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Sustainability has become a key issue in the forest industry; this research aims to analyze the quantitative techniques and metrics applied to the forest-to-lumber supply chain to achieve sustainable decision-making during the last six years. The methodology used was the PRISMA systematic literature review guide, which provides a complete and updated view of the situation. A total of 724 publications were collected from the Web of Science database. Consequently, 85 papers were selected for analysis and synthesis after applying inclusion criteria. The results show a growing interest in sustainability in the forest-to-lumber supply chain, with a peak of publications in 2019. Mathematical Programming and Simulation models are on top of the quantitative techniques applied. These techniques are applied to the supply chain components, classified according to the raw material's degree of processing or transformation level in forest entities, sawmills, transportation, and other entities. The concluding remarks highlighted that 19 published works research the social dimension, 43 explore the environmental dimension, and 55 examine the economic dimension. Moreover, in the environmental dimension, there is a concentration on the use of metrics associated with greenhouse gases, and to a lesser extent, they have been concerned with soil and water. Additionally, in the social dimension, they have concentrated mainly on the workers, leaving the local communities around the supply chain in the second place. Our systematic review reports the techniques or quantitative methodologies applied in the forest-to-lumber supply chain and the metrics used to handle the dimensions of sustainability. [ABSTRACT FROM AUTHOR]

In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature review of the use of different MCDA methods and their individual or combined utilization with other modeling techniques to support PPS problems. First, we summarize how MCDA methods are used in different modeling approaches. Second, we examine the mathematical models that are generally used to combine MCDA with mathematical programming techniques to solve PPS problems with resource constraints. Third, we present the drawbacks of combined utilization and discuss recent advances. Finally, we visualize the summary of the reviewed papers as a decision tree to assist researchers and practitioners in the use of MCDA methods in a specific PPS context and propose some future research directions. [ABSTRACT FROM AUTHOR]

In the context of project management, the attention given to project portfolio management has increased in recent years. The use of mathematical programming for portfolio management is also on the rise, because it integrates the project interactions with the multiple objectives of portfolio management into a single model. Among the possible objectives, recent studies have paid special attention to the emerging objective of future preparedness, which has not yet been incorporated into the existing mathematical models. This paper presents a mixed-integer nonlinear optimization model for portfolio selection that considers four main performance measures for project management, namely, value maximization, strategic alignment, balance, and future preparedness. Given the importance of the last measure, the purpose of this paper is to provide a more complete model that provides the marginal contribution and the best combination of projects according to the needs of the company. The model is tested using real data from two companies, one in Brazil and one in Canada, and the results obtained are coherent with their respective practices. [ABSTRACT FROM AUTHOR]

Multicriteria decision-making (MCDM) techniques have successfully been used to address a wide range of real-world decision-making issues. The best–worst method (BWM) is one of the several deterministic MCDM approaches. A recently proposed method called the multichoice best–worst method (MCBWM) takes into account several linguistic terms for pairwise comparisons of relative preferences among the criteria. It has been shown that the MCBWM approach has advantages over BWM: it reduces the calculation and determines optimal weight values by providing the choices for the optimal solution. This paper proposes a unique method for group decision-making based on MCBWM. We extended the MCBWM to solve group decision-making problems. A novel solution approach was developed and validated for multiple problems. Two examples and one case study were solved using the proposed approach to demonstrate the validity and application of the proposed method. The results were further compared with existing models to validate the proposed approach. We found that the obtained ranking order for all problems is the same and that the proposed model has a higher consistency ratio than the existing approaches. This method can be extended to other mathematical programming models for collective decision making in uncertain situations. [ABSTRACT FROM AUTHOR]

This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. Then, based on their definitions, three optimization models are constructed to obtain the weight vector of alternatives, based on which an interactive consensus adjustment algorithm is established based on the direct consensus framework. This framework adopts feedback mechanism to facilitate the information correction of decision makers. After several rounds of adjustment, the decision results with satisfactory consensus level are achieved. Finally, the practicability and effectiveness of the model are illustrated through a case study of mine accident emergency decision making. [ABSTRACT FROM AUTHOR]

The dynamic and complex environment affects the operational efficiency of automated guided vehicles (AGVs) at automated container terminals, in which artificial intelligent approaches are applied to address optimization problems in dynamic systems. This paper proposes a digital twin-based decision support approach to improve the efficiency of AGV scheduling service. Accordingly, the factors that affect AGV scheduling performance, including conflicts, failures, and battery constraints, are discussed first. Then, the framework and main steps of the proposed approach are described. The physical operation space is mapped into the virtual space, and both spaces keep synchronized to support the verification of solutions. A mathematical programming model and Q-learning algorithm are used to generate the AGV scheduling plan considering battery charging. Numerical experiments are conducted to demonstrate the effectiveness of the proposed approach. Comparisons of the digital twin-based approach, genetic algorithm (GA), and particle swarm optimization (PSO) are also made with different scale experiments. It appears that the proposed digital twin-based approach is superior to GA and PSO when solving small- and large-scale cases. A sensitivity analysis is performed concerning the battery utilization rate, task, and AGV number. Experimental results show that an optimal configuration of AGV and task can improve the battery utilization rate and reduce the completion time. • A digital twin-based decision support approach is proposed to improve scheduling. • A mathematical programming model is developed to minimize the total completion time. • Digital twin and Q-learning are used to monitor operation and obtain solutions. • Sensitivity analysis of battery utilization is made to provide equipment maintenance. • The proposed approach is superior based on the comparison of solution performances. [ABSTRACT FROM AUTHOR]

Randomized decision making refers to the process of making decisions randomly according to the outcome of an independent randomization device, such as a dice roll or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, in which deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has recently been shown that using a randomized, rather than a deterministic, strategy in nonconvex distributionally robust optimization (DRO) problems can lead to improvements in their objective values. It is still unknown, though, what is the magnitude of improvement that can be attained through randomization or how to numerically find the optimal randomized strategy. In this paper, we study the value of randomization in mixed-integer DRO problems and show that it is bounded by the improvement achievable through its continuous relaxation. Furthermore, we identify conditions under which the bound is tight. We then develop algorithmic procedures, based on column generation, for solving both single- and two-stage linear DRO problems with randomization that can be used with both moment-based and Wasserstein ambiguity sets. Finally, we apply the proposed algorithm to solve three classical discrete DRO problems: the assignment problem, the uncapacitated facility location problem, and the capacitated facility location problem and report numerical results that show the quality of our bounds, the computational efficiency of the proposed solution method, and the magnitude of performance improvement achieved by randomized decisions. Summary of Contribution: In this paper, we present both theoretical results and algorithmic tools to identify optimal randomized strategies for discrete distributionally robust optimization (DRO) problems and evaluate the performance improvements that can be achieved when using them rather than classical deterministic strategies. On the theory side, we provide improvement bounds based on continuous relaxation and identify the conditions under which these bound are tight. On the algorithmic side, we propose a finitely convergent, two-layer, column-generation algorithm that iterates between identifying feasible solutions and finding extreme realizations of the uncertain parameter. The proposed algorithm was implemented to solve distributionally robust stochastic versions of three classical optimization problems and extensive numerical results are reported. The paper extends a previous, purely theoretical work of the first author on the idea of randomized strategies in nonconvex DRO problems by providing useful bounds and algorithms to solve this kind of problems. [ABSTRACT FROM AUTHOR]

This paper focuses on a current topic of supply chain management and operations research which serves as a tool manufacturing enterprises to cope with pressure put on them by continuously changing market conditions and global economy itself. Paper presents results of research conducted on sample file of Slovak manufacturing enterprises. The main aim of this paper is to explore the extent of utilization of mathematical programming as optimization methods in production practice in Slovakia to analyse possible relationship between enterprise's size and used optimizing method. Representativeness of the sample file was confirmed by application of Pearson's chi-squared test (X2 - test) due to criterion of enterprise's size. The results of this research have an implication for business practice and may serve managers in their decision-making process. In managerial practice enterprises have to deal with many different problems concerning their supply chains. The majority of them can be resolved using mathematical programming. [ABSTRACT FROM AUTHOR]

Goal programming provides an efficient technique to deal with decision making problems with multiple conflicting objectives. This paper joins the streams of research on goal programming by providing a so-called uncertain random goal programming to model the multi-objective optimization problem involving uncertain random variables. Several equivalent deterministic forms are derived on the condition that the set of parameters consists of uncertain variables and random variables. Finally, an example is given to illustrate the application of the approach. [ABSTRACT FROM AUTHOR]

The dynamic production scheduling is a very complex process that may arise from the occurrence of unpredictable situations such as the arrival of new orders besides the ones already accepted. As a consequence, companies may often encounter several difficulties to make decisions about the new orders acceptance and sequencing along with the production of the existing ones. With this recognition, a mathematical programming model for the regenerative scheduling problem with deterministic processing times is formulated in the present paper to evaluate the economic advantage of accepting a new order in an engineer to order (ETO) manufacturing organization. The real case of an Italian ETO company which produces hydraulic marine and offshore cranes is afterwards presented. [ABSTRACT FROM AUTHOR]

In decision making with interval-valued intuitionistic fuzzy preference relations (IVIFPRs), the consistency and its improvement are key issues. The aim of this paper is to investigate a new multiplicative consistency of IVIFPRs based on interval arithmetic, and propose goal programming approach to improve consistency and consensus. Based on analysis of the drawbacks of the existing consistency definitions of IVIFPR, new definition for multiplicative consistent IVIFPR is introduced. Based on the proposed multiplicative consistency and analysis of the relationship between interval-valued intuitionistic fuzzy weights and multiplicative consistent IVIFPR, goal programming-based model is developed for deriving interval-valued intuitionistic fuzzy weights from IVIFPR. To measure the multiplicative consistency degree of IVIFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IVIFPR with unacceptable consistency, a mathematical programming approach is proposed to improve its consistency. By considering the experts' subjective and consensus weights, the experts' comprehensive weights are determined. Some numerical examples illustrate the proposed models. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson's algorithm and our new idea, which is << the gain cycles >>, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm. [ABSTRACT FROM AUTHOR]

Large construction and infrastructure projects are a billion-dollar business, but few studies have addressed the integrated operations in this unique domain of the construction supply chain (CSC). The comparison between the CSC and a conventional supply chain enables us to examine its framework and establish a quantitative optimization model for the CSC. To introduce the integrated operations concept into the CSC, many uncertainties need to be first dealt with, for which a multiobjective uncertain optimization model is developed. As the optimization of the owner and fabricator's costs and the service level are the main objectives, a hybrid genetic algorithm with fuzzy-random method is developed to solve the optimization model. An integrated multiobjective purchasing and production planning model is then constructed and applied to a hydropower construction project in Southwest China. The results illustrate that efficient integrated operations are critical for the CSC performance. The optimization results also indicate that considering of uncertain rush orders and delay times can be vital for optimum CSC performance. With this proposed method, construction managers can quickly respond to changing uncertain demand. This paper has highlighted that project managers need to collaborate with other stakeholders to ensure optimal CSC performance. [ABSTRACT FROM AUTHOR]

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among established facilities and existing demand points. In this paper, the location-routing problem with time window (LRPTW) and homogeneous fleet type and designing a multi-echelon, and capacitated reverse logistics network, are considered which may arise in many real-life situations in logistics management. Our proposed RL network consists of hybrid collection/inspection centers, recovery centers and disposal centers. Here, we present a new bi-objective mathematical programming (BOMP) for LRPTW in reverse logistic. Since this type of problem is NP-hard, the non-dominated sorting genetic algorithm II (NSGA-II) is proposed to obtain the Pareto frontier for the given problem. Several numerical examples are presented to illustrate the effectiveness of the proposed model and algorithm. Also, the present work is an effort to effectively implement the ε-constraint method in GAMS software for producing the Pareto-optimal solutions in a BOMP. The results of the proposed algorithm have been compared with the ε-constraint method. The computational results show that the ε-constraint method is able to solve small-size instances to optimality within reasonable computing times, and for medium-to-large-sized problems, the proposed NSGA-II works better than the ε-constraint. [ABSTRACT FROM AUTHOR]

Evolutions in the power system challenge the manner in which power system reliability is managed. In particular, currently used reliability criteria, typically the deterministic N-1 criterion, are increasingly inadequate. Moving to an alternative approach is difficult as quantifying benefits is hard in a multifaceted environment and system operators are reluctant to move away from the easy and transparent existing criterion. This paper presents a generic framework to evaluate and compare socio-economic and reliability performance of power system reliability criteria, focussing on the short term decision making process of transmission system operators (TSO). The framework can also be used to tune the parameters of reliability criteria. Short term operational planning and real time operation TSO decision making processes are simulated considering various reliability criteria. The framework is applied to a 5 node test system and the 24 node IEEE reliability test system, showing that the applied probabilistic reliability criterion outperforms deterministic N-0 and N-1 approaches in those systems in terms of expected reliability and socio-economic indicator values. The effect is larger in the bigger system with more operational flexibility. [ABSTRACT FROM PUBLISHER]

In this paper, we study the multiattribute decision-making (MADM) problem with intuitionistic fuzzy values that represent information regarding alternatives on the attributes. Assuming that the weight information of the attributes is not known completely, we use an approach that utilizes the relative comparisons based on the advantage and disadvantage scores of the alternatives obtained on each attribute. The relative comparison of the intuitionistic fuzzy values in this research use all the three parameters, namely membership degree (“the more the better”), nonmembership degree (“the less the better”), and hesitancy degree (“the less the better”), thereby leading to the tradeoff values of all the three parameters. The score functions (advantage and disadvantage scores) used for this purpose are based on the positive contributions of these parameters, wherever applicable. Furthermore, these scores are used to obtain the strength and weakness scores leading to the satisfaction degrees of the alternatives. The optimal weights of the attributes are determined using a multiobjective optimization model that simultaneously maximizes the satisfaction degree of each alternative. The optimal solution is used for ranking and selecting the best alternative on the basis of the overall attribute values. To validate the proposed methodology, we present a numerical illustration of a real-world case. The methodology is further extended to treat MADM problem with interval-valued intuitionistic fuzzy information. Finally, a thorough comparison is done to demonstrate the advantages of the solution methodology over the existing methods used for the intuitionistic fuzzy MADM problems. [ABSTRACT FROM PUBLISHER]

Considering the high importance of the optimization problem, this study evaluated mathematical programming models by considering various methods of estimating model coefficients. Correct and accurate data must be entered into the model to get accurate and robust result from the model. Most input data to the presented model are technical and objective function coefficients. Therefore, it is necessary to determine the information related to these coefficients with the utmost precision and, as much as possible, to develop a suitable scientific method to estimate the value of these coefficients [5]. Finding the best method for estimating the coefficients of mathematical programming models can significantly optimize the final values of the variables extracted from the mathematical programming model. For this reason, it is essential to study the methods used so far in this field and examine their advantages and disadvantages. This review study investigated various methods of estimating technical coefficients of mathematical planning models in the conditions of possible decision-making and uncertainty after reviewing 117 articles published between 1955 and 2022. These methods include fuzzy methods, statistical methods, and data analysis methods. Statistical methods such as regression methods, time series methods, exponential smoothing, and linear non-linear and non-parametric, machine learning and data mining methods were investigated in this article. The methods of data-driven analysis explained in this article can be referred to as decision trees, random forests and the Lasso methods. After evaluating and comparing these methods, suggestions for choosing the best method were provided. [ABSTRACT FROM AUTHOR]

A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index is frequently utilized by a manufacturer to gauge the quality of a process. This index can be utilized by not only an internal process engineer to assess the quality of the process but also as a communication tool for an external sales department. When the manufacturing process deviates from the target value T, the process capability index CPMK can be quickly detected, which is conducive to the promotion of smart manufacturing. Therefore, this study applied the index CPMK as an evaluation tool for process quality. As noted by some studies, process capability indices have unknown parameters and therefore must be estimated from sample data. Additionally, numerous studies have addressed that it is essential for companies to establish a rapid response mechanism, as they wish to make decisions quickly when using a small sample size. Considering the small sample size, this study proposed a 100 (1 − α)% confidence interval for the process capability index CPMK based on suggestions from previous studies. Subsequently, this study built a fuzzy testing model on the 100 (1 − α)% confidence interval for the process capability index CPMK. This fuzzy testing model can help enterprises make decisions rapidly with a small sample size, meeting their expectation of having a rapid response mechanism. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze a mathematical programming approach to expansion draft optimization in the context of the 2017 NHL expansion draft involving the Vegas Golden Knights, noting that this approach can be generalized to future NHL expansions and to those in other sports leagues. In particular, we present a novel mathematical optimization approach, consisting of two models, to optimize expansion draft protection and selection decisions made by the various teams. We use this approach to investigate a number of expansion draft scenarios, including the impact of "collaboration" between existing teams, the trade-off between team performance and salary cap flexibility, as well as opportunities for Vegas to take advantage of side agreements in a "leverage" experiment. Finally, we compare the output of our approach to what actually happened in the expansion draft, noting both similarities and discrepancies between our solutions and the actual outcomes. Overall, we believe our framework serves as a promising foundation for future expansion draft research and decision-making in hockey and in other sports. [ABSTRACT FROM AUTHOR]

Owing to the importance of internal structure of decision making units (DMUs) and data uncertainties in real situations, the present paper focuses on multi-component data envelopment analysis (MC-DEA) approach with imprecise data. The undesirable outputs and shared resources are also incorporated in the production process of multi-component DMUs to validate real problems. The interval efficiencies of DMUs and their components in MC-DEA are often challenging with imprecise data. In many practical situations, different set of weights may be resulted into valid efficiency intervals for DMUs but invalid interval efficiencies for their components. Therefore, the present study proposes a new common set of weights methodology, based on interval arithmetic and unified production frontier, to determine unique weights for measuring these interval efficiencies. It is a two-level mathematical programming approach that preserves linearity of DEA and exhibits stronger discrimination power among the DMUs as compared to some existing approaches. Theoretically, the aggregate efficiency interval of each DMU lies between the components' interval efficiencies. Further, the proposed approach is also applied to banks in India for proving its acceptability in practical applications. The performance of each bank is investigated in terms of two components: general business and bancassurance business for the years 2011-2013. The present study emphasized expanding pattern of bancassurance business in current market scenario with more percentage increase as contrasted to general business. [ABSTRACT FROM AUTHOR]

Purpose - The purpose of this paper is the need to build a novel approach that would allow flexible modeling and solving of food supply chain management (FSCM) problems. The models developed would use the data (data-driven modeling) as early as possible at the modeling phase, which would lead to a better and more realistic representation of the problems being modeled. Design/methodology/approach - An essential feature of the presented approach is its declarativeness. The use of a declarative approach that additionally includes constraint satisfaction problems and provides an opportunity of fast and easy modeling of constrains different in type and character. Implementation of the proposed approach was performed with the use of an original hybrid method in which constraint logic programming (CLP) and mathematical programming (MP) are integrated and transformation of a model is used as a presolving technique. Findings - The proposed constraint-driven approach has proved to be extremely flexible and efficient. The findings obtained during part of experiments dedicated to efficiency were very interesting. The use of the constraint-driven approach has enabled finding a solution depending on the instance data up to 1,000 times faster than using the MP. Research limitations/implications - Due to the limited use of exact methods for NP-hard problems, the future study should be to integrate the CLP with environments other than the MP. It is also possible, e.g., with metaheuristics like genetic algorithms, ant colony optimization, etc. Practical implications - There is a possibility of using the approach as a basis to build a decision support system for FSCM, simple integration with databases, enterprise resource planning systems, management information systems, etc. Originality/value - The new constraint-driven approach to FSCM has been proposed. The proposed approach is an extension of the hybrid approach. Also, a new decision-making model of distribution and logistics for the food supply chain is built. A presolving technique for this model has been presented. [ABSTRACT FROM AUTHOR]

As a useful tool, probabilistic hesitant fuzzy set is an enhanced version for hesitant fuzzy set. It could be used to model the uncertainty very effectively. However, in probabilistic hesitant fuzzy risky multiple attribute decision making problems, the occurrence probabilities of elements in a probabilistic hesitant fuzzy element and the probability of risk status are often difficult to obtain by subjective evaluation of a decision maker. This paper aims to propose two nonlinear programming models for calculating the probabilities of elements in a probabilistic hesitant fuzzy element and the probability of risk status respectively. First, a nonlinear programming model using maximum entropy principle is established for determining the probabilities of elements in a probabilistic hesitant fuzzy element. Second, by introducing the water‐filling theory, we put forward its extension and design a novel mathematical programming model to determine the probability of risk status. Moreover, we have proved that both the two mathematical programming models are convex programming models and their global optimal solutions can be found. Thirdly, the collective overall expected values of alternatives are calculated and the ranking order can be derived. Then, the selection of investment project is investigated, and comparison analysis shows the superiority of the presented approach. [ABSTRACT FROM AUTHOR]

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper. [ABSTRACT FROM AUTHOR]

To identify multiattribute utility functions under the assumption of the mutual utility independence, a decision maker must specify indifference points and subjective probabilities precisely. By relaxing this rigorous evaluation, multiattribute value models with incomplete information have been developed. In this paper, we present a new method finding the best alternative through strict preference relations derived from the decision maker by asking questions that are relatively easy to answer compared to the indifference questions. In our method, alternatives consistent with the derived strict preference relations are obtained by solving mathematical programming problems with constraints representing the preference relations, and eventually we can find the most preferred alternative by deriving additional preference relations. [ABSTRACT FROM AUTHOR]

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. [ABSTRACT FROM AUTHOR]

Engineering management plays a significant part in project construction, and it is a process involved with making decision under uncertainty. When decision makers are hesitant to assess investment projects, fuzzy set theory offers an effective tool for dealing with uncertainty. In this paper, a decision-making method is put forward for handling engineering management problems, where dual hesitant fuzzy set is adopted to model the uncertainty. Firstly, we raise an improved dual hesitant fuzzy correlation coefficient and its weighted form. Compared with the current dual hesitant fuzzy correlation coefficients, the presented one has more desirable properties. It not only can manifest the positive or negative correlation between dual hesitant fuzzy sets, but also can guarantee the dual hesitant fuzzy correlation coefficient is 1 (−1) if and only if the two dual hesitant fuzzy sets are identical (complementary). Secondly, a mathematical programming model, which integrates within-attribute and between-attribute variation information, is designed to derive the attribute weights. More importantly, it can fully utilize the decision information. Finally, the weighted correlation coefficients are calculated, and an illustrative example concerning engineering management is offered to demonstrate the rationality of the proposed technique. • Decision-making method is presented for engineering management problems. • Dual hesitant fuzzy correlation coefficient is proposed. • A mathematical model is presented to derive the attribute weights. • A case study from the engineering management cost system is taken to illustrate the approach. • The effectiveness and efficiency of our algorithm are provided. [ABSTRACT FROM AUTHOR]

Supply chain management that considers the flow of raw materials, products and information has become a focal issue in modern manufacturing and service systems. Supply chain management requires effective use of assets and information that has far reaching implications beyond satisfaction of customer demand, flow of goods, services or capital. Aggregate planning, a fundamental decision model in supply chain management, refers to the determination of production, inventory, capacity and labor usage levels in the medium term. Traditionally standard mathematical programming formulation is used to devise the aggregate plan so as to minimize the total cost of operations. However, this formulation is purely an economic model that does not include sustainability considerations. In this study, we revise the standard aggregate planning formulation to account for additional environmental and social criteria to incorporate triple bottom line consideration of sustainability. We show how these additional criteria can be appended to traditional cost accounting in order to address sustainability in aggregate planning. We analyze the revised models and interpret the results on a case study from real life that would be insightful for decision makers. [ABSTRACT FROM AUTHOR]

A multi-depot Chinese postman problem (MDCP) arises from a network (e.g. cityplan) in which several depots are located wherefrom edges (e.g. streets) have to be served. Since costs are involved with each visit to an edge, the objective is to find a minimum cost tour in the network that visits all edges of the network. Such a minimum cost tour consists of a collection of subtours such that the subtours originate from different depots, and each subtour starts and ends at the same depot. This typical OR problem turns into a multi decision maker problem if agents are assigned to the streets. In this new setting the cost of a minimum cost tour that visits all edges have to be paid by the agents. However, now each group of agents (coalition) has the opportunity to find its own minimum cost tour, i.e. a minimum cost tour that only visits the edges owned by the group of agents. Therefore, the main objective is to find allocations of the cost of a minimum tour that visits all agents in such a way that no coalition has higher costs than the costs incurred by its own minimum tour. We will use cooperative game theory to investigate whether these so-called core allocations exist. Therefore, we consider a cooperative Chinese postman (CP) game that is induced by an MDCP by associating every edge of the network with a different agent. In this paper, we characterize classes of networks that ensure the existence of core allocations, the so-called CP balanced graphs, and the existence of specific core allocations, the so-called CP submodular graphs. [ABSTRACT FROM AUTHOR]

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. [ABSTRACT FROM AUTHOR]

The analytic hierarchical process/network process (AHP/ANP) is a popular multi-criteria decision making approach for determining the optimal alternative or weights of criteria. Many papers have extended the AHP/ANP to consider the fuzzy environment to reflect the subjective uncertainty of decision-makers. However, the fuzzy ANP (FANP) is not as popular as the fuzzy AHP (FAHP), because the calculation of the fuzzy supermatrix results in the divergence of the steady-state. In this paper, we provide a novel mathematical programming model to calculate the limiting distribution of the fuzzy supermatrix by considering a fuzzy inverse matrix rather than directly calculate the fuzzy supermatrix by limiting powers. In addition, we use a numerical example to illustrate the proposed method and compare the results with the previous method. The numerical results indicate the proposed method has the least spread of the fuzzy weights, thus justifying the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

This study surveys the use of fuzzy numbers in classic optimization models, and its effects on making decisions. In a wide sense, mathematical programming is a collection of tools used in mathematical optimization to make good decisions. There are many sectors of economy that employ it. Finance and government, logistics and manufacturing, the distribution of the electrical power are worth to be first mentioned. When real life problems are modeled mathematically, there is always a trade-off between model's accuracy and complexity. By this survey, we aim to present in a concise form some mathematical models from the literature together with the methods to solve them. We will focus mainly on fuzzy fractional programming problems. We will also refer to but not describe in detail the multi-criteria decision-making problems involving fuzzy numbers and linear fractional programming models. [ABSTRACT FROM AUTHOR]

During the process of decision making with intuitionistic fuzzy preference relation (IFPR), the underlying normalized intuitionistic fuzzy priority weight vector can be obtained by a mathematical programming model. In the multicriteria group decision making (GDM) problem, it is reasonable to assume that different decision makers have different criteria weights, this is because that each decision maker has his/her own opinions and preferences, and the importance of criteria should not be the same for different decision makers. The aim of this paper is to develop two techniques for multi-criteria GDM with IFPRs based on the multiplicative consistency. In the first case where the decision maker acts as separate individual, the individual priority weight vector can be derived from the IFPR established by each decision maker with respect to each criterion, after that an overall priority weight vector can be obtained by synthesizing these priority weight vectors together. When the decision makers are taken as a group, the normalized overall intuitionistic fuzzy priority weight vector can be generated directly by building a fractional programming model without using the aggregation operator. An example is given to illustrate the validity and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

Highlights • A new method for target setting in mergers is proposed. • The method combines goal programming and inverse data envelopment analysis. • The method allows decision makers to save desired resources. • An application in banking sector is proposed. Abstract This paper suggests a novel method to deal with target setting in mergers using goal programming (GP) and inverse data envelopment analysis (InvDEA). A conventional DEA model obtains the relative efficiency of decision making units (DMUs) given multiple inputs and multiple outputs for each DMU. However, the InvDEA aims to identify the quantities of inputs and outputs when efficiency score is given as a target. This study provides an effective method that allows decision makers to incorporate their preference in target setting of a merger for saving specific input(s) or producing certain output(s) as much as possible. The proposed method is validated through an illustrative application in banking industry. [ABSTRACT FROM AUTHOR]

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mathematical programming model for use in the design of a sustainable supply chain network under uncertain conditions. The proposed model is aimed at maximizing social benefits while minimizing economic costs and environmental impacts. The objective assists in making decisions concerning the selection of production technologies and materials and determining the number and locations of production and distribution centers and the quantity of product to be transported between facilities. Uncertainty related to customer demand is dealt by using stochastic variables, whereas overall costs, carbon emissions, job opportunities, and the detrimental effects of the resulting solutions are handled using fuzzy numbers. An interactive method based on two-phase stochastic programming and fuzzy probabilistic multi-objective programing is used to overcome problems related to uncertainty. Finally, numerical analysis demonstrates the efficacy and efficiency of the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes a method of formalization and solution to a problem of mode parameters selection in CTS on the basis of mathematical modelling. Decision-making problems on a selection of effective operation modes are formalized using the example of technological complex on benzene production. Since the studied object is characterized by multicriteriality and fuzziness, initial problems are formalized as multi-criteria problems of fuzzy mathematical programming and a heuristic algorithm of their solution is developed on the basis of methods of fuzzy mathematics. Formulations of decision-making problems and an algorithm of their solution are obtained by modifying various principles of optimality based on the methods of the fuzzy set theory. [ABSTRACT FROM AUTHOR]

To avoid the complexity and time consumption of traditional statistical and mathematical programming, intelligent techniques have gained great attention in different financial research areas, especially in banking decisions’ optimization. However, choosing optimum bank lending decisions that maximize the bank profit in a credit crunch environment is still a big challenge. For that, this paper proposes an intelligent model based on the Genetic Algorithm (GA) to organize bank lending decisions in a highly competitive environment with a credit crunch constraint (GAMCC). GAMCC provides a framework to optimize bank objectives when constructing the loan portfolio, by maximizing the bank profit and minimizing the probability of bank default in a search for a dynamic lending decision. Compared to the state-of-the art methods, GAMCC is considered a better intelligent tool that enables banks to reduce the loan screening time by a range of 12%–50%. Moreover, it greatly increases the bank profit by a range of 3.9%–8.1%. [ABSTRACT FROM AUTHOR]

To the best of our knowledge, there is no method to find the product of unrestricted LR-type intuitionistic fuzzy numbers (IFNs) as well as the optimal solutions of LR-type intuitionistic fuzzy linear programming problems (IFLPPs) in which some or all the decision variables are unrestricted. Therefore it is necessary to pay attention to this issue and there is need to find the product of unrestricted LR-type IFNs as well as the optimal solutions of such programming problems. In this paper, the product of unrestricted LR-type IFNs based on the α -cut, β -cut and ( α, β )-cut is proposed. Then with the help of proposed product, a new method is proposed to find the optimal solutions of unrestricted LR-type IFLPPs. Finally, an illustrative example is given to support the proposed method and investigated the applicability of existing approaches exist in the literature. [ABSTRACT FROM AUTHOR]

Multilevel programming problems model a decision-making process with a hierarchy structure. Traditional solution methods including vertex enumeration algorithms and penalty function methods are not only inefficient to obtain the solution of the multilevel programming problems, but also lead to a paradox that the follower’s decision power dominates the leader’s. In this paper, both multilevel programming and intuitionistic fuzzy set are used to model problems in hierarchy expert and intelligent systems. We first present a score function to objectively depict the satisfactory degrees of decision makers by virtue of the intuitionistic fuzzy set for solving multilevel programming problems. Then we develop three optimization models and three interactive intuitionistic fuzzy methods to consider different satisfactory solutions for the requirements of expert decision makers. Furthermore, a new distance function is proposed to measure the merits of a satisfactory solution. Finally, a case study for cloud computing pricing problems and several numerical examples are given to verify the applicability and the effectiveness of the proposed models and methods. [ABSTRACT FROM AUTHOR]

Consistency analysis is very important to ensure the reasonable ranking order. However, all previous consistency concepts for interval multiplicative preference relations (IMPRs) are insufficient to address this type of preference relations. This paper introduces a new consistency concept for IMPRs that is a natural extension of the Saaty’s consistency concept for multiplicative preference relations. Several desirable properties are discussed, and the relationship between the new concept and two previous ones is studied. Then, a method to judge the consistency of IMPRs is proposed. Considering the inconsistent case, a 0–1 mixed programming model to derive consistent IMPRs from inconsistent ones is established. To determine missing values in incomplete HFPRs, 0–1 mixed programming models are constructed that can address the situation where ignore objects exist. Meanwhile, illustrative examples are offered to show the feasibility and efficiency of the developed theoretical results, and comparison analysis is provided. Finally, a consistency analysis based algorithm to decision making with IMPRs is developed that can address inconsistent and incomplete cases. [ABSTRACT FROM AUTHOR]

Models involving decision variables in both discrete and continuous domain spaces are prevalent in process design. Generalized Disjunctive Programming (GDP) has emerged as a modeling framework to explicitly represent the relationship between algebraic descriptions and the logical structure of a design problem. However, fewer formulation examples exist for GDP compared to the traditional Mixed-Integer Nonlinear Programming (MINLP) modeling approach. In this paper, we propose the use of GDP as a modeling tool to organize model variants that arise due to characterization of different sections of an end-to-end process at different detail levels. We present an illustrative case study to demonstrate GDP usage for the generation of model variants catered to process synthesis integrated with purchasing and sales decisions in a techno-economic analysis. We also show how this GDP model can be used as part of a hierarchical decomposition scheme. These examples demonstrate how GDP can serve as a useful model abstraction layer for simplifying model development and upkeep, in addition to its traditional usage as a platform for advanced solution strategies. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy linear assignment method is developed for multi-attribute group decision making problems. Since uncertain nature of many decision problems, the proposed method incorporates various concepts from fuzzy set theory such as fuzzy arithmetic and aggregation, fuzzy ranking and fuzzy mathematical programming into a fuzzy concordance based group decision making process. Fuzziness in the group hierarchy and quantitative type criteria are also taken into account. In order to present the validity and practicality of the proposed method, it is applied to a real life multi-criteria spare part inventory classification problem. The case study has demonstrated that the proposed method is easy to apply and able to provide effective spare parts inventory classes under uncertain environments. In addition to the practical verification by the company experts, the proposed method is also compared with some of the commonly used fuzzy multi-attribute decision making methods from the literature. According to the comparison of the results, there is an association between classes of spare parts obtained by the proposed method and the benchmarked methods. [ABSTRACT FROM AUTHOR]

This paper focuses on a multidemand multisource order quantity allocation problem with multiple transportation alternatives. To solve this problem, a bilevel multiobjective programming model under a mixed uncertain environment is proposed. Two levels of decision makers are considered in the model. On the upper level, the purchaser aims to allocate order quantity to multiple suppliers for each demand node with the consideration of three objectives: total purchase cost minimization, total delay risk minimization, and total defect risk minimization. On the lower level, each supplier attempts to optimize the transportation alternatives with total transportation and penalty costs minimization as the objective. In contrast to prior studies, considering the information asymmetry in the bilevel decision, random and fuzzy random variables are used to model uncertain parameters of the construction company and the suppliers. To solve the bilevel model, a solution method based on Kuhn-Tucker conditions, sectional genetic algorithm, and fuzzy random simulation is proposed. Finally, the applicability of the proposed model and algorithm is evaluated through a practical case from a large scale construction project. The results show that the proposed model and algorithm are efficient in dealing with practical order quantity allocation problems. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis (DEA) is a non-parametric technique for estimating the technical efficiency of a set of Decision Making Units (DMUs) from a database consisting of inputs and outputs. This paper studies DEA models based on maximizing technical efficiency, which aim to determine the least distance from the evaluated DMU to the production frontier. Usually, these models have been solved through unsatisfactory methods used for combinatorial NP-hard problems. Here, the problem is approached by metaheuristic techniques and the solutions are compared with those of the methodology based on the determination of all the facets of the frontier in DEA. The use of metaheuristics provides solutions close to the optimum with low execution time. [ABSTRACT FROM AUTHOR]

As a crucial concept of characterizing uncertainty, entropy has been widely used in fuzzy programming problems, while involving complicated calculations. To simplify the operations so as to broaden its applicable areas, this paper investigates the entropy within the framework of credibility theory and derives the formulas for calculating the entropy of regular LR fuzzy numbers by virtue of the inverse credibility distribution. By verifying the favorable property of this operator, a calculation formula of a linear function's entropy is also proposed. Furthermore, considering the strength of semi-entropy in measuring one-side uncertainty, the lower and upper semi-entropies, as well as the corresponding formulas are suggested to handle return-oriented and cost-oriented problems, respectively. Finally, utilizing entropy and semi-entropies as risk measures, two types of entropy optimization models and their equivalent formulations derived from the proposed formulas are given according to different decision criteria, providing an effective modeling method for fuzzy programming from the perspective of entropy. The numerical examples demonstrate the high efficiency and good performance of the proposed methods in decision making. [ABSTRACT FROM AUTHOR]

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in the ECLiPSe system using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets. [ABSTRACT FROM AUTHOR]

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Copyright of Valori e Valutazioni is the property of Societa Italiana di Estimo e Valutazione (SIEV) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Today, organizations try to decline academically expenses using humans and resources in addition to rising managers and operators' satisfaction. Meantime, a very important step in the process of decision is the assignment of human resources, particularly in connection with research and development (R&D) projects in which the system is highly dependent on the capabilities of human resources. In this study, we tried all the assumptions that come true in the real world, considered a model for applied R&D projects to reduce costs and increase the efficiency of projects. Therefore, an integrated multiproject scheduling and multiskill human resource assignment model under uncertainty has developed for R&D projects. Furthermore, it is assumed that the activity processing time is related to human resources assignment that means the learning effect is considered. To demonstrate the proposed model efficiency, the various dimensions instance problem was solved accurately and efficiently in GAMS software, and the results have been reported. In addition, the proposed model is validated through the input parameter sensitivity analysis. The results indicate a suitable performance of the proposed fuzzy mathematical programming model is due to the complexity of the problem. [ABSTRACT FROM AUTHOR]