A multi-objective multi-period stochastic programming model for public debt management

While raising debt on behalf of the government, public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the uncertainty with regard to the future state of the economy. In this paper, we explicitly consider the underlying uncertainties with a complex multi-period stochastic programming model that captures the trade-offs between the objectives. The model is designed to aid the decision makers in formulating the debt issuance strategy. We apply an interactive procedure that guides the issuer to identify good strategies and demonstrate this approach for the public debt management problem of Turkey.     

Fuzzy goal programming approach to multilevel programming problems

The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.     

Acceptable consistency of aggregated comparison matrices in analytic hierarchy process

The analytic hierarchy process is a method for solving multiple criteria decision problems, as well as group decision making. The weighted geometric mean method is appropriate when aggregation of individual judgements is used. This paper presents a new proof which confirms the property that if the comparison matrices of all decision makers are of acceptable consistency, then the weighted geometric mean complex judgement matrix (WGMCJM) also is of acceptable consistency. This property was presented and first proved by Xu (2000), but Lin et al. (2008) rejected the proof. We also discuss under what conditions the WGMCJM is of acceptable consistency when not all comparison matrices of decision makers are of acceptable consistency. For this case we determine the sufficient condition for the WGMCJM to be of acceptable consistency and provide numerical examples. For a special case of two decision makers with 3 × 3 comparison matrices we find out some additional conditions for the WGMCJM to be of acceptable consistency.     

Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.     

A simulated annealing approach for reliability‐based chance‐constrained programming

The chance‐constrained programming (CCP) is a well‐known and widely used stochastic programming approach. In the CCP approach, determining the confidence levels of the constraints at the beginning of solution process is a critical issue for optimality. On one hand, it is possible to obtain better solutions at different confidence levels. On the other hand, the decision makers prefer to simplify their choices instead of grappling with the details such as determining confidence levels for all chance constraints. Reliability is an effective tool that enables the decision maker to look over the system integrity. In this paper, the CCP is considered as a reliability‐based nonlinear multiobjective model, and a simulated annealing (SA) algorithm is developed to solve the model. The SA represents different solution alternatives at the different reliability degrees to the decision makers by performing different confidence levels. Thus, the decision makers have the opportunity to make more effective decisions. Copyright © 2013 John Wiley & Sons, Ltd.     

Extended VIKOR method in comparison with outranking methods

The VIKOR method was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). The VIKOR method is extended with a stability analysis determining the weight stability intervals and with trade-offs analysis. The extended VIKOR method is compared with three multicriteria decision making methods: TOPSIS, PROMETHEE, and ELECTRE. A numerical example illustrates an application of the VIKOR method, and the results by all four considered methods are compared.     

Pairwise-comparison methods in multiple objective programming,with applications in a long-term energy-planning model

We propose to use pairwise comparisons within the framework of ideal-point or reference-point methods for multi-objective programming. The decision makers are requested to estimate the ratios which are acceptable for deviations from the ideal vector. Thereafter, we seek the nearest feasible solution using the Tchebycheff norm. In this paper we sketch the pairwise-comparison methods, some aspects of magnitude scaling, and the ideal-point methods. We show the results of our numerical experiments in long-term energy planning with nine objective functions. Finally, we present a preliminary evaluation of the combined method on the basis of its possible contribution to interactive decision analysis.     

Constrained optimization using multiple objective programming

In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems.     

A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.     

Solving multiple criteria problems by interactive decomposition

An interactive decomposition method is developed for solving the multiple criteria (MC) problem. Based on nonlinear programming duality theory, the MC problem is decomposed into a series of subproblems and relaxed master problems. Each subproblem is a bicriterion problem, and each relaxed master problem is a standard linear program. The prime objective of the decomposition is to simplify and facilitate the process of making preference assessments and tradeoffs across many conflicting objectives. Therefore, the decision-maker's preference function is not assumed to be known explicitly; rather, the decision maker is required to make only limited local preference assessments in the context of feasible and nondominated alternatives. Also, the preference assessments are of the form of ordinal paired comparisons, and in most of them only two criteria are allowed to change their values simultaneously, while the remaining (l–2) criteria are held fixed at certain levels.     

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.     

Using possibilistic logic for modeling qualitative decision: Answer Set Programming algorithms

A qualitative approach to decision making under uncertainty has been proposed in the setting of possibility theory, which is based on the assumption that levels of certainty and levels of priority (for expressing preferences) are commensurate. In this setting, pessimistic and optimistic decision criteria have been formally justified. This approach has been transposed into possibilistic logic in which the available knowledge is described by formulas which are more or less certainly true and the goals are described in a separate prioritized base. This paper adapts the possibilistic logic handling of qualitative decision making under uncertainty in the Answer Set Programming (ASP) setting. We show how weighted beliefs and prioritized preferences belonging to two separate knowledge bases can be handled in ASP by modeling qualitative decision making in terms of abductive logic programming where (uncertain) knowledge about the world and prioritized preferences are encoded as possibilistic definite logic programs and possibilistic literals respectively. We provide ASP-based and possibilistic ASP-based algorithms for calculating optimal decisions and utility values according to the possibilistic decision criteria. We describe a prototype implementing the algorithms proposed on top of different ASP solvers and we discuss the complexity of the different implementations.     

Multiple criteria decision making combined with finance: A categorized bibliographic study

This paper provides a categorized bibliography on the application of the techniques of multiple criteria decision making (MCDM) to problems and issues in finance. A total of 265 references have been compiled and classified according to the methodological approaches of goal programming, multiple objective programming, the analytic hierarchy process, etc., and to the application areas of capital budgeting, working capital management, portfolio analysis, etc. The bibliography provides an overview of the literature on “MCDM combined with finance,” shows how contributions to the area have come from all over the world, facilitates access to the entirety of this heretofore fragmented literature, and underscores the often multiple criterion nature of many problems in finance.     

Multi-choice goal programming with utility functions

Goal programming (GP) has been, and still is, the most widely used technique for solving multiple-criteria decision problems and multiple-objective decision problems by finding a set of satisfying solutions. However, the major limitation of goal programming is that can only use aspiration levels with scalar value for solving multiple objective problems. In order to solve this problem multi-choice goal programming (MCGP) was proposed by Chang (2007a). Following the idea of MCGP this study proposes a new concept of level achieving in the utility functions to replace the aspiration level with scalar value in classical GP and MCGP for multiple objective problems. According to this idea, it is possible to use the skill of MCGP with utility functions to solve multi-objective problems. The major contribution of using the utility functions of MCGP is that they can be used as measuring instruments to help decision makers make the best/appropriate policy corresponding to their goals with the highest level of utility achieved. In addition, the above properties can improve the practical utility of MCGP in solving more real-world decision/management problems.     

Compromise programming: A utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions

In this paper, compromise programming (CP) is viewed as the maximization of the decision maker’s additive utility function (whose arguments are the criteria under consideration) subject to an efficient frontier of criteria and the non-negativity constraints in a deterministic context. This is equivalent to minimizing the difference (‘distance’) between utility at the ideal point and utility at a frontier point on the criteria map, a meaningful statement as minimizing distances to the utopia is the ethos of compromise programming. By Taylor expansion of utility around the ideal point, the distance to the utopia becomes the weighted sum of linear and quadratic CP distances, which gives us the composite metric. While the linear terms pursue achievement, the quadratic ones pursue balanced (non-corner) solutions. Because some decision makers fear imbalance while others prefer large achievements even to the detriment of balance, the paper defines an aversion to imbalance ratio, so that the composite linear-quadratic metric should conform to this ratio depending on the decision maker’s preferences and attitudes. As the problem of selecting an appropriate metric is an ongoing issue in CP, the paper is a contribution to theory and practice. For the sole purpose of suggesting industrial applications, an example is developed.     

Integrating stochastic programming and decision tree techniques in land conversion problems

This paper is concerned with gradual land conversion problems, placing the main focus on the interaction between time and uncertainty. This aspect is extremely relevant since most decisions made in the field of natural resources and sustainable development are irreversible decisions. In particular, we discuss and develop a scenario-based multi-stage stochastic programming model in order to determine the optimal land portfolio in time, given uncertainty affecting the market. The approach is then integrated in a decision tree framework in order to account for domain specific (environmental) uncertainty that, diversely from market uncertainty, may depend on the decision taken. Although, the designed methodology has many general applications, in the present work we focus on a particular case study, concerning a semi-degraded natural park located in northern Italy.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

A comprehensive decision support model for the evaluation of eco-designs

Due to regulatory pressures from government and non-government bodies and public awareness of the need to protect the environment, incorporating sustainability concerns in product design has become a key strategic consideration in new product development. However, selecting an appropriate sustainable design solution is a challenging task. In addition to the fact that such a decision involves conflicting objectives, there is also the issue that environmental impact considerations can occur at all stages of a product’s life cycle. Modelling and assessing new product development and operations management from a life cycle assessment (LCA) perspective is becoming increasingly popular and highly important. However, on its own it is somewhat limited. This paper presents a dynamic approach that integrates LCA, fuzzy logic and analytical network process (ANP) to support the selection of environmental sustainable product designs. A numerical example is provided as an operational guideline on how to apply it to LCA of eco-designs. The results show that the proposed fuzzy ANP approach is a viable methodology and can be used as an effective tool for the evaluation of environmental sustainable product designs.