Fuzzy extensions to Integer Programming models of cell-formation problems in machine scheduling

Abstract

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: (a) cell formation (b) machine-cell allocation, and (c) part-machine allocation.This paper will present extensions of the IP model where part-machine assignment and cell formation are addressed simultaneously, and also a significant number of constraints together with an enhanced objective function are considered. The main study examines the integration of inter-cell movements of parts and machine set-up costs within the objective function, and also the combination of machine set-up costs associated with parts revisiting a cell when part machine operation sequence is taken into account. The latter feature incorporates a key set of constraints which identify the number of times a part travels back to a cell for a later machine operation.Due to two main drawbacks of IP modelling for cell formation, i.e. (a) only one objective function can be involved and (b) the decision maker is required to specify precisely goals and constraints, fuzzy elements like fuzzy constraints and fuzzy goals will be considered in the proposed model.Overall the paper will not only include an extended and enhanced integer programming model for assessing the performance of cell formation, but also perform a rigorous study of fuzzy integer programming and demonstrate the feasibility of achieving better and faster clustering results using fuzzy theory.

The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research

“…The main aim was to determine the optimal cell configuration in each period with the maximum degree of satisfying the fuzzy objective under the given constraints. Papaioannou and Wilson (2008) proposed a comprehensive mathematical programming formulation where parts are assigned to machines and machines to cells simultaneously by taking into account part machine operation sequences, part/machine utilization amounts, part/machine set-up costs and multiple machines of the same type. The objective function combined minimising the number of distinct cells used by each part, set-up costs when allocating machines to cells and the number of times a part revisits a cell for a later machine operation.…”

Integrating Strategic and Tactical Decisions to Robust Designing of Cellular Manufacturing under Uncertainty: Fixed Suppliers in Supply Chain

“…There are also cases where, in other studies, uncertainty in products' demand is treated using fuzzy numbers [4]. Group 2) The other group is associated with the formulation of CMS problems using fuzzy coefficients in the objective function and constraints [5].…”

Fifty Years of Integer Programming: A Review of the Solution Approaches

“…The main idea behind fuzzy integer programming approaches is to reduce the problem at hand to crisp integer program through Zadeh's extension principle Dubois and Prade (1980). Examples of application fuzzy integer programming to concrete real life problems may be found in papers contributed by Papaioannou andWilson, 2009 andHuang, Baetz, Patry, 1995).…”