Title page for ETD etd-08182012-111806

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
  • Comparative Statics Analysis
  • Capacity Planning
  • Influenza Vaccine
  • Yield Uncertainty
  • Stochastic Programming
  • Game-theoretic Model
  • Stochastic Orders
Date of Defense 2012-08-08
Availability restricted
We propose a novel analytic approach for the comparative statics analysis of

operations 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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