Risk management policies for dynamic capacity control

Abstract

Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations.Numerically analyzing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the riskneutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.

Value-at-risk optimal policies for revenue management problems

“…Their model serves as an example in various recent papers, cf. Barz and Waldmann (2007), Huang and Chang (2009), Koenig and Meissner (2013a), Koenig and Meissner (2013b). Hence, it provides a basis for a comparison of different policies.…”

“…A related approach is presented by Koenig and Meissner (2013a), who provide a detailed study of several riskaverse policies for the dynamic capacity model by applying risk measures.…”

“…Levin et al (2008) incorporate risk aversion into a dynamic pricing model of perishable products by integrating constraints into the objective function. Koenig and Meissner (2013a) use the Markov decision model of the dynamic capacity control model and compute optimal policies for revenue targets.…”

“…Barz and Waldmann (2007), Huang and Chang (2009), Koenig and Meissner (2013a) and Koenig and Meissner (2013b) analyse both types of policies using the same underlying model that is used in this paper. All four approaches analyse the effects of applying different kinds of risk-sensitive polices, assuming various levels of risk aversion for a decision maker.…”

Resilient revenue management: a literature survey of recent theoretical advances

“…Revenue risk is also measured in terms of value-at-risk or conditional-value-atrisk in Koenig and Meissner (2015a), Koenig and Meissner (2015b), Gönsch and Hassler (2013), and Koenig and Meissner (2015). In contrast, Lancaster (2003) recommends relative risk measures and proposes a revenue-per-available-seat-mile indicator.…”