Type of Document Dissertation Author Zeng, Xin URN etd-08182012-111806 Title Comparative Statics Analysis of Some Operations Management Problems Degree PhD Department Industrial and Systems Engineering Advisory Committee
Advisor Name Title Bish, Ebru K. Committee Chair Bish, Douglas R. Committee Member Haller, Hans H. Committee Member Slonim, Anthony D. Committee Member Wernz, Christian Committee Member Keywords
- Comparative Statics Analysis
- Capacity Planning
- Influenza Vaccine
- Yield Uncertainty
- Stochastic Programming
- Game-theoretic Model
- Stochastic Orders
Date of Defense 2012-08-08 Availability restricted Abstract We propose a novel analytic approach for the comparative statics analysis ofoperations management problems on the capacity investment decision and the
influenza (flu) vaccine composition decision. Our approach involves exploiting
the properties of the underlying mathematical models, and linking those
properties to the concept of stochastic orders relationship. The use of
stochastic orders allows us to establish our main results without restriction
to a specific distribution. A major strength of our approach is that it is
"scalable," i.e., it applies to capacity investment decision problem with any
number of “non-independent” (i.e., demand or resource sharing) products and
resources, and to the influenza vaccine composition problem with any number of
candidate strains, without a corresponding increase in computational effort.
This is unlike the current approaches commonly used in the operations
management literature, which typically involve a parametric analysis followed
by the use of the implicit function theorem. Providing a rigorous framework
for comparative statics analysis, which can be applied to other problems that
are not amenable to traditional parametric analysis, is our main contribution.
We demonstrate this approach on two problems: (1) Capacity investment
decision, and (2) influenza vaccine composition decision. A comparative
statics analysis is integral to the study of these problems, as it allows
answers to important questions such as, "does the firm acquire more or less
of the different resources available as demand uncertainty increases? does the
firm benefit from an increase in demand uncertainty? how does the vaccine
composition change as the yield uncertainty increases?" Using our proposed
approach, we establish comparative statics results on how the newsvendor's
expected profit and optimal capacity decision change with demand risk and
demand dependence in multi-product multi-resource newsvendor networks; and how
the societal vaccination benefit, the manufacturer's profit, and the vaccine
output change with the risk of random yield of strains.
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