An exact algorithm for constrained k-cardinality unbalanced assignment problem

An assignment problem (AP) usually deals with how a set of persons/tasks can be assigned to a set of tasks/persons on a one-to-one basis in an optimal manner. It has been observed that balancing among the persons and jobs in several real-world situations is very hard, thus such scenarios can be seen as unbalanced assignment models (UAP) being a lack of workforce. The solution techniques presented in the literature for solving UAP’s depend on the assumption to allocate some of the tasks to fictitious persons; those tasks assigned to dummy persons are ignored at the end. However, some situations in which it is inevitable to assign more tasks to a single person. This paper addresses a practical variant of UAP called k-cardinality unbalanced assignment problem (k-UAP), in which only of persons are asked to perform jobs and all the persons should perform at least one and at most jobs. The k-UAP aims to determine the optimal assignment between persons and jobs. To tackle this problem optimally, an enumerative Lexi-search algorithm (LSA) is proposed. A comparative study is carried out to measure the efficiency of the proposed algorithm. The computational results indicate that the suggested LSA is having the great capability of solving the smaller and moderate instances optimally.

The institutional foundations of surf break governance in Atlantic Europe

The sport of surfing is best enjoyed with one rider on one wave, but crowding makes that optimal assignment increasingly hard to attain. This study examines the phenomenon of surf localism, whereby competitors are excluded from waves by intimidation and the threat of violence. An alternative way to accommodate crowds is contained in the surfer’s code, which sets informal rules and self-enforced regulations to avoid conflict in the water. Both regimes establish property rights over common pool resources with no state intervention, creating a setting wherein users face the question of cooperation or conflict. The disposition to cooperate and follow norms has been shown to vary substantially across different cultures, though. Employing data from over seven hundred surf spots on the European Atlantic coast, this study reports evidence that certain informal cultural norms significantly reduce the probability of violent exclusion, while formal state institutions mostly are irrelevant. The results also indicate that informal norms become more important with greater resource quality and, possibly, with increasing scarcity.

RESEARCH OF EFFECTIVE TRANSPORT AND LOGISTICS LINKS IN THE ORGANIZATION OF INTERNATIONAL MULTIMODAL TRANSPORT MINERAL FERTILIZERS

Modern agriculture cannot do without the use of mineral and organic fertilizers. Mineral fertilizers are produced by large holdings both in Russia and abroad, and Russian enterprises have subsidiaries distributed throughout the world. The latter factor makes mineral fertilizers one of the most export-oriented branches of the chemical industry in Russia. According to official statistics in 2019 Russian agricultural companies supplied more than 21 million tons of mineral fertilizers to foreign markets, which determines the peculiarities of the country's market. The purpose of the study is to determine the optimal assignment of consumers to suppliers of mineral fertilizers in the organization of multimodal transportation. The article considers the period of the beginning of the reorientation of the production of mineral fertilizers for export. The issue of creating domestic ports specialized in the transshipment of fertilizers has been studied. The volumes of production and consumption of specific countries and regions that are included in export-import operations with each other are analyzed. Routes of transportation of fertilizers with determination of the shortest distances are studied. The optimization of the existing route option for the delivery of nitrogen and potash fertilizers to Brazil is proposed.

Presenting the Multi-Objective Optimization Model of Search and Rescue Network

The Search and Rescue Network (SAR) is a kind of emergency network that pursuit people in need or imminent danger. This paper aims using a priori optimization to demonstrate the optimal assignment of HFDF receivers to the Generalized Search and Rescue (GSAR) network, which is independent of the weighting of the transmitter areas. The mathematical model seeks two objectives, the first one is maximizing the expected number of LOBs for HFDF receivers. The second is providing a fair share number of HFDF receivers allowed to cover the frequency. The result shown the efficiency of presented model ran by CPLEX toolbox of MATLAB 2020 software.

Optimizing bipartite matching in real-world applications by incremental cost computation

The Kuhn-Munkres (KM) algorithm is a classical combinatorial optimization algorithm that is widely used for minimum cost bipartite matching in many real-world applications, such as transportation. For example, a ride-hailing service may use it to find the optimal assignment of drivers to passengers to minimize the overall wait time. Typically, given two bipartite sets, this process involves computing the edge costs between all bipartite pairs and finding an optimal matching. However, existing works overlook the impact of edge cost computation on the overall running time. In reality, edge computation often significantly outweighs the computation of the optimal assignment itself, as in the case of assigning drivers to passengers which involves computation of expensive graph shortest paths. Following on from this observation, we observe common real-world settings exhibit a useful property that allows us to incrementally compute edge costs only as required using an inexpensive lower-bound heuristic. This technique significantly reduces the overall cost of assignment compared to the original KM algorithm, as we demonstrate experimentally on multiple real-world data sets, workloads, and problems. Moreover, our algorithm is not limited to this domain and is potentially applicable in other settings where lower-bounding heuristics are available.