Raha Imanirad

Data Envelopment Analysis with Nonhomogeneous DMUs

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 t...

Two-Stage Network DEA: When Intermediate Measures Can Be Treated as Outputs from the Second Stage

This paper investigates efficiency measurement in a two-stage data envelopment analysis (DEA) setting. Since 1978, DEA literature has witnessed the expansion of the original concept to encompass a wide range of theoretical and applied research areas. One such area is network DEA, and in particular two-stage DEA. In the conventional closed serial system, the only role played by the outputs from Stage 1 is to behave as inputs to Stage 2. The current paper examines a variation of that system. In particular, we consider settings where the set of final outputs comprises not only those that result from Stage 2, but can include, in addition, certain outputs from the previous (first) stage. The difficulty that this situation creates is that such outputs are attempting to play both an input and output role in the same stage. We develop a DEA-based methodology that is designed to handle what we term ‘time-staged outputs’. We then examine an application of this concept where the DMUs are schools of business.

Modeling efficiency in the presence of multiple partial input to output processes

Data envelopment analysis (DEA) is a methodology used to measure the relative efficiencies of peer decision-making units (DMUs). In the original model, it is assumed that in a multiple input, multiple output setting, all members of the input bundle affect the entire output bundle. There are many situations, however, where this assumption does not hold. In a manufacturing setting, for example, packaging resources (inputs) only influence the production of those products that require packaging. This is referred as partial input-to-output interactions where the DEA model is based on the view of a DMU as a business unit consisting of a set of independent subunits, such that efficiency of the DMU can be defined as a weighted average of the efficiencies of those subunits. The current paper presents an extension to that methodology to allow for efficiency measurement in situations where there exist multiple procedures or processes for generating given output bundles. The proposed model is then applied to the problem of evaluating the efficiencies of a set of steel fabrication plants.

A parametric testing of the Firefly algorithm in the determination of the optimal osmotic drying parameters for papaya

This study employs the Firefly Algorithm (FA) to determine optimal parameter settings for the osmotic dehydration process of papaya. The functional formulation of the osmotic dehydration model is established using a response surface technique with the format of the resulting optimization model being a non-linear goal programming problem. For optimization purposes, a computationally efficient, FA-driven method is employed and the resulting solution for the osmotic process parameters is superior to those from previous approaches. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this nature-inspired metaheuristic approach over the range of two key parameters.

Stochastic Decision-Making in Waste Management Using a Firefly Algorithm-Driven Simulation-Optimization Approach for Generating Alternatives

In solving municipal solid waste (MSW) planning problems, it is generally preferable to formulate several quantifiably good alternatives that provide multiple, disparate perspectives. This is because MSW decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult—if not impossible—to quantify and capture at the time when supporting decision models must be constructed. By generating a set of maximally different solutions, it is hoped that some of the dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This maximally different solution creation approach is referred to as modelling-to-generate-alternatives (MGA). Furthermore, many MSW decision-making problems contain considerable elements of stochastic uncertainty. This chapter provides a firefly algorithm-driven simulation-optimization approach for MGA that can efficiently create multiple solution alternatives to problems containing significant stochastic uncertainties that satisfy required system performance criteria and yet are maximally different in their decision spaces. It is shown that this new computationally efficient algorithmic approach can simultaneously produce the desired number of maximally different solution alternatives in a single computational run of the procedure. The efficacy of this stochastic MGA approach for “real world,” environmental policy formulation is demonstrated using an MSW case study.

Data Envelopment Analysis with Non-Homogeneous DMUs

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 which 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 chapter 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.

Partial input to output impacts in DEA: The case of DMU-specific impacts

Data Envelopment Analysis (DEA) is a methodology for evaluating the relative efficiencies of a set of decision-making units (DMUs). The original model is based on the assumption that in a multiple input, multiple output setting, all inputs impact all outputs. In many situations, however, this assumption may not apply, such as would be the case in manufacturing environments where some products may require painting while others would not. In earlier work by the authors, the conventional DEA methodology was extended to allow for efficiency measurement in such situations where partial input-to-output interactions exist. In that methodology all DMUs have identical input/output profiles. It is often the case, however, that these profiles can be different for some DMUs than is true of others. This phenomenon can be prevalent, for example, in manufacturing settings where some plants may use robots for spot welding while other plants may use human resources for that task. Consider a highway maintenance application where consulting services for safety corrections may not be employed on low traffic roadways, but are commonly used on high traffic, multilane highways. Thus, input to output links in the case of some DMUs are missing in the case of others. To address this, the current paper extends the methodology presented earlier by the authors to allow for efficiency measurement in situations where some DMUs have different input/output profiles than is true of others. The new methodology is then applied to the problem of evaluating the efficiencies of a set of road maintenance patrols.

Environmental decision-making under uncertainty using a biologically-inspired simulation-optimisation algorithm for generating alternative perspectives

In solving many environmental policy formulation applications, it is generally preferable to formulate several quantifiably good alternatives that provide multiple, disparate approaches to the problem. This is because environmental decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult - if not impossible - to quantify and capture at the time when supporting decision models must be constructed. By generating a set of maximally different solutions, it is hoped that some of the dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This maximally different solution creation approach is referred to as modelling to generate-alternatives (MGA). This paper provides a biologically-inspired metaheuristic simulation-optimisation MGA method that can efficiently create multiple solution alternatives to environmental problems containing significant stochastic uncertainties that satisfy required system performance criteria and yet are maximally different in their decision spaces. The efficacy of this stochastic MGA approach for environmental policy formulation is demonstrated using a municipal solid waste case study. It is shown that this new computationally efficient algorithmic approach can simultaneously produce the desired number of maximally different solution alternatives in a single computational run of the procedure.

Fireflies in the Fruits and Vegetables: Combining the Firefly Algorithm with Goal Programming for Setting Optimal Osmotic Dehydration Parameters of Produce

This study employs the Firefly Algorithm (FA) to determine the optimal parameter settings needed in the osmotic dehydration process of fruits and vegetables. Two case studies are considered. For both cases, the functional form of the osmotic dehydration model is established using response surface techniques with the resulting optimization formulations being non-linear goal programming models. For optimization purposes, a computationally efficient, FA-driven method is employed and the resulting solutions are shown to be superior to those from previous approaches for the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this nature-inspired metaheuristic approach over a range of the two key parameters that most influence its running time.

Modeling to Generate Alternatives Using Biologically Inspired Algorithms

In solving many practical mathematical programming applications, it is generally preferable to formulate several quantifiably good alternatives that provide very different approaches to the particular problem. This is because decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult—if not impossible—to quantify and capture at the time that the supporting decision models are constructed. There are invariably unmodeled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it is preferable to generate several alternatives that provide multiple, disparate perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to all known modeled objective(s) but be fundamentally different from each other in terms of the system structures characterized by their decision variables. This solution approach is referred to as modeling-to-generate-alternatives (MGA). This chapter provides a synopsis of various MGA techniques and demonstrates how biologically inspired MGA algorithms are particularly efficient at creating multiple solution alternatives that both satisfy required system performance criteria and yet are maximally different in their decision spaces. The efficacy and efficiency of these MGA methods are demonstrated using a number of case studies.