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Purpose: Only few companies were able to produce vaccine again COVID-19. Thus, one producer supplied it to many countries. The distribution was not effective. Some countries overstocked the vaccine while other countries were not able to buy enough. The purpose of the present paper is to provide with a frame such that one producer distributes the vaccine to a set of countries in a way that the shortage is minimized. Methodology: The consumption of the countries are approximated by regression functions taking into account the saturation of the process. The distribution of the vaccine is determined by MIP models of operations research. Findings: Effective distribution of vaccine can be obtained for even a large number of countries. Both the level of the shortage and the number of the consecutive shortage days in a country can be controlled. Practical implications: A group of countries can act as a single partner of a pharmaceutical company. They can get a steady supply. The company gets a well-organized delivery plan. Social implications: More people can be saved because of the steady supply of the vaccine. Originality: The paper develops a new concept for the fair distribution of vaccines between countries. This concept and the method derived from it can be applied in the event of future pandemics on a global scale., Comment: 10 pages

Flexible robotic cells are utilized to produce standardized products at a high speed production rate, and to set up the production floors based on rapid operating environment changes. In FRC, there are a number of computer numerical control machines, an input buffer, an output buffer, and a robot. The input and output buffers contain unprocessed and finished products, respectively, whereas the robot performs the loading and unloading activities and transports the items among buffers and machines. The system repeats a cyclic schedule in its run and the cycle time depends on the order of robot activities. In order to maximize the efficiency of the system, the order of the robot activities yielding the minimum cycle time should be determined. The aim of this research is to find novel exact models to solve this cycling scheduling problem. These types of problems have tight relations with traveling salesman problem. In this study, four main modeling approaches of the TSP, such as Dantzig-Fulkerson-Johnson approach, Miller-Tucker-Zemlin approach, Vajda's n-step approach, and the network flow approach are studied. Only the DFJ approach cannot be adapted to the scheduling problem. The three other approaches are adapted successfully. Similarities and differences are discussed by using several numerical examples.

Sovereign debt ratings provided by rating agencies measure the solvency of a country, as gauged by a lender or an investor. It is an indication of the risk involved in investment, and should be determined correctly and in a well timed manner. The present study reconstructs sovereign debt ratings through logical analysis of data, which is based on the theory of Boolean functions. It organizes groups of countries according to twenty World Bank defined variables for the period 2012 till 2015. The Fitch Rating Agency, one of the three big global rating agencies, is used as a case study. An approximate algorithm was crucial in exploring the rating method, in correcting the agencys errors, and in determining the estimated rating of otherwise non rated countries. The outcome was a decision tree for each year. Each country was assigned a rating. On average, the algorithm reached almost ninety eight percentage matched ratings in the training set, and was verified by eighty four percentage in the test set. This was a considerable achievement., Comment: 18 pages, 1 figure, 12 tables

Given a reaction (network) we are looking for minimal sets of species starting from which all the species will have positive concentrations for all positive times in the domain of existence of the solution of the induced kinetic differential equation. We present three algorithms to solve the problem. The first one essentially checks all the possible subsets of the sets of species. This can obviously work for only a few dozen species because of combinatorial explosion. The second one is based on an integer programming reformulation of the problem. The third one walks around the state space of the problem in a systematic way and produces all the minimal sets of the advantageous initial species, and works also for large systems. All the algorithms rely heavily on the concept of Volpert indices, used earlier for the decomposition of overall reactions [Kov\'acs \textit{et al., Physical Chemistry Chemical Physics} 2004, 6, 1236]. Relations to the permanence hypothesis, possible economic or medical uses of the solution of the problem are analyzed, and open problems are formulated at the end., Comment: 19 pages, 7 figures

The main result of this paper is that the polytope of the bipartite TSP is significantly different from that of the general TSP. Comb inequalities are known as facet defining ones in the general case. In the bipartite case, however, many of them are satisfied whenever all degree and subtour elimination constraints are satisfied, {\em i.e.}\ these comb inequalities are not facet defining. The inequalities in question belong to the cases where vertices of one of the two classes occur in less than the half of the intersections of the teeth and the hand. Such side conditions are necessary, as simple example shows that the comb inequality can be violated when each class has vertices in more than the half of the intersections.