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Determining lower bound on number of vehicle blocks in multi-depot vehicle scheduling problem with mixed fleet covering electric buses

Duda Jerzy, Fierek Szymon, Karkula Marek, Kisielewski Piotr, Puka Radosław, Redmer Adam, Skalna Iwona

Archives of Transport

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2023

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Vol. 65, iss. 1

27--38

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.

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Multi-objective optimization model for a multi-depot mixed fleet electric vehicle scheduling problem with real-world constraints

Duda Jerzy, Karkula Marek, Puka Radosław, Skalna Iwona, Fierek Szymon, Redmer Adam, Kisielewski Piotr

Transport Problems

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2022

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T. 17, z. 4

137--149

EN

This paper presents the problem of public transport planning in terms of the optimal use of the available fleet of vehicles and reductions in operational costs and environmental impact. The research takes into account the large fleet of vehicles of various types that are typically found in large cities, including the increasingly widely used electric buses, many depots, and numerous limitations of urban public transport. The mathematical multi-criteria mathematical model formulated in this work considers many important criteria, including technical, economic, and environmental criteria. The preliminary results of the Mixed Integer Linear Programming solver for the proposed model on both theoretical data and real data from urban public transport show the possibility of the practical application of this solver to the transport problems of medium-sized cities with up to two depots, a heterogeneous fleet of vehicles, and up to about 1500 daily timetable trips. Further research directions have been formulated with regard to larger transport systems and new dedicated heuristic algorithms.

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Input Sequence of Jobs on NEH Algorithm for Permutation Flowshop Scheduling Problem

Puka Radosław, Duda Jerzy, Stawowy Adam

Management and Production Engineering Review

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2022

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Vol. 13, No. 1

32--43

EN

One of the most popular heuristics used to solve the permutation flowshop scheduling problem (PFSP) is the NEH algorithm. The reasons for the NEH popularity are its simplicity, short calculation time, and good-quality approximations of the optimal solution for a wide range of PFSP instances. Since its development, many works have been published analysing various aspects of its performance and proposing its improvements. The NEH algorithm includes, however, one unspecified and unexamined feature that is related to the order of jobs with equal values of total processing time in an initial sequence. We examined this NEH aspect using all instances from Taillard’s and VRF benchmark sets. As presented in this paper, the sorting operation has a significant impact on the results obtained by the NEH algorithm. The reason for this is primarily the input sequence of jobs, but also the sorting algorithm itself. Following this observation, we have proposed two modifications of the original NEH algorithm dealing with sequencing of jobs with equal total processing time. Unfortunately, the simple procedures used did not always give better results than the classical NEH algorithm, which means that the problem of sequencing jobs with equal total processing time needs a smart approach and this is one of the promising directions for further research.

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Quick Response Manufacturing for High Mix, Low Volume, High Complexity Manufacturers

Duda Jerzy, Macioł Andrzej, Jędrusik Stanisław, Rębiasz Bogdan, Stawowy Adam, Sopińska-Lenart Monika

Management and Production Engineering Review

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2021

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Vol. 12, No. 1

72--84

EN

The market of consumer goods requires nowadays quick response to customer needs. As a consequence, this is transferred to the time restrictions that the semi-finished product manufacturer must meet. Therefore the cost of manufacturing cannot determine how production processes are designed, and the main evaluation function of manufacturing processes is the response time to customers’ orders. One of the ideas for implementing this idea is the QRM (Quick Response Manufacturing) production organization system. The purpose of the research undertaken by the authors was to develop an innovative solution in the field of production structure, allowing for the implementation of the QRM concept in a Contract Manufacturer, which realizes its tasks according to engineering-to-order (ETO) system in conditions defined as High Mix, Low Volume, High Complexity. The object of the research was to select appropriate methods for grouping products assuming that certain operations will be carried out in traditional but well-organized technological and/or linear cells. The research was carried out in one of the largest producers of sheet metal components in Europe. Pre-completed groupings for data obtained from the company had indicated that – among the classical methods – the best results had been given by the following methods: King’s Algorithm (otherwise called: Binary Ordering, Rank Order Clustering), k-means, and Kohonen’s neural networks. The results of the tests and preliminary simulations based on the data from the company proved that the implementation of the QRM concept does not have to be associated with the absolute formation of multi-purpose cells. It turned out that the effect of reducing the response time to customer needs can be obtained by using hybrid structures that combine solutions characteristic of cellular systems with traditional systems such as a technological, linear, or mixed structure. However, this requires the application of technological solutions with the highest level of organization.