Data envelopment analysis (DEA), as originally proposed, is a methodology for evaluating the relative efficiencies of a set of homogeneous decision-making units (DMUs) in the sense that each uses the same input and output measures (in varying amounts from one DMU to another). In some situations, however, the assumption of homogeneity among DMUs may not apply. As an example, consider the case where the DMUs are plants in the same industry that may not all produce the same products. Evaluating efficiencies in the absence of homogeneity gives rise to the issue of how to fairly compare a DMU to other units, some of which may not be exactly in the same "business." A related problem, and one that has been examined extensively in the literature, is the missing data problem; a DMU produces a certain output, but its value is not known. One approach taken to address this problem is to "create" a value for the missing output (e.g., substituting zero, or by taking the average of known values), and use it to fill in the gaps. In the present setting, however, the issue isn't that the data for the output is missing for certain DMUs, but rather that the output isn't produced. We argue herein that if a DMU has chosen not to produce a certain output, or for any reason cannot produce that output, and therefore does not put the resources in place to do so, then it would be inappropriate to artificially assign that DMU a zero value or some "average" value for the nonexistent factor. Specifically, the desire is to fairly evaluate a DMU for what it does, rather than penalize or credit it for what it doesn't do. In the current paper we present DEA-based models for evaluating the relative efficiencies of a set of DMUs where the requirement of homogeneity is relaxed. We then use these models to examine the efficiencies of a set of manufacturing plants.

Real world” decision-making applications generally contain multifaceted performance requirements riddled with incongruent performance specifications. There are invariably unmodelled elements, not apparent during model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it is preferable to generate numerous alternatives that provide dissimilar approaches to the problem. These alternatives should possess near-optimal objective measures with respect to all known objective(s), but be maximally different from each other in terms of their decision variables. This maximally different solution creation approach is referred to as modelling-to-generate-alternatives (MGA). This study demonstrates how the Firefly Algorithm can concurrently create multiple solution alternatives that both satisfy required system performance criteria and yet are maximally different in their decision spaces. This new approach is computationally efficient, since it permits the concurrent generation of multiple, good solution alternatives in a single computational run rather than the multiple implementations required in previous MGA procedures.

Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of peer decision-making units (DMUs), in a multiple input/output setting. Although it is generally assumed that all outputs are impacted by all inputs, there are many situations where this may not be the case. This article extends the conventional DEA methodology to allow for the measurement of technical efficiency in situations where only partial input-to-output impacts exist. The new methodology involves viewing the DMU as a business unit, consisting of a set of mutually exclusive subunits, each of which can be treated in the conventional DEA sense. A further consideration involves the imposition of constraints in the form of assurance regions (AR) on pairs of multipliers. These AR constraints often arise at the level of the subunit, and as a result, there can be multiple and often inconsistent AR constraints on any given variable pair. We present a methodology for resolving such inconsistencies. To demonstrate the overall methodology, we apply it to the problem of evaluating the efficiencies of a set of steel fabrication plants.

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