Cell formation has received much attention from academicians and practitioners because
of its strategic importance to modern manufacturing practices. Existing research
on cell formation problems using integer programming (IP) has achieved the target
of solving problems that simultaneously optimise machine-cell allocation and partmachine
This thesis presents extensions of an IP model where part-machine assignment and
cell formation are addressed simultaneously, and integration of inter-cell movements
of parts and machine set-up costs within the objective function is taking place together
with the inclusion of an ordered part machine operation sequence. The latter is
identified as a neglected parameter for the Cell Formation problem.
Due to the nature of the mathematical IP modelling for Cell Formation two main
drawbacks can be identified: (a) Cell Formation is considered to be a complex and difficult
combinatorial optimisation problem or in other words NP-hard (Non-deterministic
Polynomial time hard) problem and (b) because of the deterministic nature of mathematical
programming the decision maker is required to specify precisely goals and
constraints. The thesis describes a comprehensive study of the cell formation problem where
fuzzy set theory is employed for measuring uncertainty. Membership functions are
used to express linguistically the uncertainty involved and aggregation operators are
employed to transform the fuzzy models into mathematical programming models. The
core of the research concentrates on the investigation and development of heuristic and
. metaheuristic approaches. A three stage randomly generated heuristic approach for
producing an efficient initial solution for the CF together with an iterative heuristic
are first developed. Numerous data sets are employed which prove their effectiveness.
Moreover, an iterative tabu search algorithm is implemented where the initial solution
fed in is the same as that used in the descent heuristic. The first iterative procedure and
the tabu search algorithm are compared and the results produced show the superiority
of the latter over the former in stability, computational times and clustering results.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.