The paper presents a method of scheduling execution of technological operations in work centres in a company manufacturing seats for passenger cars. To that end, an optimization algorithm based on the B&B method was developed, aimed at minimizing the number of employees necessary for operation of the work centres and at maximizing capacity of the manufacturing process. Efficiency and effectiveness of the algorithm was verified on the grounds of real data coming from the manufacturing company.
In the paper, a problem of scheduling operations in the cyclic flexible job shop system is considered. A new, very fast method of determining the cycle time for any order of tasks on machines is also presented. It is based on the analysis of the paths in the graph representing the examined problem. The theorems concerning specific properties of the graph are proven and used in the construction of the heuristic algorithm searching the solutions space by using the so-called golf neighborhood, which is generated in a way similar to the game of golf, which helps to intensify and diversify calculations. The conducted computational experiments fully confirmed the effectiveness of the proposed method. The proposed methods and properties can be adapted and used in the construction of local search algorithms for solving many other optimization problems.
The subject of this work is the new idea of blocks for the cyclic flow shop problem with setup times, using multiple patterns with different sizes determined for each machine constituting optimal schedule of cities for the traveling salesman problem (TSP). We propose to take advantage of the Intel Xeon Phi parallel computing environment during so-called ’blocks’ determination basing on patterns, in effect significantly improving the quality of obtained results.
In the paper a variant of cyclic production with setups and two-machine cell is considered. One of the stages of the problem solving consists of assigning each operation to the machine on which it will be carried out. The total number of such assignments is exponential. We propose a polynomial time algorithm finding the optimal operations to machines assignment.
In this paper there is considered a flexible job shop problem of operations scheduling. The new, very fast method of determination of cycle time is presented. In the design of heuristic algorithm there was the neighborhood inspired by the game of golf applied. Lower bound of the criterion function was used in the search of the neighborhood.
Models of multimodal cyclic processes, i.e. processes realized with synergic utilization of various local and cyclic acting processes, play a determining role in an evaluation of functioning efficiency inter alia in public transport systems, passengers movement, cargo transport, data and energy transmission etc. We assume that the structure of a system determines repertoire of its behaviors. The paper presents a constraints satisfaction problem, which solving enables an evaluation of potential behaviors of the system of concurrently interacting local cyclic processes. Consequently, it is possible to plan and schedule the multimodal processes realized in that system. The constraints satisfaction problem, enabling the search for the structure of inter-position transport system and guaranteeing realization of assumed schedule of multi-assortment production was formulated for a declarative model of the multimodal transportation processes system. The attached calculation example illustrates the computational efficiency of the proposed approach.
Multimodal processes planning and scheduling play a pivotal role in many different domains including city networks, multimodal transportation systems, computer and telecommunication networks and so on. Multimodal process can be seen as a process partially processed by locally executed cyclic processes. In that context the concept of a Mesh-like Multimodal Transportation Network (MMTN) in which several isomorphic subnetworks interact each other via distinguished subsets of common shared intermodal transport interchange facilities (such as a railway station, bus station or bus/tram stop) as to provide a variety of demand-responsive passenger transportation services is examined. Consider a mesh-like layout of a passengers transport network equipped with different lines including buses, trams, metro, trains etc. where passenger flows are treated as multimodal processes. The goal is to provide a declarative model enabling to state a constraint satisfaction problem aimed at multimodal transportation processes scheduling encompassing passenger flow itineraries. Then, the main objective is to provide conditions guaranteeing solvability of particular transport lines scheduling, i.e. guaranteeing the right match-up of local cyclic acting bus, tram, metro and train schedules to a given passengers flow itineraries.
Dynamiczny rozwój infrastruktury komunikacji miejskiej obejmującej linie autobusowe, trolejbusowe, tramwajowe, linie metra, kolei podmiejskiej, itp. składające się na tzw. Multimodalne Sieci Transportowe (MST) rodzi wiele nowych problemów. Wśród ważniejszych z nich warto wymienić problemy planowania obsługi ruchu pasażerskiego w sytuacjach związanych z awariami elementów infrastruktury, wypadkami losowymi czy też z obsługą imprez masowych. Wiadomo, że istnienie rozwiązań dopuszczalnych gwarantujących zakładaną przepustowość infrastruktury warunkuje tzw. odporność MST na ww. zakłócenia. W tym kontekście, niniejsza praca przedstawia pewien deterministyczny model multimodalnej sieci transportowej złożonej z połączonych stacjami przesiadkowymi, linii komunikacji miejskiej. Składające się na sieć, pracujące w zamkniętych cyklach, linie komunikacji miejskiej pozwalają obsłuchiwać ruch pasażerski na wybranych kierunkach np. północ-południe. Obsługiwane strumienie pasażerów modelowane są jako tzw. multimodalne procesy transportowe. Wprowadzone miary odporności MST, umożliwiające ocenę rozważanych wariantów infrastruktury, pozwalają na wyznaczenie warunków spełnienie, których gwarantuje dopuszczalną jakość obsługi ruchu pasażerskiego. Umożliwiają, zatem zarówno planowanie obsługi pasażerów na wybranych trasach, jak i kształtowanie struktury rozbudowywanej i/lub modernizowanej sieci komunikacji miejskiej.
EN
This paper describes a declarative approach to modeling a multimodal transportation network (MTN) composed of multiple connecting transport modes, such as bus, tram, light rail, subway and commuter rail, where within each mode, service is provided on separate lines or routes. The considered model of a network of multimodal transportation processes (MTPN) provides a framework to address the needs for transportation networks robustness while taking into account their capacity and demand requirements. Therefore the work focuses on evaluation of the network robustness allowing distinguished multimodal processes to continue in order to accomplish trips following an assumed set of multimodal chains connecting transport modes between origins and destinations. Consequently, a solution to the problem of prototyping robust transits on a given multimodal network is implemented and tested. The conditions that guarantee the network robustness, taking into account disruptions of supply and demand as well as operational control, are provided. The aim of investigations is to provide a tool for evaluating the robustness of a network of multimodal transportation processes as well as different travel modes through a transportation network.
A new mixed integer programming formulation is presented for cyclic scheduling in flow lines with parallel machines and finite in-process buffers, where a Minimal Part Set (MPS) in the same proportion as the overall production target is repetitively scheduled. The cycle of parts in an MPS is not determined a priori, but is obtained along with the optimal schedule for all parts. In addition to the cyclic scheduling, a cyclic-batch scheduling mode is introduced, where within the MPS the parts of one type are processed consecutively. Numerical examples are included and some results of computational experiments are reported.
This paper concerns the domain of the multimodal transportation systems composed of buses, trains, trams and subways lines and focuses on the scheduling problems encountered in these systems. Transportation Network Infrastructure (TNI) can be modeled as a network of lines providing cyclic routes for particular kinds of stream-like moving transportation means. Lines are connected by common shared change stations. Depending on TNI timetabling the time of the trip of passengers following different itineraries may dramatically differ, e.g. the same distances along the north-south, and east-west directions may require different travel time. So, the mine question regards of TNI schedulability, e.g. the guarantee the same distances in arbitrarily assumed directions will require approximate traveled time. Considered timetabling problem belongs to NP-hard ones. The declarative model of TNI enabling to formulate cyclic scheduling problem in terms of the constraint satisfaction one is our main contribution. At last, the simulated results manifest the promising properties of the proposed model.
PL
W artykule podejmowana jest problematyka harmonogramowania marszrut pasażerskich realizowanych w multimodalnych systemach komunikacji (MSK) miejskiej obejmujących linie autobusowe, tramwajowe, pociągowe, a także linie metra i linie promowe. MSK modelowany jest jako sieć linii komunikacji miejskiej realizujących swoje cykliczne marszruty transportowe zadaną liczba odpowiednich środków transportu pasażerskiego, tzn. autobusów, tramwajów, pociągów itp. Przyjmuje się, że linie te umożliwiają przesiadanie się pasażerów na wspólnie dzielonych stacjach przesiadkowych. Rozważany problem dotyczy doboru takiej struktury i organizacji ruchu poszczególnych linii, które zapewnią podobne czasy przejazdu (na podobnych dystansach) podróżnych przemieszczających się w różnych kierunkach. Problem ten należy do problemów NP-trudnych. Proponowane w pracy rozwiązanie przyjmuje model deklaratywny MSK sprowadzając rozważany problem harmonogramowania do postaci deterministycznego problemu spełniania ograniczeń. Zamieszczone przykłady implementacji tego problemu w języku programowania z ograniczeniami potwierdzają użyteczność zaproponowanego modelu harmonogramowania MSK.
In everyday practice cyclic scheduling problems, especially timetabling ones arise in different application and service domains, e.g., class, train, crew timetabling, and so on. In many cases, e.g., caused by assumed slot size, imposing integer domain results in Diophantine character of problems considered. In that context some classes of cyclic scheduling problems can be seen as non-decidable (undecidable) ones. That means, since system constraints (i.e., parameter domains) determine its behavior (e.g., the space of feasible schedules), hence both system structure configuration and desired schedule have to be considered simultaneously. So, cyclic scheduling problem solution requires that the system structure configuration must be determined for the purpose of processes scheduling, yet scheduling must be done to devise the system configuration. In that context, this contribution provides discussion of some solubility issues concerning cyclic processes dispatching problems.
Harmonogramowanie cykliczne rozumiane jako harmonogramowanie powtarzających zdarzeń, jak np. zajęć lekcyjnych, rozkładów jazdy, itp. wiąże się z poszukiwaniem odpowiedzi na dwie klasy pytań: odpowiednio o charakterze dedukcyjnym i abdukcyjnym. Pierwsza grupa problemów dotyczy wyboru zasad rozstrzygania konfliktów zasobowych ekstremalizujących wielokryterialną funkcję celu (minimalizacja cyklu, maksymalizacja przepustowości, itp.) przy zadanych ograniczeniach narzucanych na strukturę systemu, druga z kolei poszukuje struktur, które przy zadanych regułach rozstrzygania konfliktów zasobowych gwarantują zadane ilościowe i jakościowe parametry wielokryterialnej funkcji celu. Przedstawione rozważania koncentrują się na drugiej klasie problemów. Podkreślając ich diofantyczny charakter wyjaśnią kwestie związane z nierozstrzygalnością szeregu problemów harmonogramowania cyklicznego, w szczególności tych związanych z próbą uzyskania oczekiwanych zachowań systemu przy arbitralnie zadanych ograniczeniach strukturalnych.
Cyclic scheduling concerns both kinds of questions following the deductive and inductive ways of reasoning. First class of problems concentrates on rules aimed at resources assignment as to minimize a given objective function, e.g. the cycle time, the flow time of a job. In turn, the second class focuses on a system structure designing as to guarantee the assumed qualitative and/or quantitative measures of objective functions can be achieved. The third class of problems can be seen, however as integration of earlier mentioned, i.e. treating design and scheduling or design and planning simultaneously. The complexity of these problems stems from the fact that system configuration must be determined for the purpose of processes scheduling, yet scheduling must be done to devise the system configuration. In that context, the contribution provides discussion of some Diophantine problems solubility issues, taking into.
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