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.
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