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% Template for Student Conference in Operational Research (SCOR).
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% The following template should be used for all abstracts submitted to 
% the conference.
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% Please email the completed abstract to SCOR@lancaster.ac.uk
% Please email any comments or queries to SCOR@lancaster.ac.uk
%
% 
% Please name your file as follows: 'Surname''Initials'_'First three letters of home institution'.tex
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%  For example, Joseph Anthony Bloggs from  University of Lancaster would name their file:
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%       BloggsJA_LAN.tex
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%Note: You can not build this file to view the finished abstract.
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%Please fill in your details after the colons,

%Name: Fang He          
%University: University of Nottingham
%Year of Study:     2nd
%Email address:  fxh@cs.nott.ac.uk
   
   
%Please fill in require information replacing the texted marked by astrisks, *.....*. 

\title{Hybridizing Integer Programming Models within an Adaptive
Decomposition Approach for Exam Timetabling Problems}
%e.g.
%\title{Cost optimal policies for system maintenance}


\author[NOT]{Fang He}
\address[NOT]{University of Nottingham, UK}
% e.g. 
% \author[LAN]{J.A. Bloggs}
% \address[LAN]{University of Lancaster, UK}


%Keywords: Enter each set of key words in a separate \keyword command, for example, the keywords maintenance, dynamic programming, heuristics would be entered:
%\keywords{maintenance}
%\keywords{dynamic programming}
%\keywords{heuristics}

\keywords{Integer Programming}
\keywords{Decomposition Approach}
\keywords{Exam Timetabling Problems}

%more keywords may be added by repeating the \keyword{} command as above 

%Abstract:
%Please write abstact where indicated below. 
%Note: Abstracts should be no more than 250 words.
%      No equations or references are to be included in the abstract.

\body{The idea of decomposition has been successfully applied to solve large combinatorial
optimization problems. In timetabling, it has not been widely applied due to one major
problem that early assignment may lead to later conflict in solving interrelated sub-problems
decomposed from the original problem. In our previous work, timetabling problems were
adaptively decomposed into difficult set and easy set of exams of different importance by the
information gathered from previous iterations. The approach obtained promising results and
showed that small set of difficult exams contributed to a much larger portion of the total cost
of the solution constructed. An interesting issue would then be to investigate the effect of
constructing complete solutions based on the optimal solution for this difficult set subproblem.
In this paper, we first present an IP formulation for solving the difficult set sub-problem. To
have a tighter initial formulation, we utilize a well-known valid inequality named Clique
Inequality. We then examined the combinatorial properties of the problem to introduce a new
family of cutting planes. These showed to be helpful on obtaining near optimal solution for the sub-problem, based on which the final solution is constructed. Promising results
have been obtained on several benchmark exam timetabling problems in the literature.}

