Analysis of a Production Inventory Model with Linear Time Production Rate, Holding Cost and Stock Dependent Demand

This paper focused on the analysis of a production inventory where the production rate and holding cost are linearly dependent, while the demand is stock dependent demand rate. The production inventory model is formulated using system of differential equations and integral calculus including initial boundary/matching conditions and integral calculus were also used to analyse the inventory problem. These differential equations were solved to give the best cycle length that will minimize the inventory cost per unit time. A Mathematical theorem and all its proof is presented to established the convexity of the cost function. A numerical example is also given to demonstrate the applicability of the model developed accompanied by sensitivity analysis to see the effects of the parameter changes.