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Robust Linear Optimization: On the benefits of distributional information and applications in inventory control

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2 Author(s)
Paschalidis, I.C. ; Member, IEEE, Center for Information & Systems Eng., and Dept. of Manufacturing Eng., Boston University, 15 St. Mary’s St., Brookline, MA 02446, e-mail: yannisp@bu.edu ; Seong-Cheol Kang

Linear programming formulations cannot handle the presence of uncertainty in the problem data and even small variations in the data can render an optimal solution infeasible. A number of robust linear optimization techniques produce formulations (not necessarily linear) that guarantee the feasibility of the optimal solutions for all realizations of the uncertain data. A recent robust approach in [1] maintains the linearity of the formulation and is able to strike a balance between the conservatism and quality of a solution by allowing less robust solutions. In this work we demonstrate how to use distributional information on problem data in robust linear optimization. We adopt the robust model of [1] and present an approach that exploits distributional information on problem data to decide the level of robustness of the formulation, thus, leading to much more cost-effective solutions (by 50% or more in some instances).We apply our methodology to a stochastic inventory control problem with quality of service constraints.

Published in:

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Date of Conference:

12-15 Dec. 2005