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Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization

Dimitris Bertsimas (dbertsim***at***mit.edu)
Angelos Georghiou (angelosg***at***mit.edu)

Abstract: In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions, respectively. We then propose a methodology for the optimal design of such decision rules that have finite number of pieces and solve the problem using mixed-integer optimization. We demonstrate the eff ectiveness of the proposed methods in the context of two multistage inventory control problems. We provide global lower bounds and show that our approach is (i) practically tractable and (ii) provides high quality solutions that outperform alternative methods.

Keywords: Adaptive Optimization, Decision Rules, Mixed-integer optimization.

Category 1: Robust Optimization

Category 2: Integer Programming

Category 3: Applications -- OR and Management Sciences

Citation: Dimitris Berstimas: Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, USA. Angelos Goerghiou: Process Systems Engineering Laboratory, Massachusetts Institute of Technology, USA. September 2013

Download: [PDF]

Entry Submitted: 09/03/2013
Entry Accepted: 09/03/2013
Entry Last Modified: 09/05/2014

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