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The multiple objective decision making problem arises when two or more non‐comparable objective functions are to be simultaneously optimised. There is a definite trend towards utilising interactive techniques for solving the multiple objective decision making problem. Interactive techniques allow the involvement of the DM throughout the decision process. In this paper we first provide a brief overview of multiple objective decision making, and then give a survey of literature dealing with interactive multiple objective decision making from 1965 to 1988.

This chapter presents two multicriteria optimization models with bi and triple objectives solved with weighted-sum approach. Solved problems are allocation of personnel in a health care institution. To deal with these problems, mixed integer programming formulation has been applied. Results have shown the impact of problem parameter change for importance of the different objectives. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method.

This chapter proposes a fuzzy approach to forecasting using a financial data set. The methodology used is multiple objective linear programming (MOLP). Selecting an individual forecast based on a single objective may not make the best use of available information for a variety of reasons. Combined forecasts may provide a better fit with respect to a single objective than any individual forecast. We incorporate soft constraints and preemptive additive weights into a mathematical programming approach to improve our forecasting accuracy. We compare the results of our approach with the preemptive MOLP approach. A financial example is used to illustrate the efficacy of the proposed forecasting methodology.

With the use of meta-goal programming, a portfolio model, based on Morningstar Stock Sector and Morningstar Bond Sectors, is developed. These sectors are part of an indexed mutual fund for stock and for bonds. The asset allocation is based upon a set of four meta-goals: (1) forecasted earnings growth, (2) forecasted revenue growth, (3) unwanted deviation of absolute deviation for the risk for stock investments, and (4) unwanted deviation of absolute deviation for the risk for bond investments.

This chapter presents two optimization multicriteria models (bi and triple objective) using a lexicographic approach. Solved models are formulated as assignment of workers to different jobs or services of a real hospital, taking into account the available budget and requirements of each job. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method for mixed integer mathematical programming.

Airspace sectorization is an important task, which has a significant impact in the everyday work of air control services. Especially in recent years, because of the constant increase in air traffic, existing airspace sectorization techniques have difficulties to tackle the large air traffic volumes, creating imbalanced sectors and uneven workload distribution among sectors. The purpose of this paper is to propose a new approach to find optimal airspace sectorization balancing the traffic controller workload between sectors, subject to airspace requirements.

A constraint programming (CP) model called equitable airspace sectorization problem (EQASP) relies on ordered weighted averaging (OWA) multiagent optimization and the parallel portfolio architecture has been developed, which integrates the equity into an existing CP approach (Trandac et al., 2005). The EQASP was evaluated and compared with the method of Trandac et al. (2005), according to the quality of workload balancing between sectors and the resolution performance. The comparison was achieved using real air traffic low-altitude network data sets of French airspace for five flight information regions for 24 h a day and the Algerian airspace for three various periods (off peak hours, peak hours and 24 h).

It has been demonstrated that the proposed EQASP model, which is based on OWA multicriteria optimization method, significantly improved both the solving performance and the workload equity between sectors, while offering strong theoretical properties of the balancing requirement. Interestingly, when solving hard instances, our parallel sectorization tool can provide, at any time, a workable solution, which satisfies all geometric constraints of sectorization.

This study can be used to design well-balanced air sectors in terms of workload between control units in the strategic phase. To fulfil the airspace users’ constraints, one can refer to this study to assess the capacity of each air sector (especially the overloaded sectors) and then adjust the sector’s shape to respond to the dynamic changes in traffic patterns.

This theoretical and practical approach enables the development and support of the definition of the “Air traffic management (ATM) Concept Target” through improvements in human factors specifically (balancing workload across sectors), which contributes to raising the level of capacity, safety and efficiency (SESAR Vision of ATM 2035).

In their approach, the authors proposed an OWA-based multiagent optimization model, ensuring the search for the best equitable solution, without requiring user-defined balancing constraints, which enforce each sector to have a workload between two user-defined bounds (W_min, W_max).

This chapter presents selected multiobjective methods for multiperiod portfolio optimization problem. Portfolio models are formulated as multicriteria mixed integer programs. Reference point method together with weighting approach is proposed. The portfolio selection problem considered is based on a multiperiod model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to allocate the wealth on different securities to optimize the portfolio expected return, the probability that the return is not less than a required level. Multiobjective methods were used to find tradeoffs between risk, return, and the number of securities in the portfolio. In computational experiments the data set of daily quotations from the Warsaw Stock Exchange were used.

The purpose of this study is modelling of a problem of policing strategy order using a multicriteria method.

For the construction of the impact matrix strategies under the reduction of crime rates, considering a portfolio of crimes, a questionnaire applied to specialists was used. In a second moment, defined the criteria and strategies to be ordered, the multicriteria PROMETHEE II method was used, which with the help of the Visual PROMETHEE software, emulated the systematised data in the impact matrix and produced the final ordering of the most efficient strategies, in the fight against crime, in the perception of decision makers.

As a result, this research revealed that radio patrol, when used in a non-randomised manner, is the most effective policing strategy in reducing the 18 criminal demands studied in the perception of decision makers after data emulation with the PROMETHEE II method.

As research implications, it can be inferred that the use of multicriteria methods in the modelling of problems in public security area can contribute to the rationalisation of use of the available means in the fight against crime in large cities. This research showed that it is possible to use customised policing strategies to absolute reality.

The practical impact of this research lies in optimising the resources available to law enforcement agencies in the fight against crime in general.

It can be inferred that by choosing appropriate strategies to combat local crime, there is a direct implication in optimising the resources that the government makes available to police agencies. This optimisation allows pressure reduction under the public budget for more features. The model for choosing more effective strategies contributes to local crimes decrease, increasing the sense of the population security.

The originality lies in filling a gap in the literature with the elaboration of the impact matrix of policing strategies in reducing criminal indices and in their associated use in ordering strategies through a multicriteria method. This study contributed to applied police intelligence.

This study aims to deal with a project portfolio selection problem aiming to maximize the net present value of the project portfolio and minimize the resource usage variation between successive time periods.

A bi-objective mixed integer programming model is presented under resource constraints. The parameters related to outlays and net cash flows of existing and new projects are considered to be uncertain. An augmented ε-constraint (AUGMECON) method is used to solve the proposed model, and a fuzzy approach is used to find the most preferred Pareto-optimal solutions among those generated by AUGMECON method. The effectiveness of the proposed solution method is compared with three other multi-objective optimization methods. Finally, some sensitivity analyses are performed to assess the effect of changing a number of parameters on the values of objective functions.

The proposed approach helps corporations make optimal decisions for rebalancing their project portfolio, through launching some new candidate projects and upgrading some of the existing projects.

A novel bi-objective optimization model is proposed for designing a project portfolio problem under budget constraints and profit risk controls. Two types of projects including existing and new projects are considered in the problem. Minimization of resource usage variation between successive periods is considered in the model as one objective function. An AUGMECON method is used to solve the proposed bi-objective mathematical model. A fuzzy approach is applied to find the best Pareto-optimal solutions of AUGMECON method. Results of the proposed solution approach are compared with three other multi-objective decision-making methods in different numerical examples.

This study aims to focus on the application of a multiple criteria decision analysis (MCDA) method to compare results presented by the Integrated Goals System based on the 12th edition of the Integrated Public Safety Areas (IPSAs) Award, which achieved goals established for Strategic Crime Indicators for the state of Rio de Janeiro, Brazil. The main objective of this research was to limit the compensatory effects of classification criteria on IPSAs that have achieved goals established for crime indicators by applying the MCDA method.

The methodology was based on the application of MCDA. The MCDA method selected and used was ELECTRE III, being implemented by J-Electre software.

Compared to results of the current method, the results of the ELECTRE III method showed a 94.87 per cent change in ranking positions revealed via the SIM method. This finding denotes the elimination of compensatory effects of the criteria. As a consequence, it can be affirmed that the application of resources by IPSA managers to reduce the prevalence of a single strategic crime indicator is no longer a success factor for awarding in the established goal system.

As limitations, it is possible to indicate the time cut used to carry out the research. The research may be extended to other issues of the productivity award.

The methodology applied with the use of ELECTRE III revealed that the government could reduce the cost with the incentive program to reduce criminal indices.

As the MCDA method is based on a binary pairwise comparison system, the methodology imposes a change of attitude on local managers fighting crime to reduce crime indicators and to consequently build a local sense of safety in IPSAs.

This research fills a gap in the literature because there are few studies using the MCDA method in the field of public security. The value of the work lies in the creation of a method that gives the decision-maker, of the law enforcement agency, an alternative to improve the process of rewarding by productividad of the integrated areas of public security.