Multi-objective Decision-making Method Research Articles

A Bi-Objective Inventory Model for Strategic Items in a Stochastic Environment with Partial Shortage: A Base-Stock Approach

This paper suggests an ordering policy for strategic items. Based on the base stock policy, we modeled a bi-objective, multi-product inventory control system with partial back-ordering. The model aims to minimize total costs and maximize the average service level, considering stochastic constraints such as storage space, maximum allowable shortage, and maximum allowable lost sales to match real-world conditions. We used three Multi-Objective Decision-Making methods, namely Individual optimization, Desirability function, and Goal attainment, to solve the problem. TOPSIS method showed the Goal attainment method’s superiority over the others. The sensitivity analysis revealed that the mean of storage space had the most significant impact on objective functions. Also, increasing the back-order percentage can reduce the system’s total costs.

Mix proportion and microscopic characterization of coal-based solid waste backfill material based on response surface methodology and multi-objective decision-making

The mix proportion of multi-source coal-based solid waste (CSW) for underground backfilling affects transportation and support performance of backfill materials, and even the backfilling cost. In this study, the optimal mix proportion of desulfurization gypsum (DG), furnace bottom slag (FBS) and gasification fine slag (GFS) is determined by the Response Surface Methodology–Box Behnken Design (RSM-BBD). Then the fluidity, bleeding rate, 3-day strength, 7-day strength and preparation cost are evaluation indicators, the optimal mix proportion of backfill materials is determined by the multi-objective decision-making method (MDM). Finally, the microstructure of the backfill material with optimal mix proportion was studied by TGA, MIP, SEM–EDS and XRD. The results show that the mix proportion of CSW with the optimal comprehensive index is coal gangue (CG): coal fly ash (CFA): DG: FBS: GFS = 1:1.5:0.2:0.1:0.1, the mass concentration is 78%, and ordinary Portland cement (OPC)/CSW = 7.5%. The weight loss phenomenon of the backfill material with the optimal mix proportion occurs continuously during the heating process, mainly due to the evaporation of crystal water, structural water and hydroxyl water. There are dense narrow-necked pores in the backfill material, and the pore connectivity is poor. There is no hydration reaction occurs between CSW particles, and the strength increase of the backfill material mainly depends on the hydration reaction of cement. In ettringite, part of Al2O3 is replaced by SiO2, and part of CaSO4 is replaced by CaCO3. This study provides a reference for the engineering application of underground backfilling with multi-source CSW.

Green Residential Building Design Scheme Optimization Based on the Orthogonal Experiment EWM-TOPSIS

A multi-objective decision method is proposed based on the combining orthogonal test, entropy weight method (EWM) with TOPSIS (technique for order preference by similarity to an ideal solution) in this article. The method is more objective and efficient than traditional methods in the design of green residential buildings. A villa in Nanjing was taken as an example, and the cost, building energy consumption, and daylight factors were used as decision-making indexes. A total of six control factors were selected: terrain elevation, window area, building orientation, the opening ratio of exterior windows, roof structure, and window glass material. Each factor was designed with three levels. First, a design scheme index system was constructed, and the orthogonal experimental design was used to select representative design schemes. Then, the EWM and the TOPSIS method were used to determine the weight of each index, a comprehensive evaluation of the residential building design scheme was conducted, and, finally, the optimal scheme was confirmed via range analysis. The results show that the multi-objective decision-making model based on the orthogonal experiment EWM-TOPSIS is suitable for green residential building design and the optimal solution obtained is “15 m elevation, a 1200 × 1500 mm size vacuum glass, an orientation of 170° and an external window opening ratio 45% with a 40 mm thick expanded insulation board roof”.

A Two-Warehouse Lot Sizing Problem for Defective Items with a Completely Backlogged Shortage Under Limited Storage Capacity for Rented Warehouses

Determining an economic order quantity across inventory management is vital for any production or distribution company. There is an assumption in classical lot-sizing problems that the inventories are stored in a single warehouse with unlimited capacity. However, the mentioned assumption may be unrealistic, and in many markets, owned warehouses (OW) have limited capacity, therefore, in some cases, a rented warehouse (RW) is considered for storing goods to create more flexibility in terms of space capacity. In this study, we proposed a more realistic extension of a two-warehouse system, which intends to investigate an optimal EOQ considering limited storage for both OW and RW. This paper contributes to considering multiple RWs with limited capacity. For this purpose, a two-objective MINLP lot-sizing problem with a discreet period and finite time horizon is taken into account. The complexity of the model is to determine if there is a need to rent one or multiple warehouses regarding limited storage on OWs and RWs as well as budget restrictions to hire one or multiple warehouses. Also, all parameters are considered to be stochastic which means they follow a specific probability distribution. As the capacity of RWs and the total available budget to rent them are random parameters, the constraint on budget, as well as RW’s capacity in a period, can be formulated as chance constraints. Finally, four multi-objective decision-making methods namely Goal programming, Lp-Metric, Goal Attainment, and Augmented E-Constraint are utilized to solve the concerned problem. Then, the best method is chosen based on graphical, statistical, and TOPSIS analysis. Moreover, the Lagrangian Relaxation method is applied since solving this optimization model in large-size problems requires a considerable amount of time. In the end, the effect of changing the rates of three parameters on objective function values is evaluated through sensitivity analysis.

Evaluating and optimizing the ecosystem health of China’s Yellow River Basin based on emergy analysis and multi-objective decision method

Evaluating and optimizing the ecosystem health of China’s Yellow River Basin based on emergy analysis and multi-objective decision method

Enhancing Industrial Design Competitiveness: Research and Application of a Machine Tool Industrial Design Decision-Making Method Based on Product Family Architecture and Systematic Evaluation

This study employs an innovative industrial design decision-making approach based on the notion of product family architecture and structural equation modeling. The aim is to enhance the product competitiveness of machine tool enterprises, which is crucial for their development. Key domains within machine tool industrial design were systematically analyzed, leading to the creation of a design evaluation criteria system. Through quantitative data, the importance order of indicators at all levels was determined to enhance the overall competitiveness of product industrial design. First, teachers of relevant majors and professionals from machine tool companies completed a Likert scale questionnaire to validate the PFA-SEM hypothesis model. Next, a subjective–objective integrated weighting method was introduced to guide the ranking of multiple design elements. The feasibility of this method was confirmed by applying the Entropy-Based Multi-Objective Decision-Making Method (Technique for Order Preference by Similarity to Ideal Solution). These approaches helped achieve industrial design improvements in Heatking induction vertical hardening machines. This research aids in optimizing machine tool design, guiding design iterations, and serving as a reference for the development and optimization of other machine tool design solutions.

A multi-objective decision method for the network security situation grade assessment under multi-source information

Grade assessment of network security situation is summarized as a typical multi-index grade assessment problem. However, the existed methods for grade assessment of network security situation do not consider multi-source information such as the trust information among experts, the preference information among companies and heterogeneous information of companies. The above problems are unable to be solved through traditional assessment methods. The aim of this paper is to establish a novel multi-objective decision model for the grade assessment of network security situation under multi-source information. On the basis of describing the grade assessment problem of network security situation, the membership functions of four-type thresholds for the grades on attribute eigenvalue are put forward. Two trust information uncertainty degrees in social network are defined, and the trust transfer operator based on trust information uncertainty degree and multi-path trust integration method based on the variable weight function is proposed. Afterwards, a new method to generate the incomplete social network is used to identify the weights of experts. Then, a multi-objective decision grade assessment optimization model is further established to obtain the network security situation grades and grade discrimination based on the two-tuple linguistic operator. The proposed method provides a theoretical basis for constructing and testing the grade assessment of network security situation. Meanwhile, it develops the grade assessment system of advanced network security situation and improves the ability to protect network security.

Mechanical and Microstructural Properties of B4C/W Reinforced Copper Matrix Composite Using a Friction Stir-Welding Process

Copper metal matrix composites (CMC) are broadly employed in various applications in the fields of space, aviation, automobile and electronics industries. The welding of CMC in using conventional methods is very difficult and expensive due to its crystallographic nature. Friction stir welding (FSW) is a more prominent and reliable technique for welding than conventional methods. Therefore, this work is based on work with CMC material, which is prepared with a stir-casting technique. Pure copper (Cu) is reinforced with tungsten (W) and boron carbide (B4C) particles in different combinations and welded using the FSW process to study the mechanical and micro-structural properties. Multi-objective decision-making methods, such as the technique for order preference by similarity to ideal solution (TOPSIS) and grey relational analysis (GRA) are used to find optimal parameter combination. The experiments are planned according to the L 18 orthogonal array (OA) using the most influential parameters, such as reinforcement the percentage of B4C, tool rotational speed, welding speed, and axial force. The performance of outcomes is measured based on the responses such as tensile strength, hardness, and impact strength of the weld joint. Based on the results 15 % of B4C reinforcement, 900 RPM rotational speed, 15 mm/min welding speed and 6 kN axial forces are optimal for better mechanical strength in the welding with TOPSIS and GRA techniques. Additionally, scanning electron microscopic image (SEM) analyses were carried out for better understanding of weldments’ microstructure changes.

Decision Support Frameworks in Solid Waste Management: A Systematic Review of Multi-Criteria Decision-Making with Sustainability and Social Indicators

Waste management is a critical sector that needs to co-ordinate its activities with outcomes that impact society. Multi-criteria decision-making methods for waste management have been widely considered using environmental and economic criteria. With the development of new social regulations and concerns, sustainable waste management needs to additionally target socially acceptable practices. Despite the need to aid solid waste management decision-makers in contemplating the three pillars of sustainability, a limited inclusion of social impact has been found in the multi-objective decision-making literature. This study presents a systematic literature review of multi-criteria decision-making methods in solid waste management. The purpose of this study is threefold. (1) Emphasize the application of multi-objective decision-making methods, summarizing the models that have been used and their applications; (2) provide insights into the quantification of social aspects and their inclusion in decision-making methods, providing a list of social indicators collected from the reviewed studies; (3) offer an analysis of stakeholders’ involvement in waste management. From the articles investigated, one can observe the importance of understanding the local context in which the waste management system is located and the necessity of community consultation to recognize the potential challenges and improvements to solid waste management systems. Consequently, the involvement of stakeholders is crucial during the quantification process of social indicators. In alignment with the findings and needs raised by this review, a methodological approach is suggested for integrating optimization, social aspects, and stakeholders under a waste management context.

Two-Stage Multiobjective Decision-Making Method Based on Agricultural Water-Energy-Food Nexus: Case Study in Hetao Irrigation District, China

Due to the complex feedback cycle relationship among water resources, energy, and food, the agricultural water management mode and concept with a single object or two objects as the core can no longer meet the inherent requirements of the coordinated, sustained, and healthy development of economy and society. A two-stage multiobjective decision-making method based on a θ-dominance evolutionary algorithm (θ-DEA) is proposed for the optimization of agricultural systems with a water-energy-food nexus. First, the Pareto noninferior solution set of the model is obtained by the evolutionary algorithm based on θ-DEA. Then, the economic benefit and carbon emission of each solution are evaluated, and the optimal solution is selected by using the multiobjective decision-making method based on interval-valued hesitant fuzzy sets and the technique for order preference by similarity to ideal solution (TOPSIS). Through a case study of the Hetao Irrigation District (HID), the best optimization results are obtained when the carbon footprint is 4.16×109 kg CO2 eq, and the economic benefit is 8.09×109 yuan. The example shows that the model can well select the optimal allocation solution of water resources, which not only has high economic benefits and low pollution discharge but also meets the subjective wishes of decision-makers. The model has good practicability and stability.

Multi-objective optimal dispatch strategy for power systems with Spatio-temporal distribution of air pollutants

Accurate and effective pollutant emission control models are key in mitigating the environmental impact of energy supply systems. This paper proposes a novel high-dimensional multi-objective optimal dispatching strategy for power systems considering the spatial and temporal distribution of multiple pollutants. Firstly, a spatial and temporal distribution model of pollutants in thermal power plants is constructed, which is truly applicable to power dispatch. For modeling the pollution situation, the daily changes in the atmospheric boundary layer are taken into account, fully reflecting the pollutant dispersion characteristics of thermal power plants and improving the result accuracy. Next, a high-dimensional multi-objective optimization model is developed to simultaneously reduce the cost of power generation, carbon emission and the impact air quality from VOCs (volatile organic compounds), SO2 and NO2. This model combines the spatial and temporal distribution characteristics of various pollutants and environmental capacity. Finally, a representative high-dimensional multi-objective optimization algorithm is employed to obtain an approximate Pareto-optimal solution set. And a multi-objective decision method is proposed to filter the compromise solution. The results show that the APCs of VOCs, SO2 and NO2 are reduced by 27.5%, 10.13% and 23.16%, respectively, in the pollution day model. On non-pollution days, the proposed scheduling method not only effectively improves air quality, but also achieves cost savings of $1276.59 and reduces CO2 emission by 0.168 × 104t compared to the emission limitation method. The proposed scheduling method can not only effectively improve air quality, but also make corresponding adjustments according to the spatial and temporal changes of environmental capacity, which can truly realize economic and environmental-friendly power scheduling.

A new multi-objective decision-making method with diversified weights and Pythagorean fuzzy rough sets

In reality, there are many multi-objective decision-making problems with fuzziness and uncertainty, such as the choice of clinical treatment schemes. To effectively cope with such problems, it is urgent to scientifically handle fuzzy and uncertain information. Given the fact that the Pythagorean fuzzy set is a useful tool to tackle fuzzy information, and the rough set theory is superior in dealing with uncertain data, this paper aims to establish a novel decision-making method for scheme selection from the perspective of Pythagorean fuzzy rough sets. Pythagorean fuzzy numbers (PFNs) are first employed to express fuzzy preference information, and then multi-objective Pythagorean fuzzy information systems are introduced. Subsequently, we develop a new fuzzy rough set using an improved correlation coefficient method to deal with the uncertainty of PFNs. Furthermore, considering the diversified weights, we present a weight calculation method based on approximate accuracies. Meanwhile, a weighted fuzzy rough set model is constructed to achieve multi-objective information fusion. Accordingly, a multi-objective decision-making method is put forward with the help of overlap functions. Finally, we apply the built method to three cases from different decision scenarios to illustrate the applicability of the method. By some comparative analyses, the effectiveness and superiority of the method are also exhibited. Moreover, we discuss the establishment of decision support systems regarding scheme selection. On the whole, the work of this paper is helpful to support the solution of complex multi-objective decision-making problems.

Inclusion of “managing flexibility” valuations in the pricing of PPP projects: a multi-objective decision-making method

PurposeThe Public–Private Partnership (PPP) modality plays an important role in the procurement of global infrastructure projects. Regarding PPP's complex transaction structure, pricing of a PPP project is critical to both parties where the government pursues a high value for money (VFM) and the investor strives to maximize its financial gains. Despite the straightforward win–win principle, a formidable compromise is often the case to end up with a fairly acceptable price, subject to many determinants such as the risk profile, expected return, technological innovation and capacities of both parties. Among them, this study chooses to examine the “managing flexibility” (MF) capacity of investors in pricing of a PPP project, in light of the widely recognized importance of a real-option perspective toward the long term, complex and uncertain PPP arrangement. This study addresses two major questions: (1) how is MF in PPP projects to be valued and (2) how are PPP projects to be priced when considering a project's MF value.Design/methodology/approachA binomial tree model is used to evaluate the MF value in PPP projects. Based on the developed MF pricing model, net present value (NPV) and adjusted VFM value are then calculated. Finally, a multi-objective decision-making method (MODM) was adopted to determine the optimal level of returns based on invested capital (ROIC), return on operation maintenance (ROOM) and concession period.FindingsThe applicability and functionality of the proposed model is investigated using a real project case. For a given return, extended NPV and adjusted VFM value were calculated and analyzed using sensitivity analysis. Factor influence is shown by the model to be dependent on factor impact on cash flow. Subsequently, a multi-objective decision-making (MODM) model was adopted to determine the optimal level of returns, where the solution approximates the real-world bidding price. Results confirm that the pricing model provides a reliable and practical PPP proposal pricing tool.Originality/valueThis study proposes an integrated framework for valuing MF in PPP projects and thus more accurately determine optimal pricing of PPP projects than revealed in extant research. The model offers a practical tool to aid in the valuation of PPP projects.

Evaluation Method and Application of Cold Rolled Strip Flatness Quality Based on Multi-Objective Decision-Making

Flatness is a vital quality index that determines the dimensional accuracy of the cold-rolled strip. This paper designs a local shape wave extraction algorithm and a fuzzy classification algorithm for overall flatness defect classification based on cosine distance. By introducing the small displacement buckling theory of thin plates, the plate stress buckling model of overall and local shape waves is studied, and the critical buckling elongation difference of the overall shape and the local shape under the given conditions are obtained. Finally, using the multi-objective decision-making evaluation method, a comprehensive evaluation model of the flatness quality is established. The model is applied to the actual cold rolling production. The on-site flatness data are used to verify the flatness quality determination model both locally and overall. The results show that the model can accurately identify the local and overall flatness defects of cold-rolled strips, realizes the accurate identification and evaluation of the cold-rolled flatness quality, and provides strong support for the optimization of rolling process parameters and the improvement of the quality of thin strip products.

Adaptive approximation-based multi-objective hybrid optimization method for dual-gradient top-hat structures

In this article, an adaptive approximation-based multi-objective hybrid optimization method, integrating a multi-objective decision-making method, adaptive approximation method and hybrid optimization method, is developed. In particular, a multi-objective decision-making method developed by combining a weight strategy inspired by grey relational analysis and entropy analysis is applied to normalize multiple objectives; the trust region is introduced into the support vector regression model to solve the problem of the sequential sampling for the approximation model; a hybrid optimization algorithm combining the genetic algorithm pattern search algorithm is developed to further assist the surrogate model-based optimization. Finally, a novel dual-gradient structure with graded thickness and graded material property along the axial direction is applied to the crashworthiness optimization design. The results demonstrate that the developed hybrid method has faster optimization efficiency than the Pointer algorithm built into Isight commercial software, and the final optimized structure is superior to the original one.

A chaos-coupled multi-objective scheduling decision method for liner shipping based on the NSGA-III algorithm

Reducing sailing costs, time and emissions are three important decision-making objectives for ship operators. In this paper, a multi-objective decision model for liner shipping is established to optimize ship route, speed and number of ships deployed based on the three objectives. Moreover, the above model also takes into consideration the three latest ship emission reduction policies, including Emission Control Area, the 2020 Sulfur Limit Order and maritime Carbon Emission Taxation regulations. To solve the multi-objective scheduling problem, an improved non-dominated sorting genetic algorithm-III (NSGA-III) algorithm based on a chaos mechanism is proposed to find the Pareto solutions. And then a Multi-Criteria Decision Making (MCDM) method, the Hyperplane-based ranking method (HYRM) is developed to find the trade-off solution from the Pareto solutions. The proposed method was applied to two liner shipping service routes around southeast Asia and eastern United States, the results show that the proposed method can simultaneously reduce sailing costs, time and ship emission according to the users' preferences, and it can help shipping companies cope with fuel price fluctuations effectively.

An Improved Multi-Objective Optimization Decision Method Using NSGA-III for a Bivariate Precision Fertilizer Applicator

In order to boost the performance of a bivariable granular fertilizer applicator and simplify the control methodology of fertilization rate regulation, this paper proposed a fertilization decision method to obtain the optimal combination of rotational speed and opening length by selecting the accuracy, uniformity, adjustment time, and breakage rate as the optimization objectives. We processed the outlier data collected using the indoor bench test, segmented the data with the fertilization growth rate as the index, and proved the rationality of the data segmentation by an independent sample t-test. SVM, BPNN, ELM, and RVM were used to train the two data sections to create the fertilization rate prediction model, and the models with the highest accuracy in the two data sections were selected for the assembly of the final prediction model used to describe the fertilization process of the bivariate fertilizer applicator. Moreover, the fertilization performance problem model was established with the objectives of accuracy, uniformity, adjustment time, and breakage rate and was solved using the NSGA-III algorithm to gain an optimal fertilization decision. Compared with GA and MOEA-D-DE methods, the results show that, using the new method, the average relative error declines from 8.64% and 6.05% to 3.09%, and the average coefficient of variation reduces from 6.67% and 6.81% to 6.41%, respectively. In addition, the adjustment time lowers from 2.01 s and 1.33 s to 0.78 s, and the average breakage rate drops from 1.084% and 0.845% to 0.803%, respectively. It is indicated that the presented method offers the most notable improvements in accuracy and adjustment time, while the advancements in regard to uniformity and breakage rate is slight, but both are within a reasonable range.

A subjective-objective integrated multi-objective decision-making method for reservoir operation featuring trade-offs among non-inferior solutions themselves

The key to formulating a multi-objective reservoir operation scheme is coordinating the high/low priorities and achieving balance among various targets accordingly in the decision-making process. However, the traditional decision-making methods are either completely subjective or neglect the decision-maker's preferences, making it essential to optimize these methods to address such unsatisfactory aspects. Therefore, through drawing on some universally acknowledged economic theories and studying the geometric relationships among the Pareto solutions to such multi-objective decision-making problems, the concepts of “replacement rate”, “profit-loss sensitivity ratio”, and “preference equilibrium degree” are introduced, deduced, and elaborated on in this paper. On the basis of them, the preference decision method (PDM), entrusted with strict mathematical and physical connotations, is constructed and derived in detail, especially for addressing the bi-objective and tri-objective scenarios. The PDM can quantify the complex internal feedback relationship among various targets, providing objective support for decision-makers in the subjective trade-offs of the interests of multiple subjects and achieving the unity of subjective and objective. Furthermore, the proposed method is applied to the Wujiang cascade reservoirs in China, through which the benefits of power generation, water supply and ecological protection are enabled to be considered simultaneously. The application shows that the PDM can effectively shrink the Pareto set, which greatly reduces the difficulty of decision-making, and the obtained results prove feasible and satisfactory. In addition, the PDM is based entirely on the Pareto set itself, making it simple to utilize, and can be extended into solving other multi-objective decision-making problems.

From optimal to robust climate strategies: expanding integrated assessment model ensembles to manage economic, social, and environmental objectives

Cost-benefit integrated assessment models generate welfare-maximizing mitigation pathways under a set of assumptions to deal with deep uncertainty in future scenarios. These assumptions include socio-economic projections, the magnitude and dynamics of climate impacts on the economy, and physical climate response. As models explore the uncertainty space within the boundaries of their objective functions, they risk providing scenarios which are too narrow and not sufficiently robust. Here, we apply robust and multi-objective decision-making methods to extract relevant information from a large ensemble of optimal emissions-reduction pathways generated by a regionalized cost-benefit integrated assessment model under deterministic welfare optimization. We show that shifting the focus from optimal to robust solutions reduces the uncertainty in mitigation strategies and aligns them toward the Paris goals. Moreover, we analyze the trade-offs between climatic (temperature), social (inequality) and economic (welfare) objectives and illustrate four robust pathways under various decision-making criteria. We show that robust mitigation strategies can lead to regional emission-reduction strategies which are fair. Our results show how to extract more comprehensive climate strategies from available scenario ensembles and that the highest discrepancies at the local level policies are found in the developing and most-impacted regions.

Applying Multi-Criteria Decision Making (MCDM) in Health Technology Policy Making: Background, Current Challenges, and Path to Future

Introduction: The science of health technology policy-making has, in recent years, gone beyond merely conducting health technology assessment studies, systematic reviews or economic evaluations. In fact, sciences based on decision-making in operational research, such as multi-attribute and multi-objective decision-making methods, have been added to this field.
 Methods: Examining several prominent papers in the field of applying multi-criteria decision analysis to the science of health technology assessment, this study attempts to provide guidance for policy makers in the field of health technologies to acquaint them with the history, current challenges, and the future of this field.
 Results: Mathematical approaches based on multi-criteria decision analysis began to be used in the fields of health policy making and economics in 2006 and 2008. These approaches are still being completed to adapt to the field of health. The main challenges in this regard are the existence of attributes such as equity and ethical issues facing the use of technology in health systems. The quantitative assessment of such attributes is really demanding. It is also very difficult to weight the attributes in such a way that all the considerations regarding technology stakeholders can be taken into account.
 Conclusions: In general, the application of approaches from applied mathematics to the field of health technology policy making can help us clarify the prioritization process. At the same time, however, using the efforts made so far by researchers in this field from around the world, we have, to a large extent, been able to overcome the operational shortcomings in applying those approaches in the field of health.