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

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

This paper presents a literature review of the cell formation (CF) problem concentrating on formulations proposed in the last decade. It refers to a number of solution approaches that have been employed for CF such as mathematical programming, heuristic and metaheuristic methodologies and artificial intelligence strategies. A comparison and evaluation of all methodologies is attempted and some shortcomings are highlighted. Finally, suggestions for future research are proposed useful for CF researchers

Production technologies with ratio inputs and outputs

Applications of data envelopment analysis often incorporate inputs and outputs stated as proportions or percentages, which are typically used to represent socio-economic and quality characteristics of the production process. As is well known, the use of such ratio measures is inconsistent with the assumption of convexity required by the conventional variable and constant returns-to-scale (VRS and CRS) technologies, and with the additional assumption of scalability in the case of CRS. Several existing approaches to modelling technologies with ratio data assume that either we know the exact volume numerators and denominators of all ratio measures or, alternatively, that we do not have such information. The former approaches are not always realistic and the latter are equivalent to benchmarking each decision making unit against a significantly reduced subset of observed units, which has a negative impact on the discriminating power of the model. In this paper, we develop new technologies under the assumptions of VRS and CRS that bridge the gap between the two known approaches. They are applicable in a general scenario in which we can specify some lower and upper bounds for the numerators or denominators of the ratio measures, which should be unproblematic in most practical settings. We demonstrate the usefulness and advantages of the developed approach by an application in the context of school education.</p

A single-stage optimization procedure for data envelopment analysis

In data envelopment analysis, a conventional procedure for testing efficiency of decision making units (DMUs) consists of two stages, each requiring solution of a linear program. The first stage identifies the input or output radial efficiency of a DMU, and the second stage maximizes the sum of component input and output slacks. A traditional alternative is the single-stage approximation of the two-stage procedure in which the objective functions of the first and second stages are combined, with the latter multiplied by a small positive constant epsilon. A known drawback of such approach is that very small values of epsilon may cause computational inaccuracies and large values do not allow a good approximation. In this paper, we develop a new single-stage linear programming approach that does not require the specification of a small constant epsilon and is completely equivalent to the conventional two-stage solution procedure. It produces exactly the same sets of primal and dual optimal solutions as the two separate stages of the two-stage approach. The new single-stage procedure is applicable to any convex polyhedral technology.</p

Multicomponent production technologies with restricted allocations of shared inputs and outputs

We consider production technologies in which several parallel component processes are characterized by both component-specific and shared inputs and outputs. The recently developed multicomponent variable and constant returns-to-scale (MVRS and MCRS) models of such technologies are based on the assumption that we have no information about the actual allocation of the shared inputs and outputs to the component processes, which is a common scenario in many applications. The MVRS model treats each component process as a separate convex technology. The MCRS model additionally assumes that each process is a scalable technology. Both models account for the most conservative, or worst-case, allocation of the shared inputs and outputs to the individual processes, which does not require any knowledge of the actual allocation of such measures. In the current paper, we develop a new class of MVRS and MCRS models, by integrating a mechanism for the speci?cation of lower and upper bounds on the proportions in which the shared inputs and outputs can be allocated to different component processes. We show that such bounds may be supported by data and generally lead to a larger model of technology and improved differentiation on efficiency. As an illustration, we discuss the application of the developed approach in the context of higher education.</p

Managerial DSS for implementing sustainable operations

Managerial DSS for implementing sustainable operation