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This paper describes a problem of optimal agricultural land treatment using aviation. The studied problem consists of determining the optimal routes for a given set of aircraft used for chemical treatment of arable agricultural land divided into parcels. This NP (nondeterministic polynomial time) problem is represented on a graph and a mixed integer mathematical programming model of the problem is formulated. This mathematical model is a specific variant of the multi-depot vehicle routing problem where a min-cost plan for the transportation of a homogeneous product (chemicals used for land treatment) from different supply locations (airfields) to different demand locations (agricultural parcels) should be generated. Some specifics of the agricultural land chemical treatment are described in the paper and the following specific conditions are taken into consideration: each parcel is treated only by one way of treatment and one aircraft; for each aircraft its chemical and fuel reservoir capacities are sufficient to serve its route. The complexity of the problem and the impossibility to obtain exact solutions for larger dimensions of the problem led to the formulation of a special heuristics which is presented in this paper. Numerical experiments are successfully conducted for larger problem dimensions and results are presented.

Предмет истраживања ове докторске дисертације је анализа линеарног антенског низа, анализа методе комбинације две претраге за синтезу линеарног антенског низа и примена представљене методе на проблеме синтезе линеарног антенског низа..., The primary goals of this dissertation are: analysis of the linear antenna array; analysis of a method combining two searches for the linear antenna array synthesis; and the application of the method presented to the problems of the linear antenna array synthesis...

We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on 50 and 100 vertices with the uniform distribution of integer edge weights in interval [1, 100] show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a partial theoretical explanation of this correlation.

Aircraft noise has been regarded as one of the major environmental issues related to air transport. Many airports have introduced a variety of measures to reduce its impact. Several air traffic assignment strategies have been proposed in order to allocate noise more wisely. Even though each decision regarding the assignment of aircraft to routes should consider population exposure to noise, none of the air traffic assignment strategies has addressed daily migrations of population and number of people exposed to noise. The aim of this research is to develop a mathematical model and a heuristic algorithm that could assign aircraft to departure and arrival routes so that number of people exposed to noise is as low as possible, taking into account temporal and spatial variations in population in an airport's vicinity. The approach was demonstrated on Belgrade airport to show the benefits of the proposed model. Numerical example showed that population exposure to noise could be reduced significantly by applying the proposed air traffic assignment model. As a consequence of the proposed air traffic assignment, overall fuel consumption increased by less than 1%.

We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on 50 and 100 vertices with the uniform distribution of integer edge weights in interval [1, 100] show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a partial theoretical explanation of this correlation.

Mere značajnosti (Importance measures) predstavlјaju načine merenja, tj. brojčanog iskazivanja značajnosti pojedinih komponenata u sistemu sa aspekta ukupne pouzdanosti sistema. Merama značajnosti je moguće odrediti (izdvojiti) komponente najznačajnije za pouzdanost sistema. Od šezdesetih godina, kada je koncept mera značajnosti prvi put uveden, do danas postoji neprekidno interesovanje za ovu oblast, tako da se, pored primene tradicionalnih mera značajnosti, neprestano uvode i definišu nove mere radi njihove primene na specifične sisteme. Opšti nedostatak mera značajnosti, nezavisno od kategorije kojoj pripadaju, je taj što se one utvrđuju za svaku pojedinačnu komponentu, a tek nakon toga se može izdvojiti skup najznačajnijih komponenata zadate kardinalnosti..., Importance measures are numerical representations of the importance of each system’s component considering total system reliability. Using importance measures, the most important components for system reliability can be determined. Since the sixties, when the concept of importance measures was first introduced, there is a constant interest in this area, so that, in addition to the traditional importance measures, new measures for specific systems observed are continually introduced and defined. The general weak point of importance measures, irrespective of the category they belong to, is that they are determined for each individual component, and only afterwards a certain number of most important components can be set aside...

Операциони менаџер користи скуп поступака чији је циљ да се послови ураде брже, јефтиније и квалитетније. Научници из области операционог менаџмента имају задатак да ови поступци буду изводљиви и практични. Скоро увек, менаџери покушавају да нешто оптимизују – или је то минимизација трошкова и потрошње енергије, или пак, максимизација профита, резултата, перформанси и ефикасности. Међутим, није увек могуће пронаћи оптимална решења. У пракси, менаџер мора да се задовољи решењима која можда нису оптимална, али су допустива, задовољавајућа, робустна, и достижна у разумном времену. Оваква решења се добијају применама хеуристика, које могу бити конструктивне, побољшавајуће или хибридне. Област истраживања у докторској дисертацији су конструктивне хеуристике за проблеме комбинаторне оптимизације у операционом менаџменту који припадају класи сложености НП. Представљен је нови генерализовани конструктивни алгоритам који омогућава да се разноврсне хеуристике формирају избором његових аргумената. Такође је уведено опште окружење за генерисање пермутација, које формира везу између енумерације пермутација и корака у конструктивним хеуристикама уметања. Предложен је скуп аргумената генерализованог алгоритма који омогућује паралелно праћење више парцијалних решења за време извршавања алгоритма. Могућности и предности генерализованог алгоритма су представљене кроз његову примену на проблем формирања ћелија у производним системима, проблем распореда производних ћелија и проблем редоследа послова у линији. Нови приступ даје решења која на испитиваним примерима надмашују најбоље познате резултате из литературе., Operations manager deals with a collection of methods for getting things done more quickly, more cheaply or to a higher standard of quality. It is the job of the management scientist to make sure that these methods are practical and relevant. Almost always managers try to optimize something - whether to minimize the cost and energy consumption, or to maximize the profit, output, performance and efficiency. Subsequently, it is not always possible to find the optimal solutions. In practice, managers have to settle for suboptimal solutions or even feasible ones that are satisfactory, robust, and practically achievable in a reasonable time scale. These kind of solutions are obtained with heuristics, which can be constructive, improvement heuristics or hybrid. The field of research in the doctoral thesis are constructive heuristics for NP-hard combinatorial optimization problems in operations management. A new generalized constructive algorithm is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of the generalized algorithm tracking multiple partial solutions, are identified. Features and benefits of the generalized algorithm are presented through the implemetations to the Cell Formation Problem, the Quadratic Assignment Problem and the Permutation Flowshop Problem. The new approach produces solutions that outperform, on the tested instances, the best known results from literature.

In this paper we consider some special characteristics of distances between vertices in the n-dimensional hypercube graph Q(n) and, as a consequence, the corresponding symmetry properties of its resolving sets. It is illustrated how these properties can be implemented within a simple greedy heuristic in order to find efficiently an upper bound of the so called metric dimension beta(Q(n)) of , i.e. the minimal cardinality of a resolving set in Q(n). This heuristic was applied to generate upper bounds of beta(Q(n)) for n up to 22, which are for n >= 19 better than the existing ones. Starting from these new bounds, some existing upper bounds for 23 LT = n LT = 90 are improved by a dynamic programming procedure.

This paper considers the well-known static time-continuous multiproduct economic order quantity (EOQ) based inventory management problem with the storage space constraints. This problem is modelled as a combinatorial optimization problem in the corresponding dynamic discrete time system control process. In order to solve this problem approximately, we developed two heuristics: a special heuristic based on a local search technique and a metaheuristic procedure based on the variable neighbourhood search principle. The efficiency of two heuristics is preliminary examined and compared on several randomly generated instances with the same number of products.

Operacioni menadžer koristi skup postupaka čiji je cilj da se poslovi urade brže, jeftinije i kvalitetnije. Naučnici iz oblasti operacionog menadžmenta imaju zadatak da ovi postupci budu izvodljivi i praktični. Skoro uvek, menadžeri pokušavaju da nešto optimizuju – ili je to minimizacija troškova i potrošnje energije, ili pak, maksimizacija profita, rezultata, performansi i efikasnosti. Međutim, nije uvek moguće pronaći optimalna rešenja. U praksi, menadžer mora da se zadovolji rešenjima koja možda nisu optimalna, ali su dopustiva, zadovoljavajuća, robustna, i dostižna u razumnom vremenu. Ovakva rešenja se dobijaju primenama heuristika, koje mogu biti konstruktivne, poboljšavajuće ili hibridne. Oblast istraživanja u doktorskoj disertaciji su konstruktivne heuristike za probleme kombinatorne optimizacije u operacionom menadžmentu koji pripadaju klasi složenosti NP. Predstavljen je novi generalizovani konstruktivni algoritam koji omogućava da se raznovrsne heuristike formiraju izborom njegovih argumenata. Takođe je uvedeno opšte okruženje za generisanje permutacija, koje formira vezu između enumeracije permutacija i koraka u konstruktivnim heuristikama umetanja. Predložen je skup argumenata generalizovanog algoritma koji omogućuje paralelno praćenje više parcijalnih rešenja za vreme izvršavanja algoritma. Mogućnosti i prednosti generalizovanog algoritma su predstavljene kroz njegovu primenu na problem formiranja ćelija u proizvodnim sistemima, problem rasporeda proizvodnih ćelija i problem redosleda poslova u liniji. Novi pristup daje rešenja koja na ispitivanim primerima nadmašuju najbolje poznate rezultate iz literature., Operations manager deals with a collection of methods for getting things done more quickly, more cheaply or to a higher standard of quality. It is the job of the management scientist to make sure that these methods are practical and relevant. Almost always managers try to optimize something - whether to minimize the cost and energy consumption, or to maximize the profit, output, performance and efficiency. Subsequently, it is not always possible to find the optimal solutions. In practice, managers have to settle for suboptimal solutions or even feasible ones that are satisfactory, robust, and practically achievable in a reasonable time scale. These kind of solutions are obtained with heuristics, which can be constructive, improvement heuristics or hybrid. The field of research in the doctoral thesis are constructive heuristics for NP-hard combinatorial optimization problems in operations management. A new generalized constructive algorithm is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of the generalized algorithm tracking multiple partial solutions, are identified. Features and benefits of the generalized algorithm are presented through the implemetations to the Cell Formation Problem, the Quadratic Assignment Problem and the Permutation Flowshop Problem. The new approach produces solutions that outperform, on the tested instances, the best known results from literature.

Predmet istraživanja u ovoj doktorskoj disertaciji jeste planiranje flote vazduhoplovnog prevozioca, odnosno određivanje potrebnog transportnog kapaciteta. Transportni kapacitet se određuje srednjoročno na osnovu definisane mreže linija, reda letenja i prognozirane potražnje za prevozom i dugoročno, na osnovu očekivanog godišnjeg porasta putničkog saobraćaja. Cilj ovog istraživanja je definisanje modela za planiranje flote, koji bi trebalo da služi kao podrška u odlučivanju pri donošenju odluke o nabavci vazduhoplova za vazduhoplovne prevozioce male i srednje veličine koji saobraćaj obavljaju na kratkim i na linijama srednje dužine. Razvijeni trofazni model prevoziocima pruža mogućnost određivanja srednjoročne okvirne strukture i veličine flote, kao i izbor tipa vazduhoplova za obavljanje saobraćaja na definisanoj mreži linija. U prvoj fazi modela se određuje okvirna struktura flote što podrazumeva dodeljivanje malih i srednjih vazduhoplova odgovarajućim linijama. Za određivanje okvirne strukture flote razvijen je originalni fazi logički sistem kojim se na osnovu prognozirane potražnje i dužine linije određuje preferenciju vazduhoplovnog prevozioca za upotrebu malog vazduhoplova na posmatranoj liniji. U drugoj fazi se određuje broj kako malih, tako i vazduhoplova srednje veličine koji su potrebni za obavljanje planiranog saobraćaja posmatrano na srednjoročnom nivou. Za određivanje veličine flote razvijen je heuristički algoritam, kojim se ujedno vrši i raspoređivanje vazduhoplova na letove. U trećoj fazi modela se vrši izbor tipa vazduhoplova koji u najvećoj meri odgovara potrebama vazduhoplovnog prevozioca. Kako je izbor tipa vazduhoplova problem višekriterijumskog odlučivanja, to je za njegovo rešavanje predložen metod jednakih razmena (even swaps), koji do sada nije bio korišćen za rešavanje problema ove vrste. Za dugoročno planiranje flote predložena je analitička formula, na osnovu koje se određuje dinamika nabavke vazduhoplova.., The subject of research in this doctoral dissertation is airline fleet planning, i.e. determination of the capacity that an airline needs. The capacity is determined based on defined route network, flight schedule and forecasted passenger demand for medium term, and for long term based on estimated traffic growth rate. The goal of this research is to offer a robust model for fleet planning that deals with both fleet sizing and fleet composition problems for airlines operating on short haul and medium haul routes. The developed three-phase model for mid-term fleet planning involves approximate fleet composition based on fuzzy logic, fleet sizing based on the heuristic approach and aircraft type selection based on multi-criteria decision making. Passenger demand and distance are the inputs to the first phase to get an approximate fleet mix in terms of aircraft size. Small or medium-size aircraft are assigned to each destination according to airline’s preference. After determination of approximate fleet mix, the problem transforms into independent fleet sizing problems. Using the set(s) of routes specified in the first stage, the number of needed aircraft is determined in the second stage. Using the results obtained from the previous phases, the next step is to determine which aircraft type meets the market requirements in the best way. Mathematical expression is given to support long term fleet planning and propose dynamics of aircraft purchase. The model is exemplified with the incumbent airline with its base at Nikola Tesla Airport in Belgrade...

Excess of air traffic demand over available capacity in certain segments of the European airspace network typically results in substantial delays imposed on airspace users, despite a possible parallel existence of underutilised adjacent network segments. Recent EU legislation lays down a performance scheme for air navigation services (ANS) and network functions, in an attempt to improve overall efficiency of the ANS, across the areas of safety, environment, capacity and cost-efficiency. It sets a framework for a possible introduction of incentive schemes which would drive the behaviour of involved stakeholders towards meeting the established performance objectives. In such a context, this paper examines an economic concept to incentivise a more efficient use of available network capacities. We put forward a method and develop a model for an anticipatory, time-dependent modulation of ANS charges, aiming to alleviate the demand-capacity imbalance on an airspace network, at minimal cost to airspace users. The proposed method is conceptualised as a bi-level optimisation problem, reconciling the perspectives of network manager and individual network users. The results of a medium-scale real-life case study indicate that an imposition of a revenue-neutral matrix of tolls and rebates on a congested airspace network may yield a fairly equitable route assignment, which seems capacity-wise more efficient than current administrative demand management practices.

Spredšitovi predstavljaju osnovni analitički alat u poslovanju proteklih 25 godina. U radu je opisan pristup upotrebe spredšitova za definiciju heurističkih i metaheurističkih algoritama, koji mogu unaprediti funkciju troškova i vremena u cilju pronalaska vrednosti upravljačkih promenljivih, koje daju bolje diskretne procese. U radu se predstavlja statički, vremenski kontinualni problem ekonomične količine naručivanja (EOQ) zaliha za više proizvoda sa ograničenjem skladišnog prostora, modeliran u spredšitu kao problem kombinatorne optimizacije za odgovarajući dinamički, vremenski diskretni proces upravljanja zalihama (DPUZ). Opisani problem upravljanja zalihama predstavlja široko primenljiv i poznat problem u praksi.U cilju rešavanja problema razvijena je specijalna heuristika, zasnovana na tehnici lokalnog pretraživanja i metaheuristička metoda bazirana na principu promenljivih okolina (MPO). Specijalna heuristika se koristi za određivanje broja narudžbina, a metoda bazirana na principu promenljivih okolina je primenjena za poređenje rezultata dobijenih specijalnom heuristikom. Efikasnost razvijenih metoda je preliminarno ispitana i upoređena kroz nekoliko numeričkih ekseperimenata za 21 i 102 artikla., Spreadsheets have been an essential analytical tool in business for over 25 years. This paper presents the approach of using spreadsheets for the definition of heuristics and metaheuristics algorithms, which can improve time and cost functions, in order to find control variables values, which give better discrete processes.The objective of this paper is to model a static time-continuous multiproduct economic order quantity (EOQ) based inventory management problem with storage space constraints, as a combinatorial optimization problem in the corresponding dynamic discrete time system control process. The described inventory management problem represents a widely applicable and popular problem in practice. To solve this model we have developed a special heuristics based on the local search technique and a metaheuristic technique based on the variable neighborhood search principle, and we have preliminary examined their efficiency and compared them in several numerical experiments. The special heuristics was developed in order to determine number of orders and the metaheuristic technique based on the variable neighborhood search was developed in order to compare its results with the results of the special heuristics.

In this paper, we consider the problem of determining the minimal cardinality of double resolving sets for prism graphs Y-n. It is proved that the minimal cardinality is equal to four if n is even and equal to three if n is odd.

Анализа стабла неисправности (АСН) је техника за анализу поузданости која се користи за одређивање узрока и вероватноће отказа система. АСН је базирана на стаблу неисправности (СН), графичком моделу који користи логичка кола и отказне догађаје за представљање узрочно-последичних веза између догађаја који претходе отказу система. Квалитативни део АСН састоји се у одређивању минималних скупова пресека. Скуп пресека је скуп примарних догађаја који, када се догоде истовремено, доводе до отказа ситема. Минимални скуп пресека (минипресек) је скуп пресека који је редукован на минимални број елемената који изазивају отказ система. У овој дисертацији је предложена нова метода за одређивање минипресека кохерентног СН, СН које садржи само И и ИЛИ логичка кола, са вишеструким догађајима. Метода је заснована на посебном типу Петријевих мрежа – инверзним Петријевим мрежама. Прво је представљен нови алгоритам за редукцију скупова пресека кохерентног СН. Одређивање свих минипресека кохерентног СН је НП тежак проблем. У дисертацији се разматрају приступи којима се прво одређују сви скупови пресека датог СН а затим се врши елиминисање надскупова, односно скупова пресека који нису минимални. У тим приступима, СН се трансформише у еквивалентну булову једначину у којој се, затим, елиминишу сви редундантни скупови пресека. Већ је доказано да су скупови пресека, који не садрже вишеструке догађаје, минимални. Тиме се редукција ограничава само на скупове пресека са вишеструким догађајима. У овој дисертацији се посматра још једна врста скупова пресека: они који, ако садрже неки вишеструки догађај, садрже сва његова понављања. Овакви скупови пресека су означени са C*. Показује се да је скуп пресека облика C*, ако постоји, такође минималан. Тиме се додатно скраћује поступак редукције булове једначине. Затим се, даље, доказују услови за постојање скупова пресека облика C* и одређује минимална број скупова пресека који се могу елиминисати као надскуп од C*. Предложен је нови алгоритам за редукци, The Fault Tree Analysis (FTA) is a reliability analysis technique used to determine the root causes and probability of occurrence of a specified top event. FTA is based on a Fault Tree (FT), a graphical model using logic gates and fault events to model the cause-effect relationships involved in causing the top event. Determining minimal cut sets is a qualitative part in the FTA. The cut set is a set of basic events which, when simultaneous, cause the top event to occur. The minimal cut set (minicut) is a cut set which has been reduced to the minimum number of events that cause the top event to occur. This Dissertation proposes a new method for minicuts generation of a coherent FT, constructed using AND and OR logic operator only, with repeated events. The approach is based on the special type of Petri Nets – Reverse Petri Net. First, a new algorithm for reducing cut sets in coherent fault trees is presented. Determining all minicuts of a fault tree is NP-hard problem. Coherent fault trees and the top-down approaches for minicuts generation are considered. The FT can be translated into an equivalent Boolean expression. Obtained Boolean expression then should be reduced by eliminating all redundant cut sets. It is already proved that the cut sets not containing any repeated event are minicuts. This limits the reduction only to the cut sets containing repeated events. Cut sets containing all repetitions of its events are denoted by {C*}. It is proved that C*, if exists, is also minicut. This further limits the reduction of the Boolean expression. In addition, we proved conditions for existence of C* and calculated the minimal number of cut sets that can be eliminated as subsets of C*. Finally, a new algorithm for reduction of the Boolean expression which is based on the partition of the cut sets into three families: those not containing any repeated event, those of type C*, and others, is proposed. The efficiency of the algorithm is shown by applying it to some benchma

In this paper we consider two similar optimization problems on graphs: the strong metric dimension problem and the problem of determining minimal doubly resolving sets. We prove some properties of strong resolving sets and give an integer linear programming formulation of the strong metric dimension problem. These results are used to derive explicit expressions in terms of the dimension n, for the strong metric dimension of two classes of convex polytopes D-n and T-n. On the other hand, we prove that minimal doubly resolving sets of Dn and Tn have constant cardinality for n > 7.

Analiza stabla neispravnosti (ASN) je tehnika za analizu pouzdanosti koja se koristi za određivanje uzroka i verovatnoće otkaza sistema. ASN je bazirana na stablu neispravnosti (SN), grafičkom modelu koji koristi logička kola i otkazne događaje za predstavljanje uzročno-posledičnih veza između događaja koji prethode otkazu sistema. Kvalitativni deo ASN sastoji se u određivanju minimalnih skupova preseka. Skup preseka je skup primarnih događaja koji, kada se dogode istovremeno, dovode do otkaza sitema. Minimalni skup preseka (minipresek) je skup preseka koji je redukovan na minimalni broj elemenata koji izazivaju otkaz sistema. U ovoj disertaciji je predložena nova metoda za određivanje minipreseka koherentnog SN, SN koje sadrži samo I i ILI logička kola, sa višestrukim događajima. Metoda je zasnovana na posebnom tipu Petrijevih mreža – inverznim Petrijevim mrežama. Prvo je predstavljen novi algoritam za redukciju skupova preseka koherentnog SN. Određivanje svih minipreseka koherentnog SN je NP težak problem. U disertaciji se razmatraju pristupi kojima se prvo određuju svi skupovi preseka datog SN a zatim se vrši eliminisanje nadskupova, odnosno skupova preseka koji nisu minimalni. U tim pristupima, SN se transformiše u ekvivalentnu bulovu jednačinu u kojoj se, zatim, eliminišu svi redundantni skupovi preseka. Već je dokazano da su skupovi preseka, koji ne sadrže višestruke događaje, minimalni. Time se redukcija ograničava samo na skupove preseka sa višestrukim događajima. U ovoj disertaciji se posmatra još jedna vrsta skupova preseka: oni koji, ako sadrže neki višestruki događaj, sadrže sva njegova ponavljanja. Ovakvi skupovi preseka su označeni sa C*. Pokazuje se da je skup preseka oblika C*, ako postoji, takođe minimalan. Time se dodatno skraćuje postupak redukcije bulove jednačine. Zatim se, dalje, dokazuju uslovi za postojanje skupova preseka oblika C* i određuje minimalna broj skupova preseka koji se mogu eliminisati kao nadskup od C*. Predložen je novi algorit, The Fault Tree Analysis (FTA) is a reliability analysis technique used to determine the root causes and probability of occurrence of a specified top event. FTA is based on a Fault Tree (FT), a graphical model using logic gates and fault events to model the cause-effect relationships involved in causing the top event. Determining minimal cut sets is a qualitative part in the FTA. The cut set is a set of basic events which, when simultaneous, cause the top event to occur. The minimal cut set (minicut) is a cut set which has been reduced to the minimum number of events that cause the top event to occur. This Dissertation proposes a new method for minicuts generation of a coherent FT, constructed using AND and OR logic operator only, with repeated events. The approach is based on the special type of Petri Nets – Reverse Petri Net. First, a new algorithm for reducing cut sets in coherent fault trees is presented. Determining all minicuts of a fault tree is NP-hard problem. Coherent fault trees and the top-down approaches for minicuts generation are considered. The FT can be translated into an equivalent Boolean expression. Obtained Boolean expression then should be reduced by eliminating all redundant cut sets. It is already proved that the cut sets not containing any repeated event are minicuts. This limits the reduction only to the cut sets containing repeated events. Cut sets containing all repetitions of its events are denoted by {C*}. It is proved that C*, if exists, is also minicut. This further limits the reduction of the Boolean expression. In addition, we proved conditions for existence of C* and calculated the minimal number of cut sets that can be eliminated as subsets of C*. Finally, a new algorithm for reduction of the Boolean expression which is based on the partition of the cut sets into three families: those not containing any repeated event, those of type C*, and others, is proposed. The efficiency of the algorithm is shown by applying it to some benchma