cost,
deterioration cost and the interest charged rate significantly influence the optimal cycle period
and the maximum total profit.