Fuzzy Integer Linear Programming Mathematical Models for Examination
  Timetable Problem
  ETP is NP Hard combinatorial optimization problem. It has received tremendous
research attention during the past few years given its wide use in
universities. In this Paper, we develop three mathematical models for NSOU,
Kolkata, India using FILP technique. To deal with impreciseness and vagueness
we model various allocation variables through fuzzy numbers. The solution to
the problem is obtained using Fuzzy number ranking method. Each feasible
solution has fuzzy number obtained by Fuzzy objective function. The different
FILP technique performance are demonstrated by experimental data generated
through extensive simulation from NSOU, Kolkata, India in terms of its
execution times. The proposed FILP models are compared with commonly used
heuristic viz. ILP approach on experimental data which gives an idea about
quality of heuristic. The techniques are also compared with different
Artificial Intelligence based heuristics for ETP with respect to best and mean
cost as well as execution time measures on Carter benchmark datasets to
illustrate its effectiveness. FILP takes an appreciable amount of time to
generate satisfactory solution in comparison to other heuristics. The
formulation thus serves as good benchmark for other heuristics. The
experimental study presented here focuses on producing a methodology that
generalizes well over spectrum of techniques that generates significant results
for one or more datasets. The performance of FILP model is finally compared to
the best results cited in literature for Carter benchmarks to assess its
potential. The problem can be further reduced by formulating with lesser number
of allocation variables it without affecting optimality of solution obtained.
FLIP model for ETP can also be adapted to solve other ETP as well as
combinatorial optimization problems.
