A Production-inventory Model with Variable Production Cost and Probabilistic Deterioration

This paper deals with an economic production quantity (EPQ)model for deteriorating items with price and advertisement dependent demand. We have considered three types of continuous probabilistic deterioration functions to determine the total inventory cost. Here, the rate of replenishment is considered to be a variable and the generalized unit production cost function is formulated by incorporating costs of several factors like raw material, labour, replenishment rate, advertisement and other factors of the manufacturing system. The selling price of a unit is determined by a mark-up over the production cost. This model aids in minimizing the total inventory cost of the manufacturer by finding the optimal cycle length and the optimal quantity. The optimal solution of the model is illustrated with the help of numerical examples. A numerical comparison between the three models is also given. Finally sensitivity analysis and graphical representations of the total cost functions are given to demonstrate the model. 2010 Mathematics Subject Classification. 90B05.