A stochastic inventory model with price-sensitive demand, restricted shortage and promotional efforts

Abstract

This paper is attempt to develop a stochastic inventory model with quadratic price-sensitive demand. Objective function is developed by incorporating promotional efforts to boost the market demand, preservation technology to reduce the rate of deterioration, proportionate shortage time and partial backloggings. The proposed work is to generalise the stochastic demand with different probability distributions and their comparisons. The objective is to find the optimal price, optimal replenishment, and optimal preservation technology investment while optimizing the total profit per unit time. In the case of partial backlogging and lost sale, we deduced the optimal replenishment schedules for respective price and preservation technology cost. Also, we shown analytically and graphically that the total profit per unit time is a concave function with respect to per unit time, price, and preservation cost. The theoretical implications have been validated by useful results and numericals. Also, we examine the impact of various parameters for the best course of action. The conclusions drawn from the assessment might be useful for managerial purposes.

Keywords

• optimal stochastic control
• price-sensitive demand
• deterioration
• promotional efforts
• preservation technology
• partial backlogging