An Economic Order Quantity model for Decaying Products with the Frequency of Advertisement, Selling Price and Continuous Time Dependent Demand under Partially Backlogged Shortage

An inventory model is proposed with consideration of price, frequency of advertisement, continuous time and partially backlogged shortages for instantaneous decaying products. The deterioration is considered as instantaneous i.e., when the item stock in retailer’s house immediately deterioration will start with a constant rate for a certain period. If there are any shortages allowed, then it is partially backlogged. The main objective of this paper is to find the optimal cycle length (T) and the period where deterioration occurred (td) in order to minimize the total cost (TC) of the inventory system. The corresponding inventory problem constitutes a nonlinear constraint optimization problem. Here this problem is solved by using Lingo 15 software and also give a 3D graph with the help of MATLAB2017a to show the convexity of the objective function. Finally, to illustrate and validate the inventory model, a numerical example is considered with some realistic data. A sensitivity analysis is carried out to investigate the effect of changes of different inventory parameters, changing one parameter at a time and keeping the others value of parameters is same.