Madjid Tavana

A Taxonomy and Review of the Fuzzy Data Envelopment Analysis Literature: Two Decades in the Making

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the a-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA.

A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems

In this paper, a new dynamic self-adaptive multi-objective particle swarm optimization (DSAMOPSO) method is proposed to solve binary-state multi-objective reliability redundancy allocation problems (MORAPs). A combination of penalty function and modification strategies is used to handle the constraints in the MORAPs. A dynamic self-adaptive penalty function strategy is utilized to handle the constraints. A heuristic cost-benefit ratio is also supplied to modify the structure of violated swarms. An adaptive survey is conducted using several test problems to illustrate the performance of the proposed DSAMOPSO method. An efficient version of the epsilon-constraint (AUGMECON) method, a modified non-dominated sorting genetic algorithm (NSGA-II) method, and a customized time-variant multi-objective particle swarm optimization (cTV-MOPSO) method are used to generate non-dominated solutions for the test problems. Several properties of the DSAMOPSO method, such as fast-ranking, evolutionary-based operators, elitism, crowding distance, dynamic parameter tuning, and tournament global best selection, improved the best known solutions of the benchmark cases of the MORAP. Moreover, different accuracy and diversity metrics illustrated the relative preference of the DSAMOPSO method over the competing approaches in the literature.

A group AHP-TOPSIS framework for human spaceflight mission planning at NASA

Human spaceflight mission planning is a complex task with many interacting systems and mission phases. Analog missions are Earth-based science missions whose purpose is to help understand the complexities inherent in future human spaceflight missions. The goal of performing an analog mission is to prepare crewmembers and support teams for future space missions in a low risk-low cost environment by repeatedly testing vehicles, habitats, and surface terrain simulators. This study presents a group multiattribute decision making (MADM) framework developed at the Johnson Space Center (JSC) for the Integrated human exploration mission simulation facility (INTEGRITY) project to assess the priority of human spaceflight mission simulators. The proposed framework integrates subjective judgments derived from the analytic hierarchy process (AHP) with the entropy information and the technique for order preference by similarity to the ideal solution (TOPSIS) into a series of preference models for the human exploration of Mars. Three different variations of TOPSIS including conventional, adjusted and modified TOPSIS methods are considered in the proposed framework.

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and its supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.

Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation

Project portfolio managers are multi-objective Decision-Makers (DMs) who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi-period planning horizon. However, project portfolio decisions are complex multi-objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences. We propose a Goal Programming (GP) approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities. A fuzzy goal with an aspiration level and a predefined membership function is defined for each objective. The impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations. This leads to type II fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets. The proposed model is based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and fuzzy preference relations. TOPSIS is used to reduce the multi-objective problem into a bi-objective problem. The resulting bi-objective problem is solved with fuzzy GP (FGP). The fuzzy preference relations are used to help DMs express their preferences with respect to the membership values of the fuzzy goals. The proposed approach is used to solve a real-life problem characterized as a fuzzy Multi-Objective Project Selection with Multi-Period Planning Horizon (MOPS-MPPH). The performance of the proposed approach is compared with a competing method in the literature. We show that our approach generates high-quality solutions with minimal computational efforts.

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.

A new multi-objective multi-mode model for solving preemptive time-cost-quality trade-off project scheduling problems

Considering the trade-offs between conflicting objectives in project scheduling problems (PSPs) is a difficult task. We propose a new multi-objective multi-mode model for solving discrete time-cost-quality trade-off problems (DTCQTPs) with preemption and generalized precedence relations. The proposed model has three unique features: (1) preemption of activities (with some restrictions as a minimum time before the first interruption, a maximum number of interruptions for each activity, and a maximum time between interruption and restarting); (2) simultaneous optimization of conflicting objectives (i.e., time, cost, and quality); and (3) generalized precedence relations between activities. These assumptions are often consistent with real-life projects. A customized, dynamic, and self-adaptive version of a multi-objective evolutionary algorithm is proposed to solve the scheduling problem. The proposed multi-objective evolutionary algorithm is compared with an efficient multi-objective mathematical programming technique known as the efficient @e-constraint method. The comparison is based on a number of performance metrics commonly used in multi-objective optimization. The results show the relative dominance of the proposed multi-objective evolutionary algorithm over the @e-constraint method.

Supplier selection using chance-constrained data envelopment analysis with non-discretionary factors and stochastic data

The changing economic conditions have challenged many organisations to search for more efficient and effective ways to manage their supply chain. During recent years supplier selection decisions have received considerable attention in the supply chain management literature. There are four major decisions that are related to the supplier selection process: what product or services to order, from which suppliers, in what quantities and in which time periods? Data envelopment analysis (DEA) has been successfully used to select the most efficient supplier(s) in a supply chain. In this study, we introduce a novel supplier selection model using chance-constrained DEA with non-discretionary factors and stochastic data. We propose a deterministic equivalent of the stochastic non-discretionary model and convert this deterministic problem into a quadratic programming problem. This quadratic programming problem is then solved using algorithms available for this class of problems. We perform sensitivity analysis on the proposed non-discretionary model and present a case study to demonstrate the applicability of the proposed approach and to exhibit the efficacy of the procedures and algorithms.

Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS

We use NSGA-III and MOPSO algorithms to solve a multi-objective X-bar control chart design problem.NSGA-III and MOPSO are modified to handle a constrained multi-objective problem with discrete and continuous variables.Four DEA models are proposed to reduce the number of Pareto optimal solutions to a manageable size.TOPSIS is used to prioritize the efficient optimal solutions.Several metrics are used to compare the performance of NSGA-III and MOPSO algorithms. X-bar control charts are widely used to monitor and control business and manufacturing processes. This study considers an X-bar control chart design problem with multiple and often conflicting objectives, including the expected time the process remains in statistical control status, the type-I error, and the detection power. An integrated multi-objective algorithm is proposed for optimizing economical control chart design. We applied multi-objective optimization methods founded on the reference-points-based non-dominated sorting genetic algorithm-II (NSGA-III) and a multi-objective particle swarm optimization (MOPSO) algorithm to efficiently solve the optimization problem. Then, two different multiple criteria decision making (MCDM) methods, including data envelopment analysis (DEA) and the technique for order of preference by similarity to ideal solution (TOPSIS), are used to reduce the number of Pareto optimal solutions to a manageable size. Four DEA methods compare the optimal solutions based on relative efficiency, and then the TOPSIS method ranks the efficient optimal solutions. Several metrics are used to compare the performance of the NSGA-III and MOPSO algorithms. In addition, the DEA and TOPSIS methods are used to compare the performance of NSGA-III and MOPSO. A well-known case study is formulated and solved to demonstrate the applicability and exhibit the efficacy of the proposed optimization algorithm. In addition, several numerical examples are developed to compare the NSGA-III and MOPSO algorithms. Results show that NSGA-III performs better in generating efficient optimal solutions.

A fuzzy group quality function deployment model for e-CRM framework assessment in agile manufacturing

The rapid growth of the Internet and the expansion of electronic commerce applications in manufacturing have given rise to electronic customer relationship management (e-CRM) which enhances the overall customer satisfaction. However, when confronted by the range of e-CRM methods, manufacturing companies struggle to identify the one most appropriate to their needs. This paper presents a novel structured approach to evaluate and select the best agile e-CRM framework in a rapidly changing manufacturing environment. The e-CRM frameworks are evaluated with respect to their customer and financial oriented features to achieve manufacturing agility. Initially, the e-CRM frameworks are prioritized according to their financial oriented characteristics using a fuzzy group real options analysis (ROA) model. Next, the e-CRM frameworks are ranked according to their customer oriented characteristics using a hybrid fuzzy group permutation and a four-phase fuzzy quality function deployment (QFD) model with respect to three main perspectives of agile manufacturing (i.e., strategic, operational and functional agilities). Finally, the best agile e-CRM framework is selected using a technique for order preference by similarity to the ideal solution (TOPSIS) model. We also present a case study to demonstrate the applicability of the proposed approach and exhibit the efficacy of the procedures and algorithms.