Genetic algorithm for the continuous location-routing problem

This paper focuses on the continuous location-routing problem that comprises of the location of multiple depots from a given region and determining the routes of vehicles assigned to these depots. The objective of the problem is to design the delivery system of depots and routes so that the total cost is minimal. The standard location-routing problem considers a finite number of possible locations. The continuous location-routing problem allows location to infinite number of locations in a given region and makes the problem much more complex. We present a genetic algorithm that tackles both location and routing subproblems simultaneously.Web of Science29318717

On two modifications of E-r/E-s/1/m queuing system subject to disasters

The paper deals with modelling a finite single-server queuing system with the server subject to disasters. Inter-arrival times and service times are assumed to follow the Erlang distribution defined by the shape parameter r or s and the scale parameter rλ or sμ respectively. We consider two modifications of the model − server failures are supposed to be operate-independent or operate-dependent. Server failures which have the character of so-called disasters cause interruption of customer service, emptying the system and balking incoming customers when the server is down. We assume that random variables relevant to server failures and repairs are exponentially distributed. The constructed mathematical model is solved using Matlab to obtain steady-state probabilities which we need to compute the performance measures. At the conclusion of the paper some results of executed experiments are shown.Web of Science12215814

Rozšiřující modely úlohy o pokrytí vrcholů dopravní sítě

The article deals with the problem of optimal coverage of utility centres in transport network. We can often encounter similar types of tasks in a real life. A lot of cases relate to the public utility systems that mean systems intended for providing basic public services to all population in a certain territory. These services can include services of Integrated Rescue System. The tasks of this category are called max D tiling tasks in a scientific literature. The classic version of max D cover task is known for quite a long time but its shape does not always cover real traffic conditions. The aim of the article is to show other modifications of the basic variation of the tasks. The authors expect the proposed application will enable mathematical apparatus to be used to solve problems of this type to the greater extent.Článek se zabývá problémem optimálního pokrytí dopravní sítě obslužnými středisky. S podobnými typy úloh se můžeme setkat v reálném životě velice často. Velké množství případů se vztahuje k tzv. veřejným obslužným systémům, tj. systémům, které jsou určeny k zajištění základních veřejných služeb poskytovaných všemu obyvatelstvu na určitém území. Takovými službami mohou být např. služby integrovaného záchranného systému. Úlohy této kategorie se v odborné literatuře označují jako max D pokrývací úlohy. Klasická varianta max D pokrývací úlohy je známa poměrně dlouhou dobu, svým tvarem však vždy nevyhovuje podmínkám reálného provozu. Článek si klade za cíl ukázat další vybrané modifikace základní varianty úlohy. Autoři očekávají, že navržené aplikace umožní využívat matematický aparát k řešení tohoto typu úloh ve větší míře

Locomotive assignment problem with heterogeneous vehicle fleet and hiring external locomotives

This paper focuses on solving the problem of how to assign locomotives to assembled trains optimally. To solve the problem, linear programming is applied. The situation we model in the paper occurs in the conditions of a transport operator that provides rail transport in the Czech Republic. In the paper, an extended locomotive assignment problem is modeled; the transport operator can use different classes of the locomotives to serve individual connections, some connections must be served by a predefined locomotive class, and the locomotives can be allocated to several depots at the beginning. The proposed model also takes into consideration the fact that some connections can be served by the locomotives of external transport companies or operators. The presented model is applied to a real example in order to test its functionality.Web of Science2015art. no. 58390

TRAVELLING SALESMAN PROBLEM WITH PARTIALLY DIRECTED NODES SERVICE

Úloha obchodního cestujícího patří k základním úlohám operační analýzy. V praktických aplikacích může mít celou řadu modifikací, přičemž modifikace vyplývají ze specifik řešené úlohy. V předloženém článku se zabýváme jednou z nich. Konkrétně se jedná o typ úlohy, ve které je pohyb obchodního cestujícího částečně usměrněn. V dopravních aplikacích může jít např. o situace, kdy vozidlo v rámci okružní jízdy mezi odjezdem ze střediska a příjezdem do střediska postupně realizuje přepravu více zásilek mezi vrcholy dopravní sítě.Travelling salesman problem belongs to the elementary operational research problem. In the practical applications it can have a lot of modifications. The modifications flow from specifics of solved problem. In the presented article we deal with one of them. Concretely it deals with the problem, in which the travelling salesman movement is partially directed

SELECTED METHODS USED ABROAD TO ADDRESS THE URBAN PUBLIC TRANSPORT LINE NETWORK DESIGN

Článek se zabývá zmapováním vybraných stávajících přístupů k tvorbě sítě linek MHD v zahraničí. U jednotlivých přístupů je uvedena jejich stručná charakteristika. Dále je provedeno jejich porovnání, společné rysy a rozdíly The article deals with survey of selected current approaches to a formation of network of urban public transport lines in abroad. Brief characteristics of the approaches are presented. Their common features and differences are compared

MODELLING OF SHUNTING SLOPE OPERATION USING UNRELIABLE QUEUEING SYSTEM

Článek je věnován modelování provozu na svážném pahrbku seřaďovací stanice s využitím teorie hromadné obsluhy. Studovaný proces je modelován jako nespolehlivý systém hromadné obsluhy s dokončením obsluhy požadavku při vzniku poruchy linky. Článek předkládá dva odlišné modely reálného systému – matematický model a simulační model vytvořený v prostředí Witness. V závěru článku je provedena komparace dosažených výsledků.The paper is devoted to the modelling of shunting slope operation using the queueing theory. Studied process is modelled as an unreliable queueing system with costumer service completing after breakdown occurence. The paper introduces two different models – a mathematical model and an simulation model created by using software Witness. In the end of the paper comparison of reached outcomes is carried out

Optimisation of service capacity based on queueing theory

Queueing theory is a mathematical tool which can be applied for capacity planning and optimisation of production, manufacturing or logistics systems. One of the possible applications of queueing theory is service capacity optimisation. Let us consider that an engineering company operates m homogeneous machines. We assume that the machines are successively operating and down and times between failures and times to repair are exponentially distributed. The broken-down machines are repaired by n repairmen; we assume that n < m. In the article a mathematical model of the problem is presented; the model can be used for optimisation of the number of the repairmen with respect to costs of the system. Results obtained by the mathematical model are compared with simulation results; a simulation model of the problem is based on coloured Petri nets.Web of Science20192981297

Time coordination of periodic passenger train connections in conditions of single-track lines

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.Web of Science2021art. no. 387656

Dynamic model for scheduling crew shifts

In regular as well as nonscheduled air transport, extraordinary situations occasionally occur, which may fundamentally disrupt the flight schedule. Fundamental disruptions of flight schedules affect not only passengers but also the airline. One of the areas that are negatively affected by the disruption is the crew plan. Due to extraordinary events, it happens that a flight is delayed, and the crew will not be at the destination airport at the prescribed time and the airline will not be able to assign it on further flights according to the original plan. Such situations can be resolved either by deploying any other available crew or by delaying the flight appropriately until the previously planned crew is available. Assigning a new crew entails additional costs for the airline, as it has to assign more flight staff than had been originally planned. Furthermore, delayed flights lead to paying passengers financial compensation, incurring additional costs for airlines. Therefore, it is important that the airline is able to resolve any irregularity situations so that the additional costs incurred to deal with the irregularity situations are kept at a minimum. The paper presents one possible approach, a mathematical model that can be used to solve such a situation. The presented mathematical model may be the basis for the decision support system of the operations center worker who is responsible for the operational management of flight crews. The model will primarily aim at smaller airlines that cannot afford expensive software and often rely on manual solutions. However, a manual solution may not always be the best, as the operator, who plans the processes, may not consider all the constraints. Another important factor that makes the decision processes more difficult is that it is usually necessary to decide in a short period of time. The solution proposed in this paper will allow the operator to make a quick decision that will also be the most advantageous for the airline. This is because the proposed method is an exact approach, which guarantees finding the optimum solution. In this article, we are only dealing with pilot crews.Web of Science2020art. no. 537256