Paper Info
Title
Pattern definition of the p-efficiency concept.
Abstract
This study revisits the celebrated p-efficiency concept introduced by Pr,kopa (Z. Oper. Res. 34:441-461, 1990) and defines a p-efficient point (pLEP) as a combinatorial pattern. The new definition uses elements from the combinatorial pattern recognition field and is based on the combinatorial pattern framework for stochastic programming problems proposed in Lejeune (Stochastic programming e-print series (SPEPS) 2010-5, 2010). The approach is based on the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. A combinatorial pattern provides a compact representation of the defining characteristics of a pLEP and opens the door to new methods for the generation of pLEPs. We show that a combinatorial pattern representing a pLEP constitutes a strong and prime pattern and we derive it through the solution of an integer programming problem. Next, we demonstrate that the (finite) collection of pLEPs can be represented as a disjunctive normal form (DNF). We propose a mixed-integer programming formulation allowing for the construction of the DNF that is shown to be prime and irreducible. We illustrate the proposed method on a problem studied by Pr,kopa (Stochastic programming: handbook in operations research and management science, vol. 10, Elsevier, Amsterdam, 2003).
Year
DOI
Venue
2012
10.1007/s10479-010-0803-1
ANNALS OF OPERATIONS RESEARCH
Keywords
DocType
Volume
A. Prekopa
Journal
200
Issue
ISSN
Citations 
1
0254-5330
8
PageRank 
References 
Authors
0.50
15
1
Name
Order
Citations
PageRank
Miguel A. Lejeune125321.95