Discrete Models for Intermediate Storages under Stochastic Operational Conditions

In this paper we investigate the operation of an intermediate storage assuming discrete stochastic operational conditions. The storage operates as a buffer. The material is collected into it and is withdrawn from the buffer for production. Deterministic constant withdrawal rate is supposed and the filling process is described by discrete random variables. The main question addressed here is the probability of material shortage as a function of the initial amount of material. For this purpose, an auxiliary function is defined and a difference equation is set for it. In a special case we present the solution of the difference equation, we compare the exact and simulated results, and we propose a method for the determination of unknown constants. We apply the results for expressing the initial amount of material necessary to a given reliability level. Finally, we compare the results of the discrete model with those of the continuous one

Sizing Problem of Intermediate Storages under Stochastic Operational Conditions

The operation of intermediate storages is investigated in this paper. The input process is supposed to be a batch process and the output process is assumed to be a continuous one. The operational conditions in the input process are stochastic with respect to time and the amount of material. The goal is the determination of the required size of the buffer to a given reliability. For the solution, an auxiliary function is introduced and an integral equation is set up for it. Its analytical solution is presented in a special case. In general cases we present the approximation of the reliability with the help of a hyperbolic tangent family. We compare the exact and approximate solutions and present the solution of the sizing problem. We investigate the effects of dispersions to present the uncertainties

The incomplete Analytic Hierarchy Process and Bradley-Terry model: (in)consistency and information retrieval

Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports matches) are naturally known for pairs. This paper investigates and compares pairwise comparison models and the stochastic Bradley-Terry model. It is proved that they provide the same priority vectors for consistent (complete or incomplete) comparisons. For incomplete comparisons, all filling in levels are considered. Recent results identified the optimal subsets and sequences of multiplicative/additive/reciprocal pairwise comparisons for small sizes of items (up to n = 6). Simulations of this paper show that the same subsets and sequences are optimal in case of the Bradley-Terry and the Thurstone models as well. This, somehow surprising, coincidence suggests the existence of a more general result. Further models of information and preference theory are subject to future investigation in order to identify optimal subsets of input data

A Thurstone módszer alkalmazása sporteredmények elemzésére a 2020/2021-es női kézilabda Bajnokok Ligája példáján = The Application of the Thurstone Method For Evaluating Sports Results – Presenting on the EHF Women Handball Championship

Ebben a tanulmányban sporteredmények kiértékelésének egy lehetséges módját mutatjuk be. Az alkalmazott Thurstone módszer a mérkőzések eredményeit páros összehasonlítások eredményeinek fogja fel. Az egyes csapatok teljesítményeit véletlen mennyiségeknek tekinti, amiknek a várható értékét maximum likelihood módszerrel becsüli. A becsült várható értékek sorrendje adja a csapatok sorrendjét. A módszer előnye, hogy nem csak körmérkőzés és nem csak egyforma számú lejátszott mérkőzés esetén működik; figyelembe veszi az ellenfél erősségét; alkalmas különböző csoportok összefésülésére, valamint további mérkőzések eredményeinek előrejelzésére. A módszert az EHF női kézilabda Bajnokok Ligája eredményein keresztül illusztráljuk. Megmutatjuk, hogy a csoportkörökben ténylegesen lejátszott mérkőzések eredményeit figyelembe véve az erősségek megadhatók. Az A csoport legerősebbje a Metz Handball, a hivatalos eredménnyel szemben, míg a B csoport legerősebbje a Győri Audi KC lett. Előre jeleztük a legjobb nyolc csapatot és a Final Four résztvevőit, felhasználva a csoportkörök eredményeit és a csoportbeli legjobbaknak a másik csoportbeli leggyengébbek elleni egy-egy győztes meccsét. Végezetül megállapíthatjuk, hogy a módszer helyesen jelezte előre a Vipers Kristiandsand kupagyőzelmét. = In this paper a possible method for evaluation of sports results is presented. The applied Thurstone method considers the results of the matches as the results of paired comparisons. Performances of the teams are random variables, and their expectations are estimated by maximum likelihood method. Ranking of the expectations provides ranking of the teams. The advantages of the method are the followings: it works without the requirement of equal numbers of matches, takes into consideration the strength of the opponents, and it is suitable for interweaving different groups and forecasting further results. Use of the method is illustrated through the results of the Women’s EHF Champions League. We present that ranks of the groups can be set up based on the played matches. The best team of Group A is Metz Handball, opposite to the official result; the best team of Group B is Győri Audi KC. Participants of the Quarter Final and the Final Four are forecasted based on the results in the group phase and on the results of the best teams against the weakest teams in the other groups. Finally, the method correctly predicts the winner of the Cup, namely the Vipers Kristiandsand

Profit optimization of batch-continuous production systems under stochastic processingconditions by simulation

The properties of a production system working under stochastic processing conditions are investigated. The production system consists of batch units of an input subsystem and a continuously operated deterministic output one which are coupled by an intermediate storage system. The randomness of operation is caused by the uncertainties of batch sizes and the time intervals of arrival to the storage. Taking into account the expenses and the income arising from the production the expectation of the profit is defined and investigated. An integral equation is presented for the expected profit, and is solved using Monte Carlo method. The optimal initial amount of material to be processed, storage volume and withdrawing rate are determined by simulation