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Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions
Abstract
In this paper we develop interactive approaches for the discrete alternative multiple criteria decision making problem. We develop an algorithm that finds the most preferred alternative of a decision maker (DM) assuming only that the DM has a monotonic utility function. The algorithm divides the criteria space into a number of smaller subspaces and then uses the ideal points of these subspaces to eliminate alternatives. We also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function. We present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm. We then develop a general algorithm that first identifies the type of the DM's utility function and then employs the approach that is compatible with the identified utility function type. We also present computational results for the general algorithm.
... The issues are mentioned in prior can be addressed by using Evidential Reasoning Approach (ER) also, which is a multi-criteria decision analysis (MCDA) method [7], [8]. The ER approach is developed based on decision theory; in particular utility theory [9], [10] and artificial intelligence; in particular the theory of evidence [6] [11]. This approach deals with MCDA problems, consisting of both quantitative and qualitative criteria under various uncertainties, such as incomplete information, vagueness, ambiguity etc. ...
... Due to the capability of ER approach in managing and representing uncertainty, it has been applied to many areas, such as environmental impact assessment [12], pipeline leak detection [13], and system reliability prediction [14]. It also applied to conduct safety analysis [9]. In this research ER approach is applied to identify sustainable geographical location for river bridge construction. ...
... Evidential Reasoning Approach (ER) had been introduced by Yang and Singh for multi-criteria decision and design problem analysis under uncertainty [9], [15]. It is a multicriteria decision analysis (MCDA) approach for dealing with decision and design problems in decision making environment having both quantitative and qualitative criteria with various uncertainties; such as deficient information and vagueness. ...
Geographic location selection for river bridge construction is one of the most challenging tasks because it has to deal with both numerical data and qualitative information with uncertainty. Organizational self-assessment, ensuring safety, risk measurement, supplier appraisal and many other things depend on a proper Geo-location selection. River bridge site selection is such an example in which multiple attributes; both qualitative and quantitative criteria have to be analyzed for selecting a proper bridge location. This paper demonstrates the application of a novel method named Evidential Reasoning (ER), which is a Multi Criteria Decision Analysis method applied for decision making where many criteria have to be explicitly considered for making decision. ER approach is capable for addressing the uncertainty of multi-criteria decision problem, where there exist factors of both subjective and quantitative nature. It handles uncertainties by using a degree belief structure. The evidential reasoning approach helps in aggregating degree of belief from lower level attributes to higher level attributes. To conduct the experiments of this work, Geo-location selection for The Padma Bridge construction in Bangladesh is taken as research domain and the experiment results and analysis are discussed in this paper.
... А именно сходство лежит в основе любой систематизации. Между тем, до сих пор различные направления теории принятия решений развивались изолированно, а их приверженцы претендовали на всеобщность своих подходов [1][2][3]. Это, тем более, неприемлемо для науки, в которой теоретически лучшие по всем критериям объекты называются идеальными, а теоретически худшие по всем критериям – антиидеальными [4]. Очевидно, что и те и другие могут рассматриваться только как возможные исключения. ...
... Относительные единицы измерения и фиксированные границы шкалы позволяют выполнять над аргументами обобщающей функции любые арифметические операции. Областью определения функции jго признака является интервальная или балльная шкала, характеризуемая границами [y j,min , y j,max ], n j , 1 = , а область значений функции измеряется в шкале [0, 1], отвечающей указанным требованиям. Скаляризация векторных оценок исключает необходимость в реализации третьего уровня модели многокритериального выбора, но требует выбора типа обобщающей функции и функций, отображающих значение каждого признака в шкалу [0, 1] . ...
... Областью определения функции jго признака является интервальная или балльная шкала, характеризуемая границами [y j,min , y j,max ], n j , 1 = , а область значений функции измеряется в шкале [0, 1], отвечающей указанным требованиям. Скаляризация векторных оценок исключает необходимость в реализации третьего уровня модели многокритериального выбора, но требует выбора типа обобщающей функции и функций, отображающих значение каждого признака в шкалу [0, 1] . Эти функции не могут воспроизвести предпочтения между значениями всех критериев, формируемые экспертом. ...
Mikoni S.V. System Analysis of Multi-criteria Optimization Methods on a Finite Set of Alternatives. Abstract. The functions used by different optimization methods are interpreted with expected utility viewpoint. It makes possible to distinguish two groups of methods-criterion and functional choice ones. The first group of methods sets preferences on the values of the criteria, and the second-on the values of the functions presenting the preferences of decision maker on the scales of attributes. Such an interpretation of functions that does not depend on how they are created, allowed considering methods of multi-criteria optimization and multi-dimensional utility from unified positions. The analytic hierarchy process uses the priority function calculated based on the matrix of pairwise comparisons. So, it is related to the group of methods of functional choice too. The resulting system allows one to compare their methods for quality and evaluate the effectiveness of tasks solving. of predominance; the criterion of correspondence; a normalizing function; the function of the deviation from the target; the utility function.
... These types of problems associated with AHP [8] and ANP causes serious problems in decision making. The issues as mentioned can be addressed by using Evidential Reasoning Approach (ER), which is a multi-criteria decision analysis (MCDA) method[13] [14]. ER deals with problems, consisting of both quantitative and qualitative criteria under various uncertainties such as incomplete information, vagueness, ambiguity [7].The ER approach, developed based on decision theory in particular utility theory [1] [21], artificial intelligence in particular the theory of evidence [18] [19]. ...
... It differs with other Multi Criteria Decision Making (MCDM) modeling model a judgment with uncertainty. For example, in AHP methods in that it employs evidence-based reasoning process to derive a conclusion [13] [14] [20]. The main strength of this approach is that it can handle uncertainties associated with quantitative and qualitative data, related to MCDM problems [13] [14] [20]. ...
... For example, in AHP methods in that it employs evidence-based reasoning process to derive a conclusion [13] [14] [20]. The main strength of this approach is that it can handle uncertainties associated with quantitative and qualitative data, related to MCDM problems [13] [14] [20]. ...
The word 'Job' term as a regular activity performed in exchange for payment is considered as one of the most important activities for many families worldwide .Evaluation is necessary when more than one opportunity come to an To fulfill their desired goal, it is the 'evaluation' which assesses among the factors. In addition, it is difficult to measure qualitative factors in a quantitative way, resulting incomplete-ness in data and hence, uncertainty. Besides it is essential to address the subject of uncertainty by using apt methodology; otherwise, the decision to choose a job will become inapt. There exist many methods name as Analytical Hierarchical Process (AHP), Analytical Network Process (ANP) and so on. But the mentioned methods are not suitable to address the subject of uncertainty and hence, resulting inappropriate selection to the expecting job. Therefore, this paper demonstrates the application of a novel method named Evidential Reasoning (ER), which is capable of addressing the uncertainty of multi-criterion problem, where there exist factors of both subjective and objective nature. The ER method handles uncertainties by using a belief structure is aggregating degrees of belief from lower level factors to higher level factors.
... These types of problems associated with AHP [8] and ANP causes serious problems in decision making. The issues as mentioned can be addressed by using Evidential Reasoning Approach (ER), which is a multi-criteria decision analysis (MCDA) method [13] [14]. ER deals with problems, consisting of both quantitative and qualitative criteria under various uncertainties such as incomplete information, vagueness, ambiguity [7].The ER approach, developed based on decision theory in particular utility theory [1] [21], artificial intelligence in particular the theory of evidence [18] [19]. ...
... From the results shown above, it is reasonable to say that the ER method is a mathematically sound approach towards measuring the house quality as it employs a belief structure to represent an assessment as a distribution. This approach is quite different from the other Multi Criteria Decision Making model such as the Saaty 's AHP method which uses a pair wise comparison matrix [8][9][13 [14]. Hence, the ER can handle new attribute without recalculating the previous assessment because the attribute can be arranged or numbered randomly which means that the final results do not depend on the order in which the basic attributes are aggregated. ...
... Hence, the ER can handle new attribute without recalculating the previous assessment because the attribute can be arranged or numbered randomly which means that the final results do not depend on the order in which the basic attributes are aggregated. Furthermore, any number of new houses can be added to the assessment as it does not cause a 'rank reversal problem' as in the Saaty's AHP method [8][9][13 [14]. Finally, in a complex assessment as in the house quality assessment which involved objective and subjective assessments of many basic attributes as shown in Figure 1, it is convenient to have an approach which can tackle the uncertainties or incompleteness in the data gathered. ...
House hunting meaning the activity of trying to find a house to live in, is considered as one of the most important activities for many families worldwide. This involves many criterions/factors to be measured and evaluated. These factors are expressed both in quantitative and qualitative ways. In addition, a hierarchical relationship exists among the factors. Moreover, it is difficult to measure qualitative factors in an objective/quantitative way, resulting incompleteness in data and hence, uncertainty. Therefore, it is necessary to address the issue of uncertainty by using appropriate methodology; otherwise, the decision to select a house to live in will become inappropriate. There exist many methods such as Analytical Hierarchical Process (AHP), Analytical Network Process (ANP), Inner Product Vector (IPV) to address the issue presented in this paper. However, none of them is able to address the issue of uncertainty and hence, resulting inappropriate selection of a house to live in. Therefore, this paper demonstrates the application of a novel method named Evidential Reasoning (ER), which is capable of addressing the uncertainty of multi-criterion problem, where there exist factors of both subjective and quantitative nature. The ER approach handles uncertainties by using a belief structure, the evidential reasoning approach used in aggregating degrees of belief from lower level attributes to higher level attributes [7]. This paper reports the development of DSS using ER approach, which is capable of providing overall assessment on the location of a house to live in taking account of both qualitative and quantitative factors. Chittagong, which is the second largest city of Bangladesh has been considered as the case study area to demonstrate the application of the developed DSS..
... However, this can be evaluated using some referential value such as excellent, good, average and bad. Therefore, it can be seen that qualitative criterions which have been considered in selecting hospital location involves lot of uncertainties and they should be treated with appropriate methodology is Evidential reasoning(ER) is a multi-criteria decision analysis (MCDA) method [13] [14]. ER deals with problems, consisting of both quantitative and qualitative criteria under various uncertainties such as incomplete information, vagueness, ambiguity [7].The ER approach, developed based on decision theory in particular utility theory [1] [11], artificial intelligence in particular the theory of evidence [9] [10]. ...
... Hence, the ER method can handle a new attribute without recalculating the previous assessment because the attribute can be arranged or numbered arbitrarily which means that the final results do not depend on the order in which the basic attributes are aggregated. Furthermore, any number of new location can be added to the assessment as it does not cause a "rank reversal" as in the conventional method [8][9][13 [14]. Finally, in a composite assessment as in the suitable location selection appraisal which involved objective and subjective assessments of many basic attributes as shown in Figure 1, it is convenient to have an approach which can tackle the uncertainties or incompleteness in the data gathered. ...
The general public's demand of Bangladesh for safe health is rising promptly with the improvement of the living standard. However, the allocation of limited and unbalanced medical resources is deteriorating the assurance of safe health of the people. Therefore, the new hospital construction with rational allocation of resources is imminent and significant. The site selection for establishing a hospital is one of the crucial policy-related decisions taken by planners and policy makers. The process of hospital site selection is inherently complicated because of this involves many factors to be measured and evaluated. These factors are expressed both in objective and subjective ways where as a hierarchical relationship exists among the factors. In addition, it is difficult to measure qualitative factors in a quantitative way, resulting incompleteness in data and hence, uncertainty. Besides it is essential to address the subject of uncertainty by using apt methodology; otherwise, the decision to choose a suitable site will become inapt. Therefore, this paper demonstrates the application of a novel method named Evidential reasoning methodology-based intelligent decision system, which is capable of addressing suitable site for hospital by taking account of large number of criteria, where there exist factors of both subjective and objective nature.
... PMRSO generates nondominated solutions and then makes the DM select the best solution as traditional posterior methods do. The distinctive feature of PMRSO is that it adapts an interactive selection method suggested by Köksalan and Sagala (1995) to aid the solution selection process of the DM. Usually, it is difficult to select a single solution from a large number of nondominated solutions when multiple responses are considered. ...
... Next, the DM selects the best solution from among the generated nondominated solutions. The interactive selection method (Köksalan and Sagala 1995) is adapted in this stage. Its basic idea can be referred as "divide-and-conquer. ...
In Multi-Response Surface Optimization (MRSO), responses are often in conflict. To obtain a satisfactory compromise, the preference information of a Decision Maker (DM) on the tradeoffs among the responses should be considered. One of the promising alternatives is a posterior preference articulation approach. It first generates nondominated solutions and then makes the DM select the best one from the nondominated solutions. In this article, a solution selection approach is presented. It takes the posterior approach and employs a clustering method to aid the selection process of the DM. The DM can obtain the satisfactory compromise solution easily by the proposed method.
... The interactive selection method (Köksalan and Sagala, 1995) is adopted in this phase. This method is suitable for P-SS-M due to three advantages. ...
... and weighted concave quadratic distance functions (Köksalan and Sagala, 1995), ...
The responses in multiresponse surface optimization are often in conflict. To obtain a satisfactory compromise, the preference information of a decision maker (DM) on the tradeoffs among the responses should be incorporated into the problem. In most existing works, the DM is required to provide his/her preference information through preference parameters before solving the problem. However, extracting the preference parameter values representing the preference structure of the DM is often difficult. To overcome these difficulties, several alternative methods that do not require the preference information of the DM before solving the problem have been suggested. These alternative methods assess the preference parameters of the DM in a posteriori or progressive manner and are called posterior or interactive methods, respectively. This paper reviews specific types of posterior and interactive methods, which are referred to as solution selection methods. In solution selection methods, the DM provides his/her preference information in the form of solution selection. The required information is easy for the DM to provide.
... where d i and w i are the individual utility function and the estimated weight of the i th response, respectively (Köksalan and Sagala, 1995). Step 2 Obtain two initial solutions maximising the estimated utility function. ...
... ) are estimated utility function values at x s and x t , respectively (Köksalan and Sagala, 1995). Step 6 Obtain a new solution maximising the estimated utility function – the process goes to Step 3 of the next iteration until an appropriate solution is found. ...
Criteria to solve multiresponse problems developed under the RSM framework are rarely evaluated in terms of their ability to depict Pareto frontiers and their solutions do not provide information about response properties. This manuscript contributes for positioning some optimization criteria in relation to each other based on their ability to capture solutions in convex and nonconvex surfaces in addition to the robustness, quality of predictions and bias of the generated solutions.
Results show that an appealing compromise programming-based method can compete with leading methods in the field. It does not require preference information from the decision-maker, is easy-to-implement, can generate solutions to satisfy decision-makers with different sensitivity to bias and variance based on performance metric values, and evenly distributed solutions along the Pareto frontier. The validity of these results is supported on three examples.
... In the field of mental health, particularly in addressing depression [23], the use of multi-criteria decision-making (MCDM) [24] reflects the importance placed on infrastructure development in urban settings. The diagnosis of depression is a multifaceted process [25], much like managing the various elements of city infrastructure. ...
Background A thorough psychosocial assessment is time-consuming, often requiring multiple sessions to uncover the psychological factors contributing to mental illness, such as depression. The duration varies depending on the severity of the patient’s condition and how effectively the psychotherapist can establish rapport. However, prolonged assessment periods pose a significant risk of patient deterioration.
Methods The comprehensive psychosocial intervention, led by the Multi-Criteria Decision-Making (MCDM) approach utilizing the Multi-Objective Optimization by Ratio Analysis (MOORA) method, played a pivotal role in identification of the key psychological factors contributing to the depression of the client among the 21 facotrs specified by BDI-II analysis.
Results The integration of the MCDM-MOORA strategy compared to traditional psychotherapy demonstrates a Jaccard similarity coefficient of 0.8, with a minimum error margin of 7% (vulnerability index = 0.57), indicating a significant agreement between the two approaches, both converging towards a similar solution.
Conclusion The implementation of MOORA facilitated the identification and prioritization of key psychosocial intervention strategies, making the process 45.5 times faster compared to traditional methods. This acceleration significantly contributed to the precision and efficacy of the work. Additionally, critical vulnerable factors were identified through ordered statistics and correlation analysis (Pearson (r) = 0.8929 and Spear-man’s rank (ρ) = 0.7551) on the Beck Depression Inventory-II model. These findings were supported by other MCDM schemes such as EDAS and TOPSIS, etc. Moreover, the proposed method demonstrated high stability and robustness in dynamic decision-making environments, maintaining consistency across scenarios adapted by different psychotherapists. Overall, the combined application of MCDM (MOORA) and targeted psychological interventions yielded substantial positive outcomes in enhancing the well-being of individuals with psychological illnesses e.g., depression, cognitive, affective, somatic syndromes.
... These are referred to as interactive methods or methods that require "progressive articulation of preferences". These methods have been well-developed for both the multiple criteria evaluation (see for example, Geoffrion, Dyer and Feinberg, 1972, [11] and Köksalan and Sagala, 1995 [12] ) and design problems (see Steuer, 1986 [13] ). ...
... A pairwise comparison approach is used whereby the DM is presented with the incumbent solution and another alternative and asked to select the pre- tion. While this approach has been shown to be promising [38], it requires solving several linear programming problems of special structures. Another approach is to capitalize on the "neighboring" concept of ELECTRE by Roy [14] [15] and select an outranking solution for comparison with the current solution. ...
... 0 A : # of solutions found whose %GAP is between 0% and 1% (0%< %GAP <=1%) B : # of solutions found whose %GAP is between 1% and 2% (1%< %GAP <=2%) C : # of solutions found whose %GAP is between 2% and 3% (2%< %GAP <=3%) D : # of solutions found whose %GAP is between 3% and 4% (3%< %GAP <=4%) E : # of solutions found whose %GAP is more than 4% (4%< %GAP) subspaces. These subspaces are called cells (Köksalan & Sagala, 1995). The number of cells changes between 2 and 9 for the solution sets with different number of solutions. ...
In Aerial Surveillance Problem (ASP), an air platform with surveillance sensors searches a number of rectangular areas by covering the rectangles in strips and turns back to base where it starts. In this paper, we present a multiobjective extension to ASP, for which the aim is to help aerial mission planner to reach his/her most preferred solution among the set of efficient alternatives. We consider two conflicting objectives that are minimizing distance travelled and maximizing minimum probability of target detection. Each objective can be used to solve single objective ASPs. However, from mission planner’s perspective, there is a need for simultaneously optimizing both objectives. To enable mission planner reaching his/her most desirable solution under conflicting objectives, we propose exact and heuristic methods for multiobjective ASP (MASP). We also develop an interactive procedure to help mission planner choose the most satisfying solution among all Pareto optimal solutions. Computational results show that the proposed methods enable mission planner to capture the trade-offs between the conflicting objectives for large number of alternative solutions and to eliminate the undesirable solutions in small number of iterations.
... This procedure repeats until the alternatives within the interval are considered indifferent. To handle higher dimensional response surface, Lee et al. [46] proposed a framework based on the interactive method developed by Köksalan and Sagala [47]. This approach first partitions the objective space into some equal-sized cells. ...
Decision making is an essential activity in manufacturing systems when designing production lines, scheduling, etc. Many decision making problems are characterized by multiple conflicting criteria and a large number of alternatives. For these complex decision making problems, it is rational to involve a group of decision makers (DM) for considering different aspects of the problem. This paper proposes an approach for supporting the decision making group to reduce disagreement in the group and obtain a common solution. The proposed approach allows the DMs to specify a region of acceptance, known as indifference zone, in the objective space as preference inputs. This makes the proposed approach applicable to problems with a large number of alternatives. The use of indifference zone concept captures the uncertain nature of preference articulation. Moreover, the indifference zone is shown beneficial in reducing the difficulty of reaching a group common solution. The properties of the proposed method are investigated analytically and with numerical experiments. Finally, the usefulness of the proposed method is shown by tackling a real-world packaging line configuration problem with a large alternative set.
... The existence of a value function with some pre-specified properties is a very old and important problem; See, e.g., Birkhoff [3], Debreu [4], Fishburn [5], Karsu [6], Keeney and Raiffa [7], Köksalan et al. [8], Korhonen et al. [9,10,11,12], Nasrabadi et al. [13], and Zionts et al. [16]. To the best of our knowledge, except for Korhonen et al. [11], there is no study about the existence of quasi-concave order-preserving value functions. ...
Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we establish necessary and sufficient conditions for existence of a value function satisfying aforementioned properties. This leads to an operational, tractable and easy to use test for checking the existence of a desirable value function. In addition to developing the existence test, we construct consistent linear and non-linear desirable value functions.
... By using MCA the members don't have to agree on the relative importance of the criteria or the rankings of the alternatives. Each member enters his or her own judgements, and makes a distinct, identifiable contribution to a jointly reached conclusion (Köksalan and Sagala, 1995). ...
The aim of the paper is to evaluate by means of a multi-criteria analysis (Multi Criteria Decision Making - MCDM) the multiplicity of measures regarding energy efficiency and reduction in consumption of fossil fuels, with relative implementation of integrated renewable energy sources, for planning and renovation of single family residential buildings. The work analize the energy (thermal, electrical) consumed by a building of this type (an Italian case study), and, for the choice of the best technology to adopt for environmental heating (hot sanitary water and cooling), a MCDM model was used, which, in addition to economic evaluation, incorporates too energy efficiency, the reduction of CO2 emissions, the ease of procurement of raw material and the governative incentives available. Our results underline that the best solution concerns the installation of solar thermal panels combined with the heat pump.
... The problem has been studied in many publications in recent decades; see, e.g., Keeney and Raiffa (1976) for the theory of eliciting multi-attribute value and utility functions; Roy (1973) for outranking methods; Saaty (1980) for the Analytic Hierarchy Process; Greco et al. (2001) for the rough sets approach; and Korhonen et al. (1984), Köksalan and Sagala (1995), and Korhonen et al. (2016) for interactive methods. See Olson (1996), for a good book discussing at length decision aids for selection problems. ...
In this paper we answer three important questions about the convex-cone dominance approach in Multiple Criteria Decision Making with a finite number of alternatives. These questions concern the existence of value (utility) functions and the consistency of the preference information with special forms of this function.
... However, most posterior methods have limited practical applicability because selecting the most satisfactory solution among the generated candidate solutions is difficult, especially when a large number of the responses have to be considered simultaneously. 19 P-MRSO overcomes this difficulty by adopting the interactive selection method suggested by Köksalan and Sagala 16 . This method requires a reasonable amount of cognitive effort from the DM since it requires as few as possible pairwise comparisons between the selected candidate solutions. ...
One of the most important issues in multiple response surface optimization (MRSO) is obtaining a satisfactory “compromise” solution considering a decision maker (DM)'s preference information on the tradeoffs among multiple responses. A promising alternative to incorporate the DM's preference information into the problem is the posterior preference articulation approach, which first generates all (or most) of the nondominated solutions and then makes the DM select the best one from the set of nondominated solutions a posteriori. However, it has an inefficiency problem in that it generates an excessive number of nondominated solutions in which almost all are not used for the DM's selection. This paper proposes a new posterior method called “IP-MRSO” to overcome the limitation of the existing posterior method. The proposed IP-MRSO is illustrated through a well-known MRSO case problem.
... This approach is called as prior articulation of preferences that transforms the MCDM analysis into a single criterion problem (Keeney and Raiffa, 1993). Many methods, such as those based on estimating a value function or using the concept of outranking relations, or analytical hierarchy process, and some decision rule-based methods, have tried to solve MCDM evaluation problems using interactive progressive articulation of preferences throughout the solution process (Geoffrion, Dyer and Feinberg, 1972;Köksalan and Sagala, 1995;Köksalan Wallenius, and Zionts, 2011). ...
In order to improve their business excellence, all organizations, despite their size (small, medium or large one) should manage their risk of fraud. Fraud, in today's world, is often committed by using computers and can only be revealed by digital forensic investigator. Not even small or medium-sized companies are secure from fraud. In the light of recent financial scandals that literary demolished not just economies of specific countries but entire world economy, we propose in this paper an optimal model of corporative computer incident digital forensic investigation (CCIDFI) by using adopted mathematic model of the greed MCDM – multi-criteria decision-making method and the Expert Choice software tool for multi-criteria optimization of the CCIDFI readiness. Proposed model can, first of all, help managers of small and medium-sized companies to justify their decisions to employ digital forensic investigators and include them in their information security teams in order to choose the optimal CCIDFI model and improve forensic readiness in the computer incident management process that will result with minimization of potential losses of company in the future and improve its business quality.
... where U i ðxÞ denotes the sample average of the realized utility function values with respect to the ith performance measure (i.e., Z i defined in problem P1) obtained from a number of simulation replications (when using the solution x). Subsequently, the solutions x ðrÞ p and x ðrÞ s are used to solve the following problem P3 in order to obtain the next new weight values [16]. In problem P3, let π represent a very small positive integer, and constraint (3) is imposed such that the difference of the utility functions between x ðrÞ p and x ðrÞ s is greater than a positive variable d by at least an amount π. ...
We propose a simulation-based solution framework for tackling the multi-objective inventory optimization problem. The goal is to find appropriate settings of reorder point and order quantity to minimize three objective functions simultaneously, which are the expected values of the total inventory cost, the average inventory level, and the frequency of inventory shortage. We develop new algorithms that can exploit statistically valid ranking and selection (R&S) procedures and the desirable mechanics of conventional multi-objective optimization techniques. Two simulation algorithms are proposed to be applied in different scenarios depending on the preference information revealed either during or after the actual optimization process. Experimental results are provided to evaluate the efficiency of the developed algorithms and other existing solution frameworks.
... Zionts (1981) developed an interactive algorithm to choose between discrete alternatives for a DM whose preferences are consistent with a linear preference function. Korhonen et al. (1984) developed a version that assumes a quasiconcave preference function and Köksalan and Sagala (1995) generalized for any monotone preference function. Lokman et al. (2014) also considered a quasiconcave preference function but they addressed integer programs rather than choosing from an available set of alternatives. ...
We develop an interactive algorithm for biobjective integer programs that finds the most preferred solution of a decision maker whose preferences are consistent with a quasiconvex preference function to be minimized. During the algorithm, preference information is elicited from the decision maker. Based on this preference information and the properties of the underlying quasiconvex preference function, the algorithm reduces the search region and converges to the most preferred solution progressively. Finding the most preferred solution requires searching both supported and unsupported nondominated points, where the latter is harder. We develop theory to further restrict the region where unsupported nondominated points may lie. We demonstrate the algorithm on the generalized biobjective traveling salesperson problem where there are multiple efficient edges between node pairs and show its performance on a number of randomly generated instances.
... Let Q = {(s, t): x s is preferred to x t by the DM}. The weights are estimated by solving the following problem (P) (Köksalan and Sagala, 1995): ...
In dual response surface optimization (DRSO), the mean and standard deviation responses are often in conflict. To obtain a satisfactory compromise, the preference information of a decision maker (DM) on the tradeoffs among the responses should be incorporated into the problem. Some existing works suggested an approach of minimizing weighted mean square error (WMSE) to incorporate the DM's preference information. In WMSE approach, the DM provides his/her preference information by specifying weights of mean and standard deviation responses. The weights should be determined in accordance with the DM's preference structure regarding the tradeoffs. However, it is often difficult to specify weights that are congruent with the DM's preference structure without use of a systematic method. In this study, we develop an interactive weighting method to DRSO where the DM provides preference information in the form of pairwise comparisons. Our method does not require weights to be specified in advance. Instead, it uses the results of pairwise comparisons of the DM to estimate weights in an interactive manner. The required preference information is relevant and therefore easy for the DM to provide. The method is effective in that a highly satisfactory solution for the DM can be obtained through a few pairwise comparisons.
... Return (x y), i f hn i t (Y ) ; t(X)i < 0 for each i = 1 ::k. 4. Return nothing, if otherwise. ...
In problem solving, the decision-theoretic framework is invoked when we wish to de ne a rich notion of preference over possible solutions. While decision theory provides a clean framwork for representing preference information, eliciting
... Along with the relatively easy to obtain ideal point, the nadir point is an important element of MOP, because these points define lower and upper bounds of the efficient set. In fact, there are some methods that require the nadir point as input, especially among interactive approaches such as in [18,24,27]. Hence, determination of the nadir point has been studied extensively and several exact and heuristic methods have been proposed for the problem [17]. ...
We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with p objective functions. The proposed algorithm is based on an exhaustive search of the (p−2)-dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives.
... Let Q = {(s, t): x s is preferred to x t by the DM}. The weight is estimated by solving the following linear programming problem (P) (Köksalan & Sagala, 1995): ðPÞ maximize fw;zg z s:t: WMSEðx t Þ À WMSEðx s Þ À z P e for ðs; tÞ 2 Q ; ...
In dual response surface optimization, minimizing weighted mean squared error (WMSE) is a simple yet effective way of obtaining a satisfactory solution. To minimize WMSE, the weights of the squared bias and variance should be determined in advance. Determining the weights in accordance with the decision maker (DM)'s preference structure regarding the tradeoffs between the two responses is critical and difficult. In this study, we develop an interactive weighting method where the DM provides his/her preference information in the form of pairwise comparisons. Our method estimates the weights based on the pairwise comparisons in an interactive manner. The method obtains a satisfactory solution through several pairwise comparisons in the case examples that we tested.
... to identify optimal structure of transmissions systems for offshore wind farms. Salem et. al. (2013) applied successfully rational multi-criteria decision Data Decision Model Feedback making to choose an operational plan for bridge rehabilitation. Multi-criteria optimization is an optimization of problem with more than one objective (Steuer, 1986;Köksalan et. al., 1995;Zionts and Wallenius, 1976). As an example, one is given an option to buy a certain number of Microsoft stocks and General Electric stocks and the decision is how one combines these two stocks. Chai et. al. (2013) reviewed how rational decision making has been applied successfully to choose a supplier selection whereas Badri et. al. (201 ...
In this paper the theory of flexibly-bounded rationality which is an
extension to the theory of bounded rationality is revisited. Rational decision
making involves using information which is almost always imperfect and
incomplete together with some intelligent machine which if it is a human being
is inconsistent to make decisions. In bounded rationality, this decision is
made irrespective of the fact that the information to be used is incomplete and
imperfect and that the human brain is inconsistent and thus this decision that
is to be made is taken within the bounds of these limitations. In the theory of
flexibly-bounded rationality, advanced information analysis is used, the
correlation machine is applied to complete missing information and artificial
intelligence is used to make more consistent decisions. Therefore
flexibly-bounded rationality expands the bounds within which rationality is
exercised. Because human decision making is essentially irrational, this paper
proposes the theory of marginalization of irrationality in decision making to
deal with the problem of satisficing in the presence of irrationality.
Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.
We investigate the tension between accounting and financial functions of an OEM who manufactures and remanufactures capital‐intensive products. The OEM operates a servicizing business model in which it leases a product, remanufactures the product returned at the end of the lease, and re‐leases the remanufactured product (usecycle), with multiple such usecycles. The accounting function at the firm would suggest that, the OEM: i) recovers the initial manufacturing cost of the product over its useful life as prescribed by IRS guidelines via depreciation; ii) remanufactures the product as long as its initial manufacturing cost is not fully recovered; and (iii) removes the product from the books immediately after it has completely depreciated. In contrast the financial function would consider the initial manufacturing cost of the product to be a sunk cost and would suggest that the firm continues to remanufacture the product as long as the remanufacturing cost is lower than the cost of a new unit. In this paper we investigate and prescribe ways to resolve this tension using analytical models. Specifically, we first show that the optimal durations over which the product should be used and lease prices that maximize the OEM’s accounting profit and financial profit are different. We then discuss two operational approaches to align the accounting and operational perspectives while following IRS guidelines. Finally, informed by this analysis, we develop policy prescriptions to promote remanufacturing of multiple usecycle products. Overall, this analysis highlights the role of regulatory guidelines on remanufacturing operations and the inter‐functional effort required at OEMs to successfully integrate remanufacturing operations in their business strategy.
The existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. A quasi-concave value function is equivalent to convex-to-the-origin indifference contours, a very common assumption in Economics. In this paper, we establish necessary and sufficient conditions for the existence of a value function satisfying aforementioned properties. This leads to an operational, tractable and easy to use test for checking the existence of such a value function. In addition to developing the existence test, we construct consistent linear and non-linear desirable value functions.
Multiple-response surface optimization (MRSO) aims to find a setting of the input variables that simultaneously optimizes the multiple responses. The process capability approach incorporates a decision maker’s (DM’s) preference information in the problem-solving process while considering the dispersion effects of the responses systematically through the framework of the process capability index. However, the existing process capability methods are based on an unrealistic assumption that all the preference information of the DM is given in advance. Although a few methods incorporate the DM’s preference information while solving the problem, they require too much preference information from the DM. In this article, a new interactive capability method, the pairwise comparison-based interactive process capability approach (PC-IPCA), is proposed to alleviate the DM’s burden in the solving process. The proposed method is illustrated through a well-known MRSO problem. The advantages of the proposed method compared with existing process capability methods are discussed.
Preference functions have been widely used to scalarize multiple objectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this paper, we consider a general family of functions that can take a variety of forms and has properties that allow for estimating the form efficiently. We exploit these properties to estimate the form of the function and converge towards a preferred solution(s). We develop the theory and algorithms to efficiently estimate the parameters of the function that best represent a decision maker’s preferences. This in turn facilitates fast convergence to preferred solutions. We demonstrate on a variety of experiments that the algorithms work well both in estimating the form of the preference function and converging to preferred solutions.
In multi-criteria decision making approaches it is typical to consider an underlying preference function that is assumed to represent the decision maker’s preferences. In this paper we introduce a broad family of preference functions that can represent a wide variety of preference structures. We develop the necessary theory and interactive algorithms for both the general family of the preference functions and for its special cases. The algorithms guarantee to find the most preferred solution (point) of the decision maker under the assumed conditions. The convergence of the algorithms are achieved by progressively reducing the solution space based on the preference information obtained from the decision maker and the properties of the assumed underlying preference functions. We first demonstrate the algorithms on a simple bi-criteria problem with a given set of available points. We also test the performances of the algorithms on three-criteria knapsack problems and show that they work well.
This chapter presents some multiscale approaches for process design. To illustrate the methodology, the authors employ zinc sulfide (ZnS) deposition in a chemical vapor deposition (CVD) reactor from two points of view. The first point of view employs a deterministic and multiphysics modeling approach that uses detailed physics and the associated modeling equations. This approach allows for mechanistic understanding of the process. The second point of view uses agent-based simulation in which the physics is inherently captured through pseudo evolutionary random events involving molecules or particles. Here, the traditional mechanistic understanding is sacrificed. However, a different kind of mechanistic understanding is introduced in which one observes the emergence of patterns of behavior that are consistent with an expectation of what happens in a CVD reactor. The challenge is to consider the synergistic effects of marrying both types of modeling when studying systems of this nature. The approach is also a jump-off point for studying the bridging of the scales, namely length and time.
The energy system studies include a wide range of issues from short term to long term horizons. The decision making chain is fed by input parameters which are usually subject to uncertainties. The art of dealing with uncertainties has been developed in various directions and has recently become a focal point of interest. Decision making is certainly the most important task of Oil and Gas managers and it is often a very difficult one. The purpose of this chapter is to review and investigate the decision making processes under risk and uncertainty of Oil and Gas companies. Questionnaires were distributed to eight Oil and Gas companies in Ghana to solicit their view on decision making under risk and uncertainty. Results indicate that most managers use Maximax, Minimax Regret and Expected Value when making decisions under risk and uncertainty.
Investitionen in Forschung und Entwicklung (F&E) beeinflussen in hohem Maße den langfristigen Unternehmenserfolg. Neben der eingeschlagenen Budgetierungsstrategie spielt dabei vor allem die Auswahl der „besten“Projektvorschläge eine wesentliche Rolle, weil dadurch umfangreiche Ressourcen verteilt und Prioritäten gesetzt werden, die letztlich die zukünftige Produktpalette bestimmen. Bereits seit den 1950er-Jahren wurden deshalb Dutzende Ansätze zur Unterstützung der verantwortlichen Manager bei diesem Entscheidungsproblem vorgeschlagen, wobei vor allem die moderneren Verfahren mehrfache Zielsetzungen als integralen Modellbestandteil berücksichtigen. Dieser Beitrag bietet einen Literaturüberblick zum Status Quo und diskutiert dann insbesondere unterschiedliche Möglichkeiten, mehrere divergierende Ziele in betriebswirtschaftlichen F&E-Projektauswahlmodellen abzubilden.
This chapter discusses several applications of the REPOMP procedure (Randomized Expert Panel Opinion Marginalizing Procedure). It analyzes the subjective opinion of an expert panel in a multicriteria decision making situation. It starts with an expert panel constructing a hierarchical structure of criteria to evaluate the alternatives. At a next stage, the same expert panel evaluates the relative weight of each criterion and the degree of compliance of each alternative with those criteria. Then a randomized procedure is applied to calculate the marginal indicator of each alternative and make the final ordering based on it. Additional simulation procedure is applied to analyze the distribution of that marginal indicator. The alternatives are also being allocated to indifference classes using hypothesis testing procedures. The analyzed examples refer to issues in environmental management, energy efficiency and spatial data infrastructures.
Dieser Beitrag behandelt die Problemstellung der Integration eines Entscheidungsträgers (ET) in einen interaktiven Ansatz und geht in diesem Kontext auf den offensichtlichen Bedarf von Simulationsmethoden ein. Das neuartige Simulationskonzept fokussiert hierbei die experimentelle Integration von Verhaltensmustern des ET. Solche Verhaltensweisen können beispielsweise die Ermüdung oder das Lernverhalten des ET während des Interaktionsprozesses beinhalten. In den bisherigen Ansätzen wurde dem Verhalten des Experten Rechnung getragen, indem sich viele Arbeiten mit der Anwendung von Nutzenfunktionen beschäftigen. Im Rahmen experimenteller Arbeit wird anhand von Testinstanzen für das integrierte Bestands- und Tourenplanungsproblem aufgezeigt, dass der Lösungsansatz in der Lage ist, Lösungen zu generieren, die gegen eine meistpräferierte Lösung konvergieren.
Multi-Response Surface Optimization aims at finding the optimal setting of input variables considering multiple responses simultaneously. The Weighted Mean Squared Error (WMSE) minimization approach, which imposes a different weight on the two components of mean squared error, squared bias and variance, first obtains WMSE for each response and then minimizes all the WMSEs at once. Most of the methods proposed for the WMSE minimization approach to date are classified into the prior preference articulation approach, which requires that a decision maker (DM) provides his/her preference information a priori. However, it is quite difficult for the DM to provide such information in advance, because he/she cannot experience the relationships or conflicts among the responses. To overcome this limitation, this paper proposes a posterior preference articulation method to the WMSE minimization approach. The proposed method first generates all (or most) of the nondominated solutions without the DM's preference information. Then, the DM selects the best one from the set of nondominated solutions a posteriori. Its advantage is that it provides an opportunity for the DM to understand the tradeoffs in the entire set of nondominated solutions and effectively obtains the most preferred solution suitable for his/her preference structure.
In a paper published in Management Science in 1984, Korhonen, Wallenius, and Zionts presented the idea and method based on convex-cone dominance in the discrete Multiple Criteria Decision Making framework. In our current paper, we revisit the old idea from a new standpoint and provide the mathematical theory leading to a dual-cone based approach to solving such problems. Our paper makes the old results computationally more tractable. The results provided in the present paper also help extend the theory.
In problems related to evaluations of products or services (e.g. in customer satisfaction analysis) the main difficulties concern the synthesis of the information, which is necessary for the presence of several evaluators and many response variables (aspects under evaluation). In this paper the problem of determining and comparing the satisfaction of different groups of customers, in the presence of multivariate response variables and using the results of pairwise comparisons is addressed. Within the framework of group ranking methods and multicriteria decision making theory, a new approach, based on nonparametric techniques, for evaluating group satisfaction in a multivariate framework is proposed and the concept of Multivariate Relative Satisfaction is defined. An application to the evaluation of public transport services, like the railways service and the urban bus service, by students of the University of Ferrara (Italy) is also discussed.
This article provides a review of the literature on interactive MCDM approaches, which use convex cones as a means of representing the decision maker's preference structure. We discuss the assumptions that are made about the decision maker's underlying preference relation and cover the basic theory on the convex cones approach. We review relevant studies that appear in the literature and state future research areas that await further attention.Keywords:multicriteria decision making;interactive approaches;convex cones approach;quasiconcave value function
The development of large-scale civil engineering projects requires the collaboration of experts from different specialties. However, conflicts and disputes occur regularly during the entire life cycle of large-scale projects due to the complex structure of organization and the different types of expertise involved. If these disputes or conflicts cannot be resolved or addressed quickly and effectively, the collaborative mode of the participants can be affected, creating a hostile environment in which progress of the project will slow to a halt. Therefore, better methodologies are needed to improve the collaborative process and to create more effective, efficient, and sustainable solutions to conflicts, This paper presents a methodology for facilitating the negotiation of conflicts during the development of large-scale civil engineering projects. Two fundamental theories are used in this methodology: (i) game theory, which is the study of players' actions based on the premise that the decision of any player can affect the payoff of all players; and (2) negotiation theory, which is the study of the interactions between parties, designed to reconcile their differences and produce a settlement. The strong support given by these two theories to negotiators is highlighted in the following observations. First, people need to negotiate because of their conflicting interests, From the negotiator's point of view, expressing the interests of all participants is very important in conflict resolution and can be accomplished by following the principles outlined in negotiation theory. Once the interests have been expressed correctly, the influence of positions or of conflicting interests on the overall negotiation outcome is evaluated using game theory. Based on these two fundamental theories, this paper presents a collaborative negotiation methodology and a computer agent named CONVINCER, which incorporates that methodology to facilitate or mediate the negotiation of conflicts in large-scale civil engineering projects. Hypothetical case studies and resolution processes demonstrate the effectiveness of the CONVINCER agent in conflict resolution. Results of applying the methodology to different scenarios also show that the CONVINCER agent provides efficient, effective, and sustainable solutions, thus improving the conflict resolution paradigm in the A/E/C industry.
Measuring scientific performance is currently a common practice of funding agencies, fellowship evaluations and hiring institutions. However, as has already been recognized by many authors, comparing the performance in different scientific fields is a difficult task due to the different publication and citation patterns observed in each field. In this article, we defend that scientific performance of an individual scientist, laboratory or institution should be analysed within the corresponding context and we provide objective tools to perform this kind of comparative analysis. The usage of the new tools is illustrated by using two control groups, to which several performance measurements are referred: one group being the Physics and Chemistry Nobel laureates from 2007 to 2012, the other group consisting of a list of outstanding scientists affiliated to two different institutions.
Abstract Various preference-based multi-objective evolutionary algorithms have been developed to help a decision-maker search for his/her preferred solutions to multi-objective problems. In most of the existing approaches the decision-maker preferences are formulated either by mathematical expressions such as the utility function or simply by numerical values such as aspiration levels and weights. However, in some sense a decision-maker may find it easier to specify preferences visually by drawing rather than using numbers. This paper introduces such a method, namely, the brushing technique. Using this technique the decision-maker can specify his/her preferences easily by drawing in the objective space. Combining the brushing technique with one existing algorithm PICEA-g, we present a novel approach named iPICEA-g for an interactive decision-making. The performance of iPICEA-g is tested on a set of benchmark problems and is shown to be good.
Purpose: This paper aims at improving inefficiency of an existing posterior preference articulation method proposed for dual response surface optimization. The method generates a set of non-dominated solutions and then allows a decision maker (DM) to select the best solution among them through an interval selection strategy. Methods: This paper proposes an iterative posterior preference articulation method, which repeatedly generates the predetermined number of non-dominated solutions in an interval which becomes gradually narrower over rounds. Results: The existing method generates a good number of non-dominated solutions not used in the DM`s selection process, while the proposed method generates the minimal number of non-dominated solutions necessitated in the selection process. Conclusion: The proposed method enables a satisfactory compromise solution to be achieved with minimal cognitive burden of the DM as well as with light computation load in generating non-dominated solutions.
Multiobjective combinatorial problems are commonly encountered in practice and would benefit from the development of metaheuristics where the search effort is interactively guided towards the solutions favored by the decision maker. The present study introduces such an interactive genetic algorithm designed for a general multiobjective combinatorial framework and discusses its behavior in simulations on the multiobjective knapsack problem. The evolution strategies being employed reflect the multiobjective nature of the problem. The fitness of individuals in the population is estimated on the basis of preference information elicited from the decision maker, and continuously updated as the algorithm progresses. The presented results indicate that the algorithm performs well when simulated against decision makers with different underlying utility functions.
In the research area of multiple criteria decision making, very few publications exist that explicitly design the simulation of a decision maker (DM) in an interactive approach. For this reason, we outline some methods widely used in the literature to identify common assumptions of simulating the DM's responses and the required input preference information. Our paper aims at covering the identified gap by introducing experimental concepts. Such concepts are used for theoretical analyses of a combined search-and-decision-making procedure. Simulating the DM is a fruitful idea because the algorithm can be tested without integrating a human decision maker. Finally, we conduct experiments based on the proposed settings for a multiobjective inventory routing problem, which is a relevant and challenging logistic problem. Copyright © 2014 John Wiley & Sons, Ltd.
We develop an interactive partitioning approach for solving the multiobjective decision making problem of a decision maker (DM) who has an implicit general monotone utility function. The approach reduces feasible solution space using the DM's preferences. Hypothetical solutions called partition ideals (PIs) that dominate portions of the efficient frontier are generated and those that are inferior to a feasible solution are used to eliminate the dominated regions. We investigate the issues in representation of the reduced feasible solution space. We develop procedures for locating PIs and measuring the size of feasible solution space. We incorporate these ideas into an approach that converges to a neighborhood of the most preferred solution of the DM. We demonstrate the approach on an example problem.
Multicriteria decision making (MCDM) can provide an efficient mean for considering various and conflicting objectives to reveal the alternative that maximizes the decision maker's (DM) utility. In this paper, we propose a new interactive MCDM method for implicit alternatives to help a DM obtain a most preferred solution. We employ a Tchebycheff function to generate weights for objectives consistent with the DM's responses to pairwise comparisons between alternatives and present a mixed integer linear programming formulation to generate these weights. Thus, we approximate the DM's utility function by a Tchebycheff function and generate weights consistent with the DM's responses. We test our approach with different true utility functions on various sized multiple criteria linear programming problems. The computational results show that even with non-Tchebycheff true utility functions, our method can generate alternatives very close to the optimal solution with few questions. The comparison of our results with other methods reveals its advantages. Copyright © 2013 John Wiley & Sons, Ltd.
The decision to acquire a new information technology poses a number of serious evaluation and selection problems to technology managers, because the new system must not only meet current information requirements of the organisation, but also the needs for future expansion. Tangible and intangible benefits factors, as well as risks factors, must be identified and evaluated. The paper provides a review of ten major evaluation categories and available models, which fall under each category, showing their advantages and disadvantages in handling the above difficulties. This paper describes strategic implications involved in the selection decision, and the inherent difficulties in: (1) choosing or developing a model, (2) obtaining realistic inputs for the model, and (3) making tradeoffs among the conflicting factors. It proposes a conceptual framework to help the decision maker in choosing the most appropriate methodology in the evaluation process. It also offers a new model, called GAHP, for the evaluation problem combining integer goal linear programming and Analytic Hierarchy Process (AHP) in a single hybrid multiple objective multi-criteria model. A goal programming methodology, with zero-one integer variables and mixed integer constraints, is used to set goal target values against which information technology alternatives are evaluated and selected. AHP is used to structure the evaluation process providing pairwise comparison mechanisms to quantify subjective, nonmonetary, intangible benefits and risks factors, in deriving data for the model. A case illustration is provided showing how GAHP can be formulated and solved.
We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations.Journal of the Operational Research Society (2006) 57, 532–540. doi:10.1057/palgrave.jors.2602019 Published online 29 June 2005
In a recent paper we presented a test, based on pairwise preference information, to identify to which class of functions (linear, quasi-concave, or neither) a decision-maker's (implicit) value function belongs. In this note we investigate the power of the test. Some improvements to the test are also suggested.
We consider a decision maker (DM) who has a set of possible decision alternatives, from which one (a 'best') is to be chosen. However, all decision alternatives are not at the DM's disposal initially, nor is full knowledge of his/her utility/value function. Therefore, the DM evaluates only the available subset of all decision alternatives, from which he/she chooses a most preferred one. Obviously, this decision is not necessarily 'globally' best. Two natural questions arise: How good is the most preferred solution? What are the chances of finding better solutions by considering additional alternatives? We describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically.
An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.
An interactive method is presented for solving a discrete alternative multiple criteria problem under certainty. The method is based on the approach of Zionts and Wallenius A computer program embodying the method has been written, and the results to date have been favorable. Extensions to the case in which some of the criteria are not readily quantifiable are also considered.
In this paper, we propose a new visual interactive method for solving discrete multiple criteria problems. The method is based on the use of a reference direction, which is determined by the aspiration levels for the criteria specified by the decision maker. The reference direction is projected onto the set of efficient alternatives. A subset found in this way is presented to a decision maker in a visual form using computer graphics. He can choose any efficient alternatives he pleases.We need notmake any assumptions about the properties of the utility function.The method has been implemented on an IBM/PC1 microcomputer. The name of the program is Vimda (a Visual Interactive Method for Discrete Alternatives).
Since 1971 conjoint analysis has been applied to a wide variety of problems in consumer research. This paper discusses various issues involved in implementing conjoint analysis and describes some new technical developments and application areas for the methodology.
An interactive approach is developed to help decision-makers (DMs)
find the best alternatives with few questions without making stringent
assumptions about their behavior. Theories and procedures are developed
for ranking alternatives and eliminating suboptimal ones, assuming that
the DM can respond to tradeoff- and paired-comparison questions. It is
assumed that the DM wishes to maximize an unknown quasiconcave utility
function for discrete multiple-criteria decision-making (MCDM) problems.
Several tests are developed based on convex dominating cones. Optimality
conditions for discrete MCDM problems are given for extreme, nonextreme,
and convex-dominated points without requiring the DM to enumerate the
remaining set of discrete alternatives. These optimality conditions are
based on a branching technique which converts nonextreme points to
extreme points. This substantially reduces the number of questions asked
of the DM. Finally, an exact discrete MCDM method is developed