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

Z. H.  Aliyu; H.  Ibrahim

Z. H. Aliyu Department of Mathematical Sciences, Nigerian Defence Academy, Kaduna, Nigeria.
H. Ibrahim Department of Mathematical Sciences, Nigerian Defence Academy, Kaduna, Nigeria.

Keywords: Non-instantaneous deterioration, Two-level trade credit, Two-phase demand

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.

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