Solving Multiple Objective Programming Problems Using Feed-Forward Artificial Neural Networks: The Interactive FFANN Procedure

Multi-objective analysis of hospital delivery systems

In reliability allocation, certain reliability values are assigned to subsystems and components to achieve the required system reliability. One big challenge in solving such reliability‐based design problems is how to handle the uncertain preferences of a decision maker on multiple attributes of interest. In this paper, we propose a new ordered weighted averaging (OWA) method based on an analytic hierarchy process to address the decision maker's uncertain preferences in reliability allocation. In the proposed OWA operator, a bi‐objective mathematical programming model considering both maximal entropy and minimal variance is transformed into a single‐objective mathematical programming model using an ideal‐point method. The maximum entropy minimal variance OWA operator takes full advantage of available information and avoids overestimating the decision maker's preferences. A detailed computational procedure is presented to facilitate the implementation of the proposed method in practice. An illustrative example about the powertrain of fuel cell vehicles is provided to demonstrate the effectiveness of this method in handling multiple attributes with uncertain preferences in reliability allocation. Copyright © 2015 John Wiley & Sons, Ltd.

The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehensive interaction trend preference information oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints, as well as the goal objective function, we give a new and more flexible approach to representing the decision maker's explicit preference information on the kind and degree of the interaction of any given combination of decision criteria as well as on the degree of the importance of any decision criterion, and construct the nonempty set interaction indices based capacity identification method, which can be considered as the detailed explicit preference information oriented identification method. Finally, two illustrative examples are respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the comparison analysis between these two kinds of methods and some existing capacity identification methods are also mentioned.

Data envelopment analysis (DEA) model has been applied for evaluating bank branches and recognizing efficient and inefficient branches can help bank managers to provide appropriate strategies to improve the inefficient branches' performance. Conventional DEA models are based on the ‘black box’ approach. However, the process of providing services in banks is made up of interactive and interdependent processes. Additionally, some managers tend to incorporate their preferences in evaluation process. In this paper, best worst method (BWM) is used for incorporating decision maker (DM) preferences in two‐stage DEA model. First, BWM model is applied to obtain the weights of inputs, intermediate measures and outputs based on DM's judgement. Second, generated weights are imposed on two‐stage DEA model as additional constraints and a novel bi‐objective BWM‐two stage DEA model is introduced. Finally, the proposed bi‐objective BWM‐two stage DEA model is solved using min‐max approach. To illustrate the capability of proposed model, 45 Agricultural Bank (Agribank) branches in West Azerbaijan province of Iran are evaluated. The branches' processes are considered as two stages ‘production’ and ‘profitability’ and efficiency of branches are calculated in each stage. According to the efficiencies of each sub‐stage, branches are divided to four groups and recommendations are made for each group.

Consider a finite set of alternatives under risk which have multiple attributes. MARPI is an interactive computer-based procedure to find an efficient choice in the sense of linear expected utility. The choice is based on incomplete information about the decision maker's preferences which is elicited and processed in a sequential way. The information includes qualitative properties of the multivariate utility function such as monotonicity, risk aversion, and separability. Further, in case of an additively separable utility function, bounds on the scaling constants are elicited, and preferences (not necessarily indifferences) between sure amounts and lotteries are asked from the decision maker. The lotteries are Bernoulli lotteries generated by MARPI using special strategies. At every stage of the procedure the efficient set of alternatives is determined with respect to the information elicited so far.

We assume a multi-attribute decision making problem under uncertainty with partial information on the decision maker's preferences, by a vector utility function with two components and imprecision over their scaling constants. We propose an approximation set whose determination may be easier than the one of the utility efficient set and we consider an interactive procedure which uses such approximation to decision aid. We study some nesting and convergence properties based on the interactive reduction of the approximation set. Finally, we illustrate the procedure with a numerical example.

Purpose: To develop an interactive version of the conventional process capability-based approach, called ‘Interactive Process Capability-Based Approach (IPCA)’ in multi-response surface optimization to obtain a satisfactory compromise which incorporates a decision maker(DM)'s preference information precisely. Methods: The proposed IPCA consists of 4 steps. Step 1 is to obtain the estimated process capability indices and initialize the parameters. Step 2 is to maximize the overall process capability index. Step 3 is to evaluate the optimization results. If all the responses are satisfactory, the procedure stops with the most preferred compromise solution. Otherwise, it moves to Step 4. Step 4 is to adjust the preference parameters. The adjustment can be made in two modes: relaxation and tightening. The relaxation is to make the importance of one of the satisfactory responses lower, which is implemented by decreasing its weight. The tightening is to make the importance of one of the unsatisfactory responses higher, which is implemented by increasing its weight. Then, the procedure goes back to Step 2. If there is no response to be adjusted, it stops with the unsatisfactory compromise solution. Results: The proposed IPCA was illustrated through a multi-response surface problem, colloidal gas aphrons problem. The illustration shows that it can generate a satisfactory compromise through an interactive procedure which enables the DM to provide his or her preference information conveniently. Conclusion: The proposed IPCA has two major advantages. One is to obtain a satisfactory compromise which is faithful to the DM preference structure. The other is to make the DM’s participation in the interactive procedure easier by using the process capability index in judging satisfaction/unsatisfaction. The process capability index is very familiar with quality practitioners as well as indicates the process performance levels numerically.

We develop an interactive method for multiple objective linear programming based on aspiration levels of a decision maker. The method assumes an unknown pseudoconcave preference structure of a decision maker throughout the decision process, and the decision maker's ability to select a preferred solution from p + 1 alternatives, where p is the number of objectives. In addition to presenting the supporting theory and algorithm, we perform a comparative study using a fictitious decision maker, comparing our approach to those of Steuer and Choo (Steuer, R. E., E. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Prog. 26 326–344.) and Reeves and Franz (Reeves, G. R., L. Franz. 1985. A simplified interactive multiple objective linear programming procedure. Comp. & Oper. Res. 12 589–601.). All three methods are interactive. During an iteration, each method presents several solution alternatives to the decision maker simultaneously. Our approach utilizes a Tchebycheff function that facilitates attainment of an optimum at a nonextreme point solution. The statistics collected in the comparative study provide insights into the nature of the algorithms and the behavior of the solution techniques with different categories of problem structure and different underlying utility functions.

Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures

A procedure to approximate the non‐dominated set for general (continuous) bi‐criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non‐dominated point of interest and based on primal–dual relationships associated with the weighted Tchebycheff scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed‐form description of the non‐dominated set. A numerical example is included. Copyright © 2001 John Wiley & Sons, Ltd.

This paper aims to compare two tools for decision makers that intend to support the decision of the selection of the appropriate supplier. Suppliers are crucial to both the efficiency and effectiveness of the performance of companies. A critical success factor of these companies is the selection of the appropriate supplier. A methodology is proposed to optimise the evaluation process based on different criteria. The proposed approach extends the one proposed by Ordoobadi (2009, Development of a supplier selection model using fuzzy logic. Supply Chain Management: An International Journal, 14 (4), 314–327) who proposed the application of fuzzy logic (FL) where we use the same example case study in order to compare the analytic hierarch process (AHP) with FL. In this paper we demonstrate how we can achieve the same objective of expressing human assessments in the form of linguistic expressions by using AHP. Moreover, we demonstrate the capability to run a sensitivity analysis which helps to understand the causal relationships among the different factors. We demonstrate how this capability can help us to explain and predict the different relationships among criteria and alternatives. Moreover, we provide a measure that is able to capture the consistency of the decision maker's preferences. In our approach we provide a single unit of scale that is not only capable of ranking suppliers but also provides an understanding of the difference in scale between different suppliers which can then help to allocate resources accordingly. These facilities are not offered by Ordoobadi (2009). The proposed approach here can help companies to identify the best supplier in changing environments. The paper describes a decision model that incorporates a decision maker's subjective assessments and applies a multiple criteria decision making technique to manipulate and quantify these assessments. Unlike many similar studies, two techniques have been performed on the same case study in order to improve our understanding of the differences in the proposed techniques.

Information technology (IT) is defined as the obtainment, procedure, storage and propagation of sounding, drawing, and textual information by combining microelectronics-based computing and telecommunications. Nowadays, IT is starting to spread further from the conventional personal computer and network technologies to integrations of other fields of technology such as the use of cell phones, televisions, automobiles, etc. In other words, IT has penetrated in daily life of human beings and become one part of the whole society. The importance of IT has become momentous. Therefore, to understand the performance of efficiency and productivity of the IT firms is critical for managers as well as for personal investors. Until now, there are very few researches tried to analyze final performance of the IT firms. As a result, this research intends to use traditional Data Envelopment Analysis (DEA) CCR or BCC models to evaluate the performance of IT firms. The Decision Making Units (DMUs) on this research are chosen from IT firms in S&P 500. However, the traditional DEA models are not fair models from the aspect of improper weight derivations. Thus, this paper intends to analyze the efficiency of IT firms in S&P 500 efficiencies by using multiple objective programming (MOP) based Data Envelopment Analysis (DEA). In a MOP based DEA approach, DMUs will be evaluated based on an equal standard and the results will be evaluated more fairly. The world’s leading IT firms in S&P 500 will be evaluated based on publicly available financial reports of the fiscal year 2010. In addition, the newly developed MOP can improve the traditional DEA’s unfair weights problems and benchmark the efficiency of IT firms in S&P 500 correctly. In the empirical study, the MOP based DEA demonstrated that F5 Networks should be the communications equipment companies of IT worthwhile to be invested. In the future, performance evaluation results can be served as foundations for investment strategies definition.KeywordsInformation Technology (IT)Standard and Poor’s 500 indexPerformance EvaluationData Envelopment Analysis (DEA)Multiple Objective Programming (MOP)

Order structures such as linear orders, weak orders, semiorders and interval orders are often considered as models of a decision maker's preferences. In this paper we introduce and study new order structures characterized by their symmetric part belonging to certain classes of co-comparability graphs. We outline possible interpretations and suggest special representations of these structures and we point out their potential use for approximating relations obtained through a multicriteria aggregation procedure. We provide various characterizations of the new structures (as well as of older ones) in terms of minimal forbidden configurations and by algebraic conditions.

A CHIM-based interactive Tchebycheff procedure for multiple objective decision making

Relationships between the Tchebycheff scalarization and the augmented Lagrange multiplier technique are examined in the framework of general multiple objective programs (MOPs). It is shown that under certain conditions the Tchebycheff method can be represented as a quadratic weighted-sums scalarization of the MOP, that is, given weight values in the former, the coefficients of the latter can be found so that the same efficient point is selected. Analysis for concave and linear MOPs is included. Resulting applications in multiple criteria decision making are also discussed.