A Production Inventory Model with Linear Time Dependent Production Rate, Linear Level Dependent Demand and Demand and Constant Holding Cost

In this paper, a production inventory model with linear time dependent production rate is considered. The market demand is assumed to be linear level dependent while the holding cost is a constant. The model considered a small amount of decay without having any shortage. Production starts with a buffer stock reaching its maximum desired level and then the inventory begins to deplete due to demand and deterioration. The model is formulated using a system of differential equations and typical integral calculus was used to analyze the inventory problems. These differential equations were solved to give the best cycle length T_1^*=0.8273(303 days), Optimal time for maximum inventory t_1^*= 0.7015, Optimal order quantity Q_1^*=38.3404 and total average inventory cost per unit time TC(T_1)* =170.5004. The cost function has been shown to be convex and a numerical example to show the application of the model has been given. A sensitivity analysis is then carried out to see the effects of parameter changes