Production Inventory Model with Three Levels of Production and Demand for Deteriorating Item under Price, Stock and Advertisement Dependent Demand

Abstract

Demand rate is not constant in real-life situations. Many factors affect the demand rate like advertisement, selling price, and stock displayed in the market, and sometimes demand rate changes according to seasons and other factors, like demand for refrigerators increases in summer, but decreases in winter or demand of pharmaceutical products increases rapidly in pandemic situations. Also, some items deteriorate over time. By taking inspiration from these real-life situations, a production-inventory model with price, stock, and advertisement-dependent demand for instantaneously deteriorating items is developed here with three demand levels. To avoid shortages, three levels of production rate are considered here. We have assumed the instantaneous deterioration rate is a linear function of time. This model extends the basic EPQ model to three levels of production and demand with instantaneous deterioration items. The total cost function of the proposed model has been derived. The goal of the model is to determine the production time and production rate to the manufacturer to minimize the total average cost. To demonstrate the model’s feasibility, numerical examples have been provided and solved by the graphical method. The total average cost’s convexity is graphically illustrated. Sensitivity analysis is used to illustrate the findings of the suggested production inventory model and to demonstrate managerial insights. The significant finding of this work is that this model assists manufacturers in determining production rate and time according to different rates of demand. Sensitivity analysis helps them identify the critical cost parameter that significantly impacts the total average cost. This model can be used in many manufacturing processes where the demand for the product is highly volatile like seasonal products, etc.