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Assignment problems were widely applied in the field of production planning, telecommunication VLSI design, economic etc. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using pentagonal fuzzy numbers which are further decomposed into triangular fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

In 1982, Pawlak set up a fresh approach to deal with uncertainties namely rough set theory, Multiple-Criteria Decision Making (MCDM) first traced by Benjamin Franklin in 17th century. Several researchers did significant contribution to MCDM thereafter. An assignment problem involves what happens to the effective function when each of a number of sources is associated with the same number of destinations. Using MCDM, Rough matrices and Assignment model we are inducing an idea to pick Best'11 in all three formats (Test, One Day Internationals (ODI), Twenty20 International matches (T20I)) in the game of cricket with players from two nationals. Using the existing data, we are providing best batting position for any player to maximize team's run. In addition, based on the preprocessing of informations, we are bringing some new indices to pick Indian squad for the 2019 World Cup cricket held in England from May 2019 to July 2019. After making a selection from our framework, we will compare the list of selected players by Board of Cricket Control Board in India (BCCI) and giveaway the percentage of similarity between the our selection against BCCI's selection. We pick 11 players after selecting 15 players from 24 players to formulate the assignment model and offer the best batting order to optimize team's run. [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. [ABSTRACT FROM AUTHOR]

Abstract Several studies have found that students' academic achievement is as much determined by the socioeconomic composition of their school as their own socioeconomic status. In this paper we provide a methodology for assigning students to schools so as to balance the socioeconomic compositions of the schools while taking into consideration the total travel distance. Our technique utilizes a biobjective general 0–1 fractional program that is linearized into a mixed 0–1 linear program that can be submitted directly to a standard optimization package. We show how a parametrized model could be utilized to provide a spectrum of different possible assignments so that a decision maker can decide how to balance socioeconomic factors with transportation costs. As a test case for our approach we analyze data from the Greenville County School District in Greenville, South Carolina. [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]

Abstarct: This paper presents a technique that uses the Wang recurrent neural network with the “Winner Takes All” principle to solve the traveling salesman problem (TSP). When the Wang neural network presents solutions for the assignment problem with all constraints satisfied, the “Winner Takes All” principle is applied to the values in the neural network''s decision variables, with the additional constraint that the new solution must form a feasible route for the TSP. The results from this new technique are compared to other heuristics (SOM, SA and heuristics of remotion and insertion of arcs), with data from the traveling salesman problem library (TSPLIB). The 2-opt local search technique is applied to the final solutions of the proposed technique and shows a considerable improvement of the results. The advantages of this new technique are the easy computational implementation, the low computational complexity, the good results obtained and the possibility of solving symmetrical and asymmetrical problems with the same technique. [Copyright &y& Elsevier]

• 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]