Revenue Management & Maximizing Profit in the Presence of Uncertain Demand Management Assignment Help

Assignment Task

1 Introduction
The question of maximizing profit in the presence of uncertain demand has long been central to
revenue management. A classical example of such a setting is the newsvendor problem, which
Porteus summarizes in [11]. As one of the building blocks of inventory theory, it has received
much attention in the literature, often under the assumptions that the demand distribution is
known exactly and that the decision-maker is risk-neutral. In practice however, the volatility
of the demand for most perishable products makes it difficult to obtain accurate forecasts. In
Scarf’s words [14], “we may have reason to suspect that the future demand will come from
a distribution which differs from that governing past history in an unpredictable way”. This
unpredictability provides a strong incentive for the decision-maker to implement robust solutions,
which will perform well for a wide range of actual demand outcomes. 
information has been addressed in the past by assuming that only the first two moments are
known. In 1958, Scarf [14] derived the optimal ordering quantity for the classical newsboy
problem with mean and variance given, and his work was later extended by Gallego et. al.
[6, 9, 10]. However, such a worst-case methodology relies on the correct estimation of the
first two moments and lacks a strong connection to risk preferences, which in practice play a
key role in the choice of the solution implemented. Specifically, the decision-maker will often
accept a smaller expected return if it also yields a decrease in the standard deviation of his
revenue, i.e., he will prefer solutions which exhibit less variability, although riskier approaches
can potentially bring higher profits. In this paper, we refer to the process of trading off a high
value of the expected return for a decrease in the downside risk as incorporating robustness.
The first attempt in the literature to model risk preferences in the newsboy problem is due to
Lau [7], who considers two alternative criteria to the expected revenue: the expected utility and
the probability of reaching a prespecified profit target. More recently, Eeckhoudt et. al. [5] have
revisited the framework based on the expected utility of the newsvendor. In practice, however,
it is difficult to articulate a particular individual’s utilit

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