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EN
Scheduling buses in public transport systems consists in assigning trips to vehicle blocks. To minimize the cost of fuel and environmental impact of public transport, the number of vehicle blocks used should be as small as possible, but sufficient to cover all trips in a timetable. However, when solving real life transportation problems, it is difficult to decide whether the number of vehicle blocks obtained from an algorithm is minimal, unless the actual minimal number is already known, which is rare, or the theoretical lower bound on the number of vehicles has been determined. The lower bound on the number of vehicle blocks is even more important and useful since it can be used both as a parameter that controls the optimization process and as the minimum expected value of the respective optimization criterion. Therefore, methods for determining the lower bound in transportation optimization problems have been studied for decades. However, the existing methods for determining the lower bound on the number of vehicle blocks are very limited and do not take multiple depots or heterogeneous fleet of vehicles into account. In this research, we propose a new practical and effective method to assess the lower bound on the number of vehicle blocks in the Multi-Depot Vehicle Scheduling Problem (MDVSP) with a mixed fleet covering electric vehicles (MDVSP-EV). The considered MDVSP-EV reflects a problem of public transport planning encountered in medium-sized cities. The experimental results obtained for a real public transport system show the great potential of the proposed method in determining the fairly strong lower bound on the number of vehicle blocks. The method can generate an estimated distribution of the number of blocks during the day, which may be helpful, for example, in planning duties and crew scheduling. An important advantage of the proposed method is its low calculation time, which is very important when solving real life transportation problems.
2
Content available remote Retraction: Clusters analysis application on transportation network
EN
The government of Sri Lanka established several economic centres in the provinces according to the budget proposals in the year 1998. The Dambulla economic centre was the first such centre that was established on the 01st of April 1999. Thereafter, a number of economic centres were established throughout the island. However, the Dambulla main hub remained the central warehouse of vegetables in the island. This paper deals with a vehicle scheduling problem related to transportation, and investigates a method whereby a solution can be arrived at to overcome the problem using linear programming (LP). Marketing Department Logistics (MDL) Ltd needs to distribute vegetables and fruits to different provinces. Its main hub is situated near the Dambulla vegetable and fruit market, and minor hubs are situated in different provinces in Sri Lanka. The main objective of this research is building a cost minimized model which creates a suitable method for delivering vegetables and fruits from the Dambulla major hub through its minor hubs to outlets in the provinces. Hence, to optimize the cost of outbound distribution, a mathematical model has been developed by using Integer Linear Programming, and by using reliable sources to collect data. Software assistance was obtained using the LINGO 06 optimizer, Java, MS Access and MS Excel tools to solve this mathematical model. This study is based on the Dambulla economic centre. This is an initial step to bring a correct protocol to arrange a transport model to distribute the vegetables and fruits from this centre in a cost-effective way. According to this study, all districts in Sri Lanka could be divided into four clusters. At the beginning of this research, we assumed that each district contains two warehouses and three vendors. This model is flexible enough to be re-scheduled at any request. It paves the way to create a larger model for solving any type of transportation planning problem.
PL
W pracy przedstawiono sposób wyznaczania i harmonogramowania tras pojazdów przy wykorzystaniu metody BBS (Branch and Bound Simulation) dla pojazdów przewożących jednocześnie ładunki pochodzące z wielu zleceń. Uwzględniono ograniczenia dotyczące ładowności pojazdów i okien czasowych w punktach załadunku i rozładunku. Opracowany algorytm wyznacza najkrótsze, najszybsze i najtańsze trasy z pewną znaną dokładnością.
EN
The work presents a method of the vehicle routing and scheduling using the Branch and Bound Simulation method for vehicles simultaneously carrying loads from multiple orders. Limitations concerning vehicle loads and time windows in points of loading and unloading are taken into consideration. The developed algorithm appoints the shortest, the fastest and the cheapest routes with a certain known accuracy.
EN
Commonly, public transit agencies, with a view toward efficiency, aim at minimizing the number of vehicles in use to meet passenger demand, and therefore at reducing crew cost. This work contributes to achieving these two objectives by proposing the use of two predominant characteristics of public-transit operations planning: (a) different resource requirements between peak and off-peak periods, and (b) working during irregular hours. These characteristics result in split duties (shifts) with unpaid in-between periods. The outcome of this work is an optimal solution for maximizing the unpaid shift periods with the assurance of complying with the minimum number of vehicles attained. The optimization problem utilizes a highly informative graphical technique (deficit function) for finding the least number of vehicles; this enables the construction of vehicle chains (blocks) that take into account maximum unpaid shift periods. The latter consideration is intended to help construct crew schedules at minimum cost. The methodology developed was implemented by two large bus companies and resulted in a significant cost reduction.
EN
In the paper, the problem of minimizing the mean flow time in a FMS is considered. We present two different approaches to the problem. Firstly, we show the way of checking the feasibility of vehicle scheduling provided a production schedule is given. Secondly, assuming that vehicles have the possibility to change their speeds, we show in which way one can obtain a feasible schedule for vehicles taking in to account the optimal schedule (from the view-point of mean flow time) for parts. At the end we discuss a few other heuristic approaches to the problem.
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