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Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority. [ABSTRACT FROM AUTHOR]

Assignment problem (AP) is well- studied and important area in optimization. In this research manuscript, an assignment problem in neutrosophic environment, called as neutrosophic assignment problem (NAP), is introduced. The problem is proposed by using the interval-valued trapezoidal neutrosophic numbers in the elements of cost matrix. As per the concept of score function, the interval-valued trapezoidal neutrosophic assignment problem (IVTNAP) is transformed to the corresponding an interval-valued AP. To optimize the objective function in interval form, we use the order relations. These relations are the representations of choices of decision maker. The maximization (or minimization) model with objective function in interval form is changed to multi- objective based on order relations introduced by the decision makers' preference in case of interval profits (or costs). In the last, we solve a numerical example to support the proposed solution methodology.

In general, studies are carried out to determine the location and to resolve trade-offs in the management of forests according to ecosystem services. The government of Turkey also has been advancing this type of analysis in the practical management of forests. The creation of ecosystem services (ES) suitability map for forests through a participatory approach can provide forest managers valuable information that informs ecosystem-based management plans. The objective of this paper is to formulate and solve the problem of assigning management actions to forest stands in order to optimally provide ecosystem services that are consistent with, and based on Sustainable Development Goals (SDG). We outline a model for a participatory process that has seven steps: (1) determine the possible ES that can be supported on the landscape, (2) create a suitability map for each management unit (stand of trees), (3) define SDG for each ES, (4) create the stakeholder groups, (5) determine the importance of each SDG, (6) determine the contribution of ES to each SDG, and (7) assign ES to each management unit in an optimal manner. We used pairwise comparisons and the Delphi method to determine stakeholder preferences. This information guided the assignment of management actions to management units when optimizing ES outcomes. This approach was applied to a case study centered on the Belgrad Forest, located in northwest Turkey. The percent of land assigned to ES was respectively, water regulation (71%), cultural heritage (17%), education (9%), water supply (2%), and carbon (1%). Through this process, for this case study area, there were no assignments for recreation and aesthetic quality services. As a result, the Belgrade Forest was zoned into management classes unlike the current situation. The pairwise comparisons and the Delphi method can help formalize public participation in the decision-making process. Results from these can inform a resource allocation optimization model through the development of coefficients and constraints.

Assignment problem (AP) is well-studied and important area in optimization. In this research manuscript, an assignment problem in neutrosophic environment, called as neutrosophic assignment problem (NAP), is introduced. The problem is proposed by using the interval-valued trapezoidal neutrosophic numbers in the elements of cost matrix. As per the concept of score function, the interval-valued trapezoidal neutrosophic assignment problem (IVTNAP) is transformed to the corresponding an interval-valued AP. To optimize the objective function in interval form, we use the order relations. These relations are the representations of choices of decision maker. The maximization (or minimization) model with objective function in interval form is changed to multi- objective based on order relations introduced by the decision makers' preference in case of interval profits (or costs). In the last, we solve a numerical example to support the proposed solution methodology. [ABSTRACT FROM AUTHOR]

Factors contributing to winning games are imperative, as the ultimate objective in a game is victory. The aim of this study was to identify the factors that characterize the game of cricket, and to investigate the factors that truly influence the result of a game using the data collected from the Champions Trophy cricket tournament. According to the results, this cricket tournament can be characterized using the factors of batting, bowling, and decision-making. Further investigation suggests that the rank of the team and the number of runs they score have the most significant influence on the result of games. As far as the effectiveness of assigning bowlers is concerned, the Australian team has done a fabulous job compared to the rest of the teams. [ABSTRACT FROM AUTHOR]

Abstract: In view of the simplex-type algorithm, the assignment problem is inherently highly degenerate. It may be the optimal basis has changed, but the optimal assignment is unchanged when parameter variation occurs. Degeneracy then makes sensitivity analysis difficult, as well as makes the classical Type I range, which identifies the range the optimal basis unchanged, impractical. In this paper, a labeling algorithm is proposed to identify two other sensitivity ranges – Type II range and Type III range. The algorithm uses the reduced cost matrix, provided in the final results of most solution algorithms for AP, to determine the Type II range which reflects the stability of the current optimal assignment. Thus, the algorithm generates a streamlined situation from searching the optimal solution until performing the sensitivity analysis of the assignment problem. The Type III range, reflecting the flexibility of optimal decision making, can be obtained immediately after the Type II range is determined. Numerical examples are presented to demonstrate the algorithm. [Copyright &y& Elsevier]

We consider the problem of multi-robot task-allocation when robots have to deal with uncertain utility estimates. Typically an allocation is performed to maximize expected utility; we consider a means for measuring the robustness of a given optimal allocation when robots have some measure of the uncertainty (e.g. a probability distribution, or moments of such distributions). We introduce the interval Hungarian algorithm, a new algorithm that extends the classic Kuhn—Munkres Hungarian algorithm to compute the maximum interval of deviation, for each entry in the assignment matrix, which will retain the same optimal assignment. The algorithm has a worst-case time complexity of O(n4); we also introduce a parallel variant with O(n3) running time, which is able to exploit the concurrent computing capabilities of distributed multi-robot systems. This provides an efficient measurement of the tolerance of the allocation to the uncertainties and dynamics, for both a specific interval and a set of interrelated intervals. We conduct experiments both in simulation and with physical robots to validate the approach and to gain insight into the effect of location uncertainty on allocations for multi-robot multi-target navigation tasks. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes modified particle swarm optimization to solve the problem of activity assignment of fourth party logistics (4PL) with preemptive structure. In practice, decision makers must consider goals of different importance when they encounter 4PL decision problems. Previous studies have adopted weighted fuzzy goal programming to design optimization problems. However, it is difficult for decision makers to determine proper weights. This paper proposes a decision making method based on preemptive fuzzy goal programming and a modified PSO. The proposed method does not require weights, and prevents results without feasible solutions caused by improper resource setting. Furthermore, this paper proposes a modified PSO with mutation operator extension. Numerical analysis shows that proposed modified PSOs prevent algorithms from caving prematurely into local optimums. [Copyright &y& Elsevier]

Alternative optimal solutions can give more choice for practical decision making. Therefore, the provision of methods for finding alternative optimal solutions is an important component part of the solution techniques for optimization models. The aim of this paper is to present a branch-and-bound algorithm for finding all optimal solutions of the linear assignment problem. Numerical experimental results are also given. [ABSTRACT FROM AUTHOR]

In recent years, there has been a proliferation of database systems in all types of organizations. In many cases, these databases are developed in different departments and maintained autonomously. Much is to be gained, however, if databases across departments, divisions, or even organizations can be related to one another. One main problem of relating data stored in different databases is the differences in their representation of real-world entities, such as the use of different identifiers or primary keys. We present a decision theoretic model for matching entities across different databases. The decision to match two entities from two different databases inherently involves some uncertainty since an exact match may not be found because of errors in data collection, data entry, and data representation. We model this uncertainty using probability theory and propose an integer programming formulation that minimizes the total cost associated with the entity matching decision. The model has been implemented and validated on real-world data. [ABSTRACT FROM AUTHOR]

• We developed a seven-step process to optimally assign ESs to a landscape. • A Delphi technique and pairwise comparisons were used to assign ESs. • Three ES were most important for the case study landscape. • The process allowed an examination of trade-offs among ESs. • The process established relationships between SDGs and ESs. In general, studies are carried out to determine the location and to resolve trade-offs in the management of forests according to ecosystem services. The government of Turkey also has been advancing this type of analysis in the practical management of forests. The creation of ecosystem services (ES) suitability map for forests through a participatory approach can provide forest managers valuable information that informs ecosystem-based management plans. The objective of this paper is to formulate and solve the problem of assigning management actions to forest stands in order to optimally provide ecosystem services that are consistent with, and based on Sustainable Development Goals (SDG). We outline a model for a participatory process that has seven steps: (1) determine the possible ES that can be supported on the landscape, (2) create a suitability map for each management unit (stand of trees), (3) define SDG for each ES, (4) create the stakeholder groups, (5) determine the importance of each SDG, (6) determine the contribution of ES to each SDG, and (7) assign ES to each management unit in an optimal manner. We used pairwise comparisons and the Delphi method to determine stakeholder preferences. This information guided the assignment of management actions to management units when optimizing ES outcomes. This approach was applied to a case study centered on the Belgrad Forest, located in northwest Turkey. The percent of land assigned to ES was respectively, water regulation (71%), cultural heritage (17%), education (9%), water supply (2%), and carbon (1%). Through this process, for this case study area, there were no assignments for recreation and aesthetic quality services. As a result, the Belgrade Forest was zoned into management classes unlike the current situation. The pairwise comparisons and the Delphi method can help formalize public participation in the decision-making process. Results from these can inform a resource allocation optimization model through the development of coefficients and constraints. [ABSTRACT FROM AUTHOR]