Multiple Criteria Decision Making in the New Millennium

Almost all living things, organizations, and technology change with time. As a consequence, our value systems, belief systems, and perceptions change with time and situations, and our understanding, attitudes, and methods toward solving non-trivial MCDM decision problems evolve with time. For instance, mathematical programming or optimal control of single criterion has evolved into that of multiple criteria. A number of solution concepts and techniques have been generated and developed. Another example is by incorporating the discovery of neural science and psychology into system theory, habitual domains (HD), the stealth human software that determines our lives, has been developed. Habitual domains systematically describe the dynamic changes of optimization of our objectives, perceptions and behaviors. Because of stable HD, human decisions, and behaviors, to a large degree, are predicable. However, human beings still have a very large capability for innovation and revolution. As the science and technology has been exponentially exploded in the last decades, our MCDM, including its formulation, solution concepts, solution techniques and computation, will be changed or evolved rapidly in order to be effective in this rapid changing world. In this talk, forces and paths of MCDM evolution will be described, and some emerging concepts of MCDM will be introduced.

The seven pillars of the AHP, some highlights of which are discussed in the paper, are: 1) ratio scales derived from reciprocal paired comparisons; 2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; 3) conditions for sensitivity of the eigenvector to changes in judgments; 4) homogeneity and clustering to extend the scale from 1–9 to 1- ∞; 5) additive synthesis of priorities, leading to a vector of multi-linear forms as applied within the decision structure of a hierarchy or the more general feedback network to reduce multi-dimensional measurements to a unidimensional normalized ratio scale, that is thus an absolute “dominance” scale, free of a measurement unit; 6) allowing rank preservation (ideal mode) or allowing rank reversal (distributive mode); and 7) group decision making using a mathematically justifiable way for synthesizing individual judgments which allows the construction of a cardinal group decision compatible with the individual preferences.

Multiple criteria tasks often involve high levels of subjectivity and uncertainty. Decision making also is usually dynamic, with many changes in environment along with new understanding on the part of decision makers. This makes it attractive to view multiple criteria support as support to a flexible learning process. Some recent multiple criteria decision aids have sought to provide this type of support.This paper considers a decision process including steps of problem structuring, decision strategy, preference elicitation, and analysis of results. Aspects of how various decision aids support each step of this process are reviewed. Suggestions for stronger support in various aspects of the decision process are provided.

Today, the issue of information overload is now commonly addressed in the popular press using phrases such as “Information Fatigue Syndrome.” Information overload is increasingly perceived as having an adverse affect on decision making. This is somewhat in contrast to much of the decision making literature which assumes that individuals start from a position of a lack of information or simply have sufficient information. This paper examines the perceived existence of information overload and its effect on decision making. A sample of MBA students from New Zealand and the USA responded to a questionnaire on this topic. Nearly all respondents held professional appointments in organizations. A quantitative and qualitative analysis of results is presented, concluding with a discussion of implications for MCDM.

A lot of multiple criteria decision-making methods require the use of weights or importance of coefficients. Usually authors of the methods do not mathematically define these coefficients. Therefore, their methods are only heuristic. In order to successfully elicit and apply the relative importance of criteria, it is necessary to have a rigorous definition for the coefficients. In this paper a mathematical definition of the assertion ‘a group of criteria A is more important than a group of criteria B with two sets of positive parameters‘ is given. Based on the definition the numerical relative importance coefficients are mathematically defined. The main objective of the paper is to demonstrate how to apply those notions in decision making in order to restrict the well-known Pareto set.

This paper describes a decision-maker (DM) centred approach to finding preferences in multiple criteria decision-making (MCDM). Its features include being “Decision-Interactive”: i.e. the DM is able to confirm or change scores at appropriate points in the process. Also it uses “Structured-Criteria”: i.e. the criteria trees are based on naturally formed clusters that are informed by Nomology, the science of the laws of the mind. It reports favourable responses by DMs to tests of the Decision-Interactive Structured-Criteria (DISC) approach. DMs generally prefer to put weights on criteria using a simple system based on sharing of 10 points to pairwise comparison methods or swing weights. Two forms of scoring alternatives were compared, one based on utility scores, the other a ratio (AHP-type) approach, whose scores are synthesised using a power function. DMs generally prefer the utility approach because it is easier to use. The ratio approach took more effort, but was preferred where there were few alternatives, or there was uncertainty about the upper and lower thresholds that determine the intervals within which utilities are scored, such as where some of the criteria are very intangible. The simpler utility approach is recommended as a first phase to reduce the number of alternatives. If it fails to provide a clear preference the ratio approach is then recommended, but only if there are four or fewer alternatives.

Numerical decision analysis, derived from statistical decision theory, is very well known. Verbal decision analysis, oriented toward so-called unstructured problems, where the qualitative and uncertain factors dominate, is a newer direction in decision theory and practice. Verbal and numerical decision analysis have been compared in an experimental setting, with groups of students. This paper presents the results of a comparison in the context of live practical tasks. Both approaches were attempted on two comparable choices, facing Russian and US government agencies, involving a choice between oil and gas transportation options in the Arctic. The resulting methodological insights are generalized into a systematic comparison of the strong and weak features of each approach.

Factors, which increase negotiation effectiveness challenge researchers to investigate methods supporting negotiation and to verify performance of negotiation support procedures. Increase of complexity of economic organizations as well as global range of their operation result in growing interest in negotiation involving remote parties coping with ambiguities of cross-cultural interactions. Trials to create distributed negotiation environment (DNE) answer the call for integrated set of tools, methods and procedures organized to support remote parties in negotiation. The DNE requires consideration of three functions of Distributed Negotiation Support System (d-NSS): communication, advice and mediation. Prototype d-NSS, which were presented in the literature, usually do not perform all three functions simultaneously. However, fully functional d-NSS should allow flexible switching between the three functions as well as to profit from the opportunity of their joint use. Such approach enables to reduce cost of tedious, expensive, time-consuming negotiation process. The paper reports on outcomes of a series of experiments dealing with DNE. The communication function was investigated in a distributed environment, initially asynchronous then synchronous. Advice and mediation functions were analyzed in experiments with well-structured data set. The results encourage efforts to include the issue of cautious use of a d-NSS in relevant cases as a topic in the pre-negotiation agenda.

This paper presents an intelligent decision support system based on neural network technology for multicriteria model selection. This paper categorizes the problem as simple, utility / value, interactive and outranking type of problem according to six basic features. The classification of the problem is realized based on a two-step neural network analysis applying back-propagation algorithm. The first Artificial Neural Network (ANN) model that is used for the selection of an appropriate solving method cluster consists of one hidden layer. The six input neurons of the model represent the MCDM problem features while the two output neurons represent the four MCDM categories. The second ANN model is used for the selection of a specific method within the selected cluster.

The recent interest in multiobjective combinatorial optimization problems resulted in the development of several exact algorithms and metaheuristics for the a posteriori solution of these problems. However, there are as yet no commonly used, reliable methods to compare approximations generated by these algorithms. In this paper, we introduce a new measure for this purpose: Integrated Convex Preference (ICP). We compare the performance of ICP with that of the existing measures using approximations generated by two different genetic algoithms for an NP-hard, bi-criteria parallel machine scheduling problem. Our results show that our measure outperforms existing measures previously used in the literature, and that ICP can handle approximate solution sets with diverse geometric features effectively.

There are practical tasks where plurality and redundancy of data that characterize objects, alternatives, situations, and their properties are peculiar. This paper considers the techniques for classifying the collection of objects, which are described with many qualitative attributes and sorted beforehand into some classes when a lot of copies of objects, values of attributes, and individual sorting rules can exist. These tools are based on the theory of multiset metric spaces and allow generating classes of qualitative objects and defining a general decision rule, which approximates the set of diverse individual rules.

Given a problem stated as a Multiple Objective Linear Integer Program, the Decision Maker might be interested in identifying the problem’s nondominated solutions and assigning them to a set of predefined categories. The authors suggest a new approach which uses an interactive “branch-and-bqund like” technique to progressively build the nondominated set, combined with the ELECTRE TRI method to classify the identified solutions. The ELECTRE TRI outranking model is a commonly used multiple criteria classification method which requires the Decision Maker to set many preference parameters. Since this is often a difficult task, the proposed method tries to infer some of these parameters from solution assignment examples based on holistic evaluations made by the Decision Maker.

Because of rapid change of our technology and environment, many problems we are facing are new, complex, and nontrivial. The solutions to these problems are usually outside our day-to-day experience, competence, or our habitual domains. Thus, they are fuzzy and challenging. In order to effectively solve this kind of fuzzy or challenging problem, we need to continually expand our competence or habitual domains so that we can make a good decision with confidence. This paper is to describe a holistic picture of using competence set analysis to solve this kind of decision problem. First, two types of competence set analysis, problem-oriented and skill-oriented, are introduced. Next, the concept of selecting optimal competence set that maximizes the net return is discussed. We then briefly describe a number of algorithms to find the optimal path for expanding our competence set. Finally, we gave some applications of expanding competence set with minimum cost.

The purpose of this paper is two-fold: (1) to present a new methodological framework for the design of database architectures in a distributed database environment using multiple criteria, and (2) to provide support for the Defense Information Systems Agency’s (DISA) guidelines in the segmentation of databases for use by DoD systems and programs. The first problem considered addresses design options in the partitioning of a single large database into multiple, smaller database segments. The second problem considers multiple data sources and determines a preferred subset of these to form a single, composite, virtual database while satisfying requirements and multiple criteria. The structured approach considered here is that of non-linear, zero-one mathematical programming (MP) to yield insight into the choice of designs possible given a set of system requirements and criteria.

Several methods for the processing of incomplete preference information in additive preference models have been proposed. Due to the lack of adequate decision aiding tools, however, only a few case studies have been reported so far. In this paper, we present PRIME Decisions, a decision aiding tool which supports the analysis of incomplete preference information with the PRIME method. PRIME Decisions also offers novel features such as decision rules and guided elicitation tours. The application of PRIME Decisions is illustrated with a case study on the valuation of a high-tech company.

Sensitivity analyses have been long used to assess the impacts of uncertainties on the outcomes. Several approaches have been suggested, but it has been problematic to get a quick overview of the total impact of the uncertainties. Here it is suggested that interval analyses could be used for global sensitivity analyses and a nuclear emergency case is used to illustrate the method. With intervals the decision maker can include all the possible uncertainties and quickly estimate their combined impact on the outcome. This is especially useful in high-risk decisions where this type of worst case analysis is essential. By varying the intervals it can also be examined which uncertainties have the greatest impact and thus which factors possibly need more consideration. A global sensitivity analysis reveals how stable the outcome is to many small simultaneous variations in the model.

It is the aim of this paper to present some sufficient and necessary conditions for Benson properly efficient solutions of nonconvex optimization problems via scalarization. We consider a nonconvex vector optimization problem on a real normed space, partially ordered by a pointed convex cone with a closed bounded base. We introduce a class of convex cone-monotone functions and characterize the Benson properly efficient elements as minimal points of such functions. These characterizations are presented without any convexity, cone convexlikeness or cone boundedness assumptions on the vector optimization problem.

A general approach to different types of scalarization in multicriteria optimization is discussed. Several special results which can be deduced from this approach are proved. These results refer to efficient, weakly efficient and properly efficient solutions of the vector optimization problem, where proper efficiency is defined in the sense of Geoffrion and turns out to be essential in approximating the efficient point set. The statements do not require convexity.

Giving a Multiobjective linear program with the interval-valued cost coefficients, this study proposed a decision procedure to support finding a final efficient decision. After defining the complete efficient solution set, a decision maker’s preference is articulated based on his/her ranking order and the levels of desire for the objectives if provided; otherwise, the principle of “more is better” in maximization problems is incorporated in the decision procedure.

In this paper we investigate the problem of finding the Nadir point for multicriteria optimization problems (MOP). We review some existing methods and heuristics and propose a new exact algorithm for three objective problems. We describe a method to compute Nadir values for the case of three objectives, based on theoretical results valid for any number of criteria. We also investigate the use of the Nadir point for compromise programming. We show the possibilities and limitations of finding all Pareto optimal solutions in this way

The paper presents a multiple objective genetic local search algorithm for multiple objective combinatorial optimization. The algorithm hybridizes recombination operators with local improvement heuristics. In each iteration of the algorithm a scalarizing function is drawn at random. Then, two solutions being good on the current scalarizing function are recombined and a local improvement heuristic is applied to the offspring. The paper describes also results of an experiment on the multiple objective 0/1 knapsack problem with multiple knapsack constraints.

Multiobjective combinatorial optimization problems are important tools for modeling real world decision problems. It is well known that they are very difficult to solve, therefore bounds on efficient solutions can contribute to obtaining good solutions quickly. We propose to generalize the notion of lower and upper bounds for single objective problems to lower and upper bound sets in multiobjective optimization. We distinguish the cases of polynomial and NP-hard single objective problems. We prove some general results on bound sets. Finally, we consider the 0-1 knapsack problem and report some numerical experiments.

Multiobjective combinatorial optimization problems are important tools for modeling real world decision problems. It is well known that they are very difficult to solve, therefore approximation of efficient solutions can contribute to obtaining overview solutions quickly. We consider the 0-1 knapsack problem with two objectives and we underline the problem difficulties. We propose a preprocessing using some properties to reduce the decision space with a simple local search-based method. Finally, we report and analyse numerical experiments.

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 this paper, three evolutionary algorithms have been discussed for solving three-criteria optimization problem of finding a set of Pareto-optimal program module assignments. An adaptive evolutionary algorithm has been recommended for solving an established multiobjective optimization problem. Moreover, a multi-criterion genetic algorithm and an evolution strategy have been considered. Some numerical results have been submitted.

We consider discrete co-operative group decision-making problems and suggest a method that is aimed at providing descriptive information about the acceptability of different decision alternatives. The method is a new variant of the Stochastic Multicriteria Acceptability Analysis (SMAA) method for discrete multicriteria decision-making problems with multiple decision makers. The new method is designed for problems where criterion information is completely or partially ordinal, that is, experts (or decision makers) have ranked the alternatives criterion-wise. The approach is particularly suitable for group decision making where either no or only partial preference information is available assuming that the group can agree on the shape of the underlying value function involving weights.

Nominal Group Technique (NGT) is a useful group decision making tool. The technique has been applied to solve various kinds of group decision making problems. The use of NGT can improve quality of virtually any kind of meeting by improving the group’s productivity and circumventing many of the problems inherent in group activities. The technique has the following steps: (i) Silent generation of ideas in writing, (ii) Round-robin recording of ideas, (iii) Serial discussion on the ideas, and (iv) Voting to select the most important ideas. In the 4th step, each participant needs to find out the most important 5 ideas. In the existing set-up of the methodology, there is no guidance to select the best 5 ideas, rather the participants need to do it by holistic approach. The present research proposes and validates the use of the Analytic Hierarchy Process (AHP), a popular MCDM tool, to guide the participants to choose the best 5 ideas. To show the validity, we considered the question “What are the major challenges to the mankind in the new millennium?” in a nominal group session. The first ten ranked challenges are picked up by applying the modified NGT.

The Analytic Hierarchy Process (AHP) is one of the most popular methods for multiple criteria decision-making that has been also applied for group decision-making. The recent modifications of the AHP to group decision analysis deal with equal importance of the individual members in the team, defined as a “power” of the member. However, not every member of the group is an expert in all fields and providing a single value that represents the power of the member regarding all criteria is inappropriate. Each member should have different power values for the different criteria.A new approach is proposed to aggregate the priorities concerning different criteria provided by members having number of different powers. The members submit judgments regarding the criteria, while the priorities are derived by standard prioritization method, used in the AHP. Then these priorities are aggregated using a new weighted geometrical mean approach. The main advantage of this approach is that it can deal with incomplete data. Examples are included to evaluate the improvements.

In this communication we consider a two person cooperative game involving unknown parameters. In our model, we suppose that the players know the domain where these parameters can take their values but completely ignore their behaviour., we propose a solution, which is based on the notion of Pareto optimality and takes into account the two aspects involved in this game: cooperation between the two players and the problem of decision making under uncertainty in the case of complete ignorance. We transform the problem of determination of this solution into the problem of determination of a couple of Pareto optimal solutions a special couple of dependent multiple criteria problems. We then give sufficient conditions for the existence of such couples and study the problem of their determination.

In this paper, a three-dimensional multi-criteria mathematical model for class based warehouse layout is proposed. This model is intended to increase the effective use of space and decrease the material handling cost through allocating items with different sizes and volumes to the most appropriate locations within the warehouse. This model incorporates the realistic constraints normally present in a real-world warehouse planning such as aisle structures, closeness relationships, loading/unloading docks, products orientation, number of stacking and safety. The capability of the model is shown by applying it to a warehouse layout design for a dynamic food manufacturing and packaging company.

This paper presents a mixed integer goal-programming model that provides a solution for planning component recovery from products with component commonality. The objective of the component recovery model is to determine the aggregate number of a variety of products to disassemble in order to economically fulfill the demand of a multitude of components, and yet have an environmentally benign policy of minimizing waste generation. A numerical example is presented to illustrate the methodology.

Some years ago Kaplan and Norton introduced the approach of the Balanced Scorecard to help executives implement their strategies. In contrast to many other well-known concepts the Balanced Scorecard is basically a multiple criteria approach to management. This paper demonstrates how some results of the MCDM research can be applied to support the Balanced Scorecard approach for supply chain management. In particular, Saaty’s AHP is used for budgeting, the “generalized criteria” defined by Brans, Vincke, and Mareschal are adapted to evaluate initiatives, the selection is supported with AIM proposed by Lotfi, Stewart, and Zionts, and the visualization is based on Korhonen’s “harmonious houses”.

Following preliminary investigation of soil contamination at 40 lightstations on Canada’s West Coast, the Canadian Coastguard — Pacific Region (CCG-PR) asked the Environmental Research Group at Royal Military College for help in consolidating the reports from different consultants, and prioritizing future work. The paper begins with an overview of the criteria and steps for evaluating contaminated sites, then describes the workshop held to help CCG-PR decide their criteria. The workshop, plus subsequent discussion, succeeded in creating a set of criteria, and scales for those criteria, onto which could be mapped the findings in the different environmental consultants’ reports. While the process achieved the aim of creating a tool that is understandable and will be used by CCG-PR, the high correlation between the criteria gave some concern to the author. The paper ends with a brief discussion of the correlation between the values awarded on the different CCG-PR criteria.

Multiple-criterion screening of environmental decision strategies in the framework of decision support system for water quality improvement is described. Screening technology is based on integration of diverse knowledge and information on water quality processes and on application of the Feasible Goals Method for exploration of the integrated model. The Feasible Goals Method provides graphic display of aggregated decision information that informs decision makers on efficient tradeoffs among screening criteria and helps to select preferable decision alternatives by identification of feasible goals directly on display. The DSS was developed on request of Russian Ministry of Natural Resources in the framework of the Federal program “Revival of the Volga River”.

We describe a real-life application of a multicriteria method in the context of repairing a landfill in Finland. Different reparation options were evaluated based on 13 criteria. For some criteria, cardinal measures with associated uncertainties were obtained. For other criteria, only ordinal (ranking) information was available. The problem was analyzed using the SMAA-O (Stochastic Multicriteria Acceptability Analysis with Ordinal criteria) multicriteria method, which is able to handle this kind of mixed data. The main results of the analysis are so-called acceptability indices for alternatives describing how large a variety of preferences support an alternative for the first rank or any given rank. The analysis also aided the decision makers in forming a new alternative as a combination of two original alternatives. This new alternative was identified as the preferred solution.

A variety of factors that are considered in personnel selection such as personality, leadership, and communication skills represent subjective and vague assessments. The fuzzy set theory appears as an effective tool to incorporate imprecise judgments inherent in the personnel selection process. In this paper, a fuzzy multi-criteria decision making (MCDM) framework based on the concepts of ideal and anti-ideal solutions is developed for selecting the most appropriate candidate from the short-listed applicants. The proposed method enables us to incorporate data in the forms of linguistic variables, triangular fuzzy numbers and crisp numbers into the personnel selection decision analysis. Linguistic variables are also used to indicate the criteria’s subjective importance weights assigned by the decision-makers. A comprehensive example illustrates the application of the multi-criteria decision analysis.

The policies Spanish Universities have followed for decades to hire and promote staff in University departments has caused serious structural problems, making it difficult to achieve quality teaching and research. MCDM is highly suitable in a situation, where a restricted budget has to be distributed between several units taking into account several objectives regarding the efficiency, internal equity, and quality of the system. The Málaga University authorities wished to ease this situation and commissioned this study which resulted in the following Goal Programming model.

Organisations are increasingly ranked according to their performance. This is usually done by some third party for general consumption. Two considerations then become important: first, that those making the ranking wish to appear to be doing so as objectively as possible; second, that it is desirable that the rationale for the relative performance measures are transparent and easily appreciated by the non-expert consumer.A simple weighted sum of attributes provides a measure that is easy to explain but there remains the “problem of weight determination. In other circumstances equivocation over the determination of parameter values is addressed via risk analysis. It is argued that it is similarly meaningful to give probability distributions for the values of weights. Consequently, it will not always be possible to discriminate between organisations and so some idea of clustering is more appropriate than ranking. Multidimensional Scaling may be used to present visually the dispositions of organisations according to the degree to which their relative performances are significantly different and performance clusters thereby determined.The method is illustrated by application to thirty international airlines.

The objective of this research is to search an alternative data mining approach that could outperform the current approaches in credit card portfolio management. A multiple criteria linear programming (MCLP) approach has been identified as the potential technology to predict the cardholders’ future behavior. The testing results on development samples showed that (i) the MCLP approach is fully controlled by the formulation; (ii) the 3000 is a stable sample size for the robustness in the separation process; and (iii) the MCLP model can be easily adapted from two-group to multi-group separation problems.

The paper presents insights into the process of optimising the parameters of a road-user responsive traffic signal controller with respect to several conflicting objectives. A multi-objective genetic algorithm (MOGA) was used to identify the parameter sets lying on the pareto-optimal front. This resulted in a collection of parameter settings that could be used to set the relative priority given by the signal controller to different road user groups (e.g. vehicles and pedestrians) when allocating green time dynamically in response to data from vehicle detectors and pedestrian push-button detectors.Issues covered in the paper include the choice and treatment of performance measures, the implementation of Pareto ranking to assign fitness, the use of niching to prevent convergence on a single area in the solution space and the use of stochastic simulation to obtain fitness values, with particular reference to the need to ensure robust results.Finally, the results of the use of the MOGA in this project will be presented.

An experimental application of a multifactorial model has been developed, at a Regional level, to acquire significant information on accidents in the workplace and to organize a systematic Information System for accident analysis and prevention. The structured analysis of eighteen accidents and their official investigations made a statistical analysis impossible, because of the limited number of cases, and the data were analyzed using a fuzzy classification multicriteria procedure which is oriented to identify a decision reference system. In this case, the procedure recognized closely interconnected reference elements and underlined critical combinations of factors, which are useful to orient preventive action. These results were considered significant and sufficient to stimulate the setting up of a new step of data acquisition and an information system development project for the prevention of workplace accidents.

Traditionally optimization of the Israeli power generation expansion planning was based on economic criteria only. However, the present situation requires the joint consideration of multiple criteria (economic, reliability, environmental, etc). In order to solve this multi-criteria optimization problem a new approach is proposed to select a predetermined number of “reasonable” alternatives from their vast initial set according to an arbitrary (but finite) number of optimization criteria and accounting for uncertainty factors. This approach uses an intuitive methodology developed to account for uncertainty. The methodology is based on performing multi-variant computations (MVC) and finding their “stable-optimal” solutions. The above mentioned is performed in a framework of a hierarchical multi-level system (HMLS) of MVC series, where each HMLS level includes a set of appropriate scenarios. These scenarios, at different HMLS levels, may reflect various versions of the used calculation methods and procedures (multi-criteria optimization techniques, modified to account for uncertainty; calculation algorithms and models to construct initial alternatives and their criteria assessment vectors, etc.) as well as varying conditions and parameter values, involved in the problem. Although the proposed approach was applied only to the Israeli power generation expansion planning, it may also be used in other similar problems.

Determining the naval force structure is a complicated decision making process, since it requires taking into consideration several conflicting factors. The purpose of this study is to propose two integrated models for determining the ship types combination for the TNSG by considering cost, force level, manpower, and the required potential factors needed to meet threat’s power in different warfare areas. Accordingly, we propose two integrated AHP and GP models. The comparison of the real cases is made with the results of the proposed two models. Thus, this study aims to supply a decision support system to the DM during the decision-making process for determining the naval force structure.