Essays on variational inequalities and competitive supply chain models
Name
60405894-MIT.pdf
Description
Full printable version
Size
5.57 MB
Format
Adobe PDF
Checksum (MD5)
7803b3083a80a7524816bfe19dcb7aae
Author(s)
Zaretsky, M. (Marina)
Advisor(s)
Georgia Perakis.
Date Issued
2004
Publisher
Massachusetts Institute of Technology
Abstract
In the first part of the thesis we combine ideas from cutting plane and interior point methods to solve variational inequality problems efficiently. In particular, we introduce "smarter" cuts into two general methods for solving these problems. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence results for both methods, as well as complexity results for one of the methods. Finally, we compare the performance of an approach that combines affine scaling and cutting plane methods with other methods for solving variational inequalities. The second part of the thesis considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multi-period environment. At each period the retailer places orders to the suppliers in response to the prices and capacities they announce. Our model allows the retailer to carry inventory. Furthermore, suppliers can expand their capacity at an additional cost; the retailer faces exogenous, price-dependent, stochastic demand. We analyze discrete as well as continuous time versions of the model: (i) we illustrate the existence of equilibrium policies; (ii) we characterize the structure of these policies; (iii) we consider coordination mechanisms; and (iv) we present some computational results. We also consider a modified model that uses option contracts and finally present some extensions.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.
Includes bibliographical references (p. 103-107).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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