Choi, S., A. Ruszczynski, Y. Zhao (2008). The Multi-Product Risk Averse
Newsvendor with Law-invariant Coherent Measures of Risk. Operations
Research 59: 346-364
Abstract: This paper studies the
portfolio effect in a multi-product newsvendor model under the
law-invariant coherent measure of risk. We first establish a few
fundamental properties for the model regarding the convexity of the
problem, the symmetry of the solution and the impact of risk aversion. For
a large but finite number of heterogeneous products with independent
demands, we derive closed-form approximations for the optimal order
quantities. The approximations are as simple as the classical risk-neutral
solutions. We also show that as the number of products tends infinity, the
risk averse solution approaches the risk
neutral solution, and thus risk aversion has no impact in this limit. For a
two-product newsvendor with dependent demand, we show that under certain
conditions, positively (negatively) dependent demand leads to a lower
(higher) optimal order quantity than independent demand under risk
aversion. Using a numerical study, we examine the convergence rates of the
approximations and thoroughly study the interplay of dependent demand and
risk aversion. Finally, we compare the portfolio effect in this inventory
system to the financial portfolio effect.
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