Multiple Objective Programming Research Articles

Merging decision-making units in the simultaneous presence of desirable and undesirable factors

This paper is devoted to applying the inverse Data Envelopment Analysis (InvDEA) in the simultaneous presence of desirable and undesirable factors. One of the most common ways to improve units’ performance in the business environment is through activity synergies called units’ merging. The present study models how to identify the inherited input/output from the units participating in the merger process to achieve the desired efficiency goal. The proposed models are established based on the InvDEA approach and multiple-objective programming tools. Sufficient conditions to estimate desirable and undesirable data are obtained using Pareto solutions to multi-objective programming problems. The theory extended in the study is explained by an application in the banking sector.

Balancing bank profits and nonperforming loans: a multiple objective programming approach

Balancing bank profits and nonperforming loans: a multiple objective programming approach

Topsis for multiple objective programming with rough decision set

Many optimization problems have competing objectives that require being optimized at the same time. These problems are called ?multiple objective programming problems (MOPPs)?. Real-world MOPPs may have some imprecision (roughness) in the decision set and/or the objective functions. These problems are known as ?rough MOPPs (RMOPPs)?. There is no unique method able to solve all RMOPPs. Accordingly, the decision maker (DM) should have more than one method for solving RMOPPs at his disposal so that he can select the most appropriate method. To contribute in this regard, we propose a new method for solving a specific class of RMOPPs in which all the objectives are precisely defined, but the decision set is roughly defined by its lower and upper approximations. Our proposed method is a modified version of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). TOPSIS was chosen as the foundation for our method because it is one of the most widely applied methods for solving MOPPs. The basic concept underlying TOPSIS is that the compromise solution is closer to the ideal solution while also being farther away from the anti-ideal solution. The conventional TOPSIS can only solve MOPPs with precise (crisp) definitions of the two main parts of the problem. We extend TOPSIS to optimize multiple precise objectives over an imprecise decision set. The proposed approach is depicted in a flowchart. A numerical example is given to demonstrate the effectiveness of our proposed method to solve RMOPPs with a rough decision set at different values of objectives? weights and using different Lp-metrics.

A common weights multiplicative aggregation approach for composite indicators: the case of Global City Competitiveness Index

We propose a mathematical programming approach to assess a set of entities against a composite index. The weights used to construct the composite index are derived via optimization process. Specifically, we adopt the multiplicative method for the aggregation of the components (sub-indicators) of the evaluated index, which reduces the effect of compensation between the components. Also, we model the problem of identifying a common weighting scheme for the evaluated entities as a multiple objective programming (MOP) problem, with the performance of each entity being a distinct objective-criterion. This allows for comparisons and inferences between the assessed entities as a common ground is established. We stick to the concept of multiplicative aggregation by scalarizing the MOP problem using the weighted product method. Utilizing the multiplicative aggregation method in our modelling approach results in a nonlinear model that is scale invariant. However, using logarithms we show that is straightforwardly converted to a linear equivalent model, which is translation invariant. We examine whether the derived weighting scheme is unique, and in case there are alternative optimal solutions, we employ a max–min achievement function to identify a unique solution. We demonstrate our approach using synthetic datasets and compare it to other multiplicative approaches in the literature. We show that the proposed approach has neglective computational requirements and discriminates to a greater extent than those approaches with which we are compared, while at the same time provides a similar ranking. Similarities and dissimilarities in the results are justified. Since our approach is translation invariant, it enables us to apply it to cases where the data needs translation. We further illustrate our approach for such a case using the Global City Competitiveness Index, developed by Citigroup's Economist Intelligence Unit (EIU), which evaluates the competitiveness of 120 major cities worldwide.

How will ecosystem carbon sequestration contribute to the reduction of regional carbon emissions in the future? analysis based on the MOP-PLUS model framework

Carbon neutralization of land use and land cover (LULC) has become an important way for countries to cope with future climate change. Existing studies focus on the quantification and analysis of historical and current carbon storage and emissions but lack an understanding of future LULC carbon storage and emissions, which limits the practical guiding value of research findings for regional dynamic management and scientific decision-making. In this study, the temporal and spatial distribution patterns of carbon dynamics in different ecosystems, such as forest, cropland and grassland, in the West Liao River Basin (WLRB) since 1990 were quantitatively assessed. Grey multiple objective programming (G-MOP) and patch‑generating land use simulation (PLUS) models were used to predict the LULC distribution, carbon emissions and carbon storage under the sustainable development scenario (SDS) in the WLRB in 2030 and 2060, and a comparative analysis was performed with other development scenarios. The overall area of grassland and forest ecosystems showed an upwards trend from 1990 to 2020, while the area of farmland ecosystems slightly decreased. In the western part of the WLRB, net ecosystem production (NEP) showed high aggregation, and low NEP showed an aggregation effect in the urban area. Under the economic development scenario (EDS) in 2030 and 2060, cropland and impervious layers will be further expanded, carbon emissions will be the highest, and the carbon storage amount will be the lowest. Under the ecological protection scenario (EPS), the water area and forest area increased significantly, carbon emissions were the lowest, and carbon storage was the highest. Under the SDS scenario, the areas of cropland, forest, impervious layer and water body are moderate, and the carbon budget is better than that under the natural development scenario (NDS). Under these three scenarios, the barren area is lower than that of the natural development scenario. Considering the economic benefit, ecological benefit and carbon budget, the SDS scenario has the best performance. This study provides a new perspective for discussing the future carbon budget status of small-scale watershed areas and combines the goals of “sustainable development” and “dual carbon”. It provides a data-supported basis for discussing the diversified ecological compensation mechanism of the WLRB from the perspective of carbon neutrality as well as insights for the formulation of regional LULC optimization management policies.

Fuzzy Multi-Objective Optimization to Evaluate the Performance of Suppliers Taking Into Account the Visibility and Supply Chain Risk

Abstract Adequate and desirable connections between suppliers and customers necessitate an appropriate flow of information. Therefore, a promising and proper data collaboration in the supply chain is of tremendous significance. Thus, the study’s main objective is to provide multiple objective programming models under uncertain conditions to assess the performance of suppliers. To meet that aim, a case study for the reliability assessment of the presented model is carried out. That section is associated with supply chain visibility (SCV). Likewise, the likelihood of unpredicted and undesirable incidents involving supply chain risk (SCR) is taken into consideration. The intimate relation between visibility and risk of the supply chain is deemed efficient for the performance of the supply chain. Incoherence in maximization and minimization of SCR and SCV and other factors, including costs, capacity, or demand, necessitates multiple objective programming models to assess suppliers’ performance to accomplish the before-mentioned aims. The study’s results indicate the high reliability of the proposed model. Besides, the numeral results reveal that decision-makers in selecting suppliers mainly decrease SCR and then attempt to enhance SCV. In conclusion, the provided model in the study can be a desirable model for analyzing and estimating supplier performance with SCR and SCV simultaneously.

Preface to the Special Issue on Multidimensional Finance, Insurance, and Investment

In the literature, many researchers have investigated methods and procedures designed to solve problems in finance, insurance, and investment, formulated through analytical operational research models in a multidimensional framework that takes into consideration multiple conflicting and incommensurable decision objectives. To promote the development of multidimensionality within these research fields, the International Transactions in Operational Research has devoted a special issue to this subject. Topics of interest covered by this volume include: Multi-attribute portfolio selection, Multi-criteria decision aid in finance, Multiple objective programming in finance, Stochastic programming in finance, Option pricing, Portfolio analysis, Asset and liability management, Financial economics, Interest rate models, Bank management, Capital budgeting, Finance applications, Corporate governance, Insurance applications, Fuzziness and uncertainty in finance, Financial planning, and Financial engineering. This special issue attracted much interest and many submissions. After a rigorous peer review and selection process, we proudly announce that twenty-four papers have been included in this volume, covering a wide diversity of financial problems, application areas ranging from finance to insurance and investments, modelling, and solution methodologies. With more details, the following topics have been presented and discussed: volatility transmission analysis across international equity markets using multivariate fractional models; health insurance risk assessment using cognitive mapping and multiple criteria decision analysis; investment rating in commercial real estate; information game modelling in financial markets with multi-agent systems; efficiency of SRI and conventional mutual funds by a diversification-consistent DEA model; dynamics of social credit determinants using fuzzy cognitive mapping and system dynamics; measurement of multiscale dependence between Saudi and selected foreign stock markets using wavelets; volatility models using DEA; optimal strategies of contract-farming supply chain under the cooperative mode of bank-insurance; credit scoring methods in a decision support system of investment for peer-to-peer lending; the role of commodity futures in portfolio diversification; efficient frontier approximation with low-cardinality portfolios in the presence of the risk-free asset; penalty decomposition algorithms with greedy improvement for mean-reverting portfolios with sparsity and volatility constraints; bank performances under COVID‒19 using the inverse DEA efficiency approach; efficient credit portfolios under IFRS 9; firm ranking based on financial and diversity performance using multiple-stage un-weighted TOPSIS; sustainability efficiency and profitability efficiency in corporate social responsibility; omega portfolio models with dynamic return thresholds; multi-objective reference point techniques to optimize profitability-growth-risk in the non-life insurance industry; geometric compromise programming in portfolio selection; attractiveness index for foreign direct investments; crypto-assets in portfolio selection; augmented Lagrangean algorithms for optimal portfolio liquidation with market impact; and portfolio selection problem with real-world constraints under value-at-risk measure. We thank all colleagues and researchers who submitted their work for consideration and the anonymous reviewers whose work and suggestions were instrumental for completing the peer-review process and guaranteeing the quality of the accepted papers.

Optimization of the Territorial Spatial Patterns Based on MOP and PLUS Models: A Case Study from Hefei City, China.

Optimization of the territorial spatial patterns can promote the functional balance and utilization efficiency of space, which is influenced by economic, social, ecological, and environmental factors. Consequently, the final implementation of spatial planning should address the issue of sustainable optimization of territorial spatial patterns, driven by multiple objectives. It has two components-the territorial spatial scale prediction and its layout simulation. Because a one-sided study of scale or layout is divisive, it is necessary to combine the two to form complete territorial spatial patterns. This paper took Hefei city as an example and optimized its territorial spatial scale using the multiple objective programming (MOP) model, with four objective functions. A computer simulation of the territorial spatial layout was created, using the patch-generating land use simulation (PLUS) model, with spatial driving factors, conversion rules, and the scale optimization result. To do this, statistical, empirical, land utilization, and spatially driven data were used. The function results showed that carbon accumulation and economic and ecological benefits would be ever-increasing, and carbon emissions would reach their peak in 2030. The year 2030 was a vital node for the two most important land use types in the spatial scale-construction land and farmland. It was projected that construction land would commence its transition from reduced to negative growth after that time, and farmland would start to rebound. The simulation results indicated that construction land in the main urban area would expand primarily to the west, with supplemental expansion to the east and north. In contrast, construction land in the counties would experience a nominal increase, and a future ecological corridor would develop along the route south of Chaohu County-Chaohu Waters-Lujiang County-south of Feixi County.

SIMULATION OF ECOLOGICAL RISK IN BEIJING USING MOP-PLUS MODEL

Abstract. The accelerated urbanisation, threatening the integrity of ecological environment. The lack of future simulation in ecological risk assessment in current studies. Especially in metropolis, to address this problem, this study uses the Multiple objective programming (MOP) and the improved patch-generating land use simulation (PLUS) models to simulate land use in Beijing in 2035 under the Natural Development (ND) scenario and the Liveable City (LC) scenario; the changes in land types and land transfers under different scenarios are analysed. In addition, a landscape ecological risk assessment method was applied to analyse the ecological risks caused by land use in each scenario. The study found that, in general, the dominant trend of land use change in Beijing is the shift from construction land to ecological land. The spatial pattern of ecological risk is polarized from east to west, and the conversion of a large amount of built-up land to arable land or grassland, and the high vulnerability of arable land and grassland to human destruction, are the reasons for the continuous increase in ecological risk in Beijing. The area of construction land in the LC scenario is closer to the planned area than in the ND scenario, and the ecological risks faced by the LC scenario are slightly lower than those of the ND scenario. Therefore, it is reasonable to use the LC scenario to simulate the land use situation in Beijing in 2035.

Evaluating the future terrestrial ecosystem contributions to carbon neutrality in Qinghai-Tibet Plateau

China has proposed to achieve the carbon neutrality target by 2060. It is important for China to clearly understand the carbon sink of ecosystems. Most current studies focus on accounting for the carbon sink or carbon emission in the past and ignore the contribution of ecosystems to carbon neutrality in the future. The work presented in this paper projects land use changes in 2030 and 2060 under the business as usual (BAS), rapid economic development (RED), and ecological land protection (ELP) scenarios based on Multiple Objective Programming and GeoSOS-FLUS and calculates the carbon budgets and contributions of ecosystems to carbon neutrality in Qinghai during 2000–2060. The key findings are that the contributions of the terrestrial ecosystem to carbon neutrality in Qinghai are 9.92% (BAS), 10.03% (ELP) and 7.56% (RED) in 2030, and 3.23% (BAS), 3.28% (ELP) and 2.91% (RED) in 2060. These results indicate that the Qinghai ecosystem has carbon sink potential and the reduction of carbon emissions by humans is the core challenge in achieving carbon neutrality. Therefore, some recommendations have been made: 1) optimizing the land use structure to enhance the ecosystem sink in Qinghai; 2) continuing to implement the policies of ecological protection in Qinghai; 3) reducing the anthropogenic carbon emissions is the key to achieving carbon neutrality in 2060. This study not only offers data support and related policy recommendations to realize carbon neutrality goals but also provides a feasible method for future ecosystem contribution assessments under the goal of carbon neutrality.

An omega portfolio model with dynamic return thresholds

AbstractThe Omega ratio grants flexibility to a decision‐maker regarding the selection of a return threshold (τ). Although the return threshold can affect the effectiveness of the Omega portfolio, the literature has not soundly concluded how to determine it. In this paper, we develop a multiple objective programming model to generate time‐varying return thresholds by maximizing the τ value and maximizing the deviation between gain and loss, considering short sales and trading costs in portfolio rebalances. The empirical results using the daily returns of the composite stocks in the S&P 500 index over 13 years suggest that the proposed Omega (Max τ) model realizes higher performances than the widely applied portfolio models and the fixed‐τ Omega models under different rebalancing frequencies. The time‐varying return thresholds generated by our model capture the dynamics of the overall market and can be suitable for index enhancement.

A DANP-Based NDEA-MOP Approach to Evaluating the Patent Commercialization Performance of Industry–Academic Collaborations

The industry–academic collaboration (IAC) in developed and developing countries enables these economies to gain momentum in continuous innovation and, thus, economic growth. Patent commercialization is one major channel of knowledge flow in IAC. However, very few studies consider the flow of knowledge between industrial firms and universities. Moreover, ways that the patent commercialization performance of IACs can be evaluated are rarely discussed. Therefore, defining an analytic framework to evaluate the performance of IAC from the aspect of patent commercialization is critical. Traditionally, data envelopment analysis (DEA) models have widely been adopted in performance evaluation. However, traditional DEA models cannot accurately evaluate the performance of IACs with complex university–industry interconnections, the internal linkages, or linking activities of knowledge-flow within the decision-making units (DMUs), i.e., the IACs. In order to solve the abovementioned problems, this study defines a multiple objective programming (MOP)-based network DEA (NDEA), with weighting derived from the decision-making trial and evaluation laboratory (DEMATEL)-based analytic network process (ANP), or the DANP. The proposed analytic framework can evaluate the efficiency of decision-making units (DMUs) with a network structure (e.g., supply chains, strategic alliances, etc.) based on the weights that have been derived, based on experts’ opinions. An empirical study based on the performance of the patent commercialization of Taiwanese IACs was used to demonstrate the feasibility of the proposed framework. The results of the empirical research can serve as a basis for improving the performance of IAC.

Inverse data envelopment analysis with stochastic data

The inverse Data Envelopment Analysis (InvDEA) is an exciting and significant topic in the DEA area. Also, uncertain data in various real-life applications can degrade the efficiency results. The current work addresses the InvDEA in the presence of stochastic data. Under maintaining the efficiency score, the inputs/outputs-estimation problem is investigated when some or all of its outputs/inputs increase. A novel optimality concept for multiple-objective programming problems, stochastic (weak) Pareto optimality in the level of significance α ∈[0,1], is introduced to derive necessary and sufficient conditions for input/output estimation. Furthermore, the performance of the developed theory in a banking sector application is verified.

A multi-objective optimization strategy of steam power system to achieve standard emission and optimal economic by NSGA-Ⅱ

In this work, the models of desulfurization and denitrification are added to solve the problem of SO2 and NOX standardized discharge. The design and optimization strategy of steam power system (SPS) considering contaminant emissions reduction technology is proposed to achieve the trade-off between economic and environmental goals. Detailed superstructure networks of desulfurization based on wet limestone flue gas desulfurization and denitrification based on selective catalytic reduction were established and embedded in the SPS model. Then, based on this combined superstructure model, a mathematical formulation of multiple objective mixed integer nonlinear programming describing the SPS coupled with desulfurization and denitrification was established. The steam flow rate, outlet enthalpy, the consumption of the turbine power of the direct drive equipment and the electricity generated by the turbine, the flow rate and efficiency of desulfurization and denitrification are chosen as the optimization variables. The operating conditions and equipment parameters of the global system are optimized. Finally, the second-generation non-dominated sorting genetic algorithm (NSGA-II) was applied to obtain the Pareto optimization curve, exploring trade-offs between economic and environmental goals. Two case studies are used to assess the applicability and performance of the optimization formulation and solution algorithm.

Multi-objective programming for energy system based on the decomposition of carbon emission driving forces: A case study of Guangdong, China

Energy-related carbon emissions are increasing the rate of climate change, and controlling carbon emissions is a common challenge for the international public. Despite attempts to restrict the utilization of fossil energy and advancing technology for cleaner production, there has been little discussion on the determinants of change in carbon emissions for future scenarios and planning energy systems according to the analysis of low carbon development. In this study, a comprehensive energy optimization planning framework under a low-carbon mode is established. A framework based on the gray model (GM) and logarithmic mean Divisia index (LMDI) method are constructed to predict the emission mitigation potential and decompose the carbon emission driving factors. The decomposition results are key input prerequisites for the following energy optimization model: An interval parameter multiple-objective programming (IPMOP) optimization model, which is developed to support regional energy system administration by seeking the trade-offs among economic development, energy utilization, and environmental protection under multiple uncertainties. Furthermore, the proposed approach is applied to a case study in Guangdong, China. The results reveal that (a) the clean production effect (GDP per unit of atmospheric pollutants emission) would become the primary positive force for carbon emission increase, and the pollutant reduction effect (total atmospheric pollutants emission) would play the primary negative role; (b) the coal-dominated energy structure in Guangdong is expected to be transformed to a petroleum-dominated energy structure; (c) the GDP in Guangdong would steadily increase over time, but the pace of economic growth will decelerate, and the annual average growth rate of GDP for the coming fifteen years will be [3.67%, 4.26%]. This study provides a new pathway for policymakers to identify the determinants of carbon emission increase and to generate optimal solutions on a regional scale.

Ranking Function to Solve a Fuzzy Multiple Objective Function

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions

Technology roadmaps have been widely adopted as an important management tool during the past three decades after their invention by Motorola in the 1980s. Technology roadmapping processes can be integrated with a firm’s competence sets and play dominant roles in strategy definitions. Although the issue of how multiple objectives can be dealt with in technology roadmaps by including the uncertainties of the modern management environment is important, it has seldom been addressed. To remedy this, we aim in this research to propose a competence set expansion method based on fuzzy multiple objective programming (FMOP). An empirical study based on the roadmapping of silicon intellectual properties (SIPs) of automotive applications will be used to demonstrate the feasibility of the proposed roadmapping method. In the future, the proposed analytic technique can be integrated with the data mining results of academic research database, patent libraries, etc. The well-verified mathematical programming method can serve as a basis for research and development (R&D) strategy definitions by managers of high-technology firms as well as policy makers of governments.

A Comparative Analysis of Farmers’ Livelihood Strategies by Optimizing Resource Use in Farming Areas of Adamawa State, Nigeria and Eastern Uttar Pradesh, India: An Application of Sen’s Multi-Objectve Programming Approach

This paper explores the likelihoods of optimal allocation of resources as livelihood strategies for the farmers in Eastern Uttar Pradesh, India and Adamawa State, Nigeria. The study compared and determined the best production plan and resource allocation among food crop farmers in the two location of the study area Eastern Uttar Pradesh and Adamawa State, Nigeria. The objective of the study was to examine the socio-economic characteristics of food crop famers and to formulate alternative farm plans for improving farm economy. A multistage random sampling technique was used to select a total of 300 food crop farmers, the data for the study were randomly collected from 150 farmers from the eight district of Varanasi District of Eastern Uttar Pradesh and 150 from eight villages of the 21 local government area of Adamawa state. Structured questionnaire survey was used to obtained data from the respondents in the study area. Descriptive statistics and Sen’s Multi-Objective Programming (MOP) Model was used to analyze the data obtained from the field survey. The study shows that in Eastern Uttar Pradesh and Adamawa State, majority 96% and 68.7% were full time farmers with average mean of 46.5 and 31 years of age respectively. They had average agricultural farming experience of 27 years for farmers in Uttar Pradesh and 30.96 years of farming experience for farmers in Adamawa State Nigeria. Majority (94%) Eastern Uttar Pradesh and (85.3%) Adamawa State were male farmers and only 18.7% in Uttar Pradesh and 15.3% of the respondent had no formal education with average land holding of 0.73 (Uttar Pradesh) and 3.1 (Adamawa State) hectares. The result of the multiple objective programming reveals that the existing average income of ₹58168 (Uttar Pradesh) and ₹69348.97 (Adamawa State) was realized while the optimal income obtained from the multi-objective programming was ₹61251.40 Uttar Pradesh and ₹71979.95 Adamawa State which is 5.30 and 3.79 per cent higher over present income respectively. Consequently, for employment, the existing plan was 80.92 man days for Uttar Pradesh and 156.5 man days for Adamawa State while the optimal plan for the maximization of employment recommends 81.32 man days which represent 0.49 per cent increase for Uttar Pradesh and 162 man days which represent 3.51per cent increase for Adamawa State. Lastly for the minimization of fertilizer the existing plan allocated 218.97 kg for farmers in Uttar Pradesh and 282.15 kg for farmers in Adamawa State of fertilizer while the optimal plan for minimization of fertilizer use recommends 204 kg Uttar Pradesh and 218.03 kg Adamawa State which represents a decrease of 6.83 per cent and 22.73 per cent respectively. It is recommended among others that the food crop farmers be educated on allocation of resources for optimum utilization to raise their level of production and income for a better livelihood.

A multi-objective optimization approach for the selection of overseas oil projects

Most good quality overseas oil projects, high in investment returns and abundant in resources, are located in politically unstable regions, where competing objectives present great challenges for investors to make informed decisions. Moreover, most of the existing models are single objective and do not adequately incorporate the unique characteristics of overseas oil investment. To bridge these gaps, this study develops a Non-linear Multi-objective Binary Program (NMBP) to optimize the investment portfolios under three competing objectives. A solution algorithm is developed to solve this multiple objective program by integrating Non-dominated Sorting Genetic Algorithm II (NSGA-II) with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). NSGA-II searches for the pareto set of optimal investment portfolios and TOPSIS determines the best compromise solution based on the investors’ preferences. Finally, China’s oil investment in the Belt and Road Initiative countries is taken as a case study to demonstrate the feasibility and effectiveness of the proposed approach.

Integrating fuzzy goal programming and data envelopment analysis to incorporate preferred decision-maker targets in efficiency measurement

Data envelopment analysis (DEA) is a nonparametric frontier assessment method used to evaluate the relative efficiency of similar decision-making units (DMUs). This method provides benchmarking information regarding the removal of inefficiency. In conventional DEA models, the view of the decision maker (DM) is ignored and the performance of each DMU is solely determined by the observations retrieved. The current paper exploits the structural similarity existing between DEA and multiple objective programming to define a model that incorporates the preferences of DMs in the evaluation process of DMUs. Given the potential unfeasibility of the input and output targets selected by the DM, the model defines an interactive procedure that considers minimum and maximum acceptable objective levels. Given the feasible levels located closer to the targets selected by the DM, a program improving upon the feasible allocations is designed so that the suggested benchmark approximates the requirements fixed by the DM as much as possible. A real-life case study is included to illustrate the efficacy and applicability of the proposed hybrid procedure.