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51Electronic scientific and practical journal
INTELLECTUALIZATION OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
I I vi WWW.SMART-SCM.ORG linpj ISSN 2708-3195
¡1—1 I DOI.ORG/10.467S3/SM ART-SCM/2020-3
fQ E ectronic scientific and practical izollectijn
jintellectuali7atiqn of logistics ]j and supply chain management
Electronic scientific and practical publication in economic sciences
ISSN 2708-3195
DOI: https://doi.org/10.46783/smart-scm/2020-3
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№ 3 (2020) October 2020
Kyiv - 2020
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Editor in Chief: Deputy editors-in-chief:
Hryhorak M. Yu. - Doctor of Economics, Ass. Professor. Koulyk V. A. - PhD (Economics), Professor. Marchuk V. Ye. - Doctor of Tech. Sci., Ass. Professor.
Technical editor: Executive Secretary:
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Members of the Editorial Board:
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TRUSHKINA N. V. - PhD (Economics), Corresponding Member of the Academy;
KOLOSOK V. M. - Doctor of Economics, Professor;
ILCHENKO N. B. - Doctor of Economics, Ass. Professor;
SOLOMON D. I. - Doctor of Economics, Professor (Moldova);
ALKEMA V. H. - Doctor of Economics, Professor;
Henryk DZWIGOt - PhD (Economics), Professor (Poland);
SUMETS O. M. - Doctor of Economics, Ass. Professor;
STRELCOVA Stanislava - PhD (Economics), Ass. Professor, (Slovakia);
RISTVEJ Jozef (Mr.) PhD (Economics), Professor, (Slovakia);
ZAMIAR Zenon - Doctor of Economics, Professor, (Poland);
SMERICHEVSKA S. V. - Doctor of Economics, Professor;
GRITSENKO S. I. - Doctor of Economics, Professor;
KARPENKO O. O. - Doctor of Economics, Professor;
PATKOVSKYI S. A. - Business practitioner.
The electronic scientific and practical journal is registered in international scientometric data bases, repositories and search engines. The main characteristic of the edition is the index of scientometric data bases, which reflects the importance and effectiveness of scientific publications using indicators such as quotation index, h-index and factor impact (the number of quotations within two years after publishing).
In 2020, the International Center for Periodicals (ISSN International Center, Paris) included the Electronic Scientific and Practical Edition "Intellectualization of Supply Chain Management" in the international register of periodicals and provided it with a numerical code of international identification: ISSN 2708-3195 (Online).
Recommended for dissemination on the Internet by the Academic Council of the Department of Logistics NAU (No. 7 of February 26, 2020). Released 6 times a year. Editions references are required. The view of the editorial board does not always coincide with that of the authors.
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Contents
INTRODUCTION 6
FEDOROV E. E. Doctor of Technical Science, Associate Professor, Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine), NIKOLYUK P. K., Doctor of Physics and Mathematics Sciences, Professor, Professor of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine), NECHYPORENKO O. V., PhD, Associate Professor, Associate Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine), CHIOMA E. V., Student of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine)
INTELLECTUALIZATION OF A METHOD FOR SOLVING A LOGISTICS PROBLEM TO OPTIMIZE COSTS WITHIN THE FRAMEWORK OF LEAN PRODUCTION TECHNOLOGY 7 - 17
HRYHORAK M. Yu. Doctor of Science in Economics, Associate Professor, Head of
Logistics Department of National Aviation University (Ukraine), LEHA V. O., Students
of Logistics Department of National Aviation University (Ukraine)
CORPORATE CULTURE REENGINEERING STRATEGY OF A MULTINATIONAL LOGISTICS
COMPANY 18 - 28
HOBELA V. V. PhD of Economics, Senior Lecturer of the Department of Management of Lviv State University of Internal Affairs (Ukraine)
LOGISTICS AS A SUPPLY TOOL ECOLOGICAL AND ECONOMIC SECURITY OF THE STATE 29 - 37
BUGAYKO D. O. PhD in Economics, Associate Professor, Acting Director International Cooperation and Education Institute, Instructor of ICAO Institute of National Aviation University (Ukraine), KHARAZISHVILI Yu. M., Doctor of Economic Sciences, Senior Researcher, Chief Researcher of Institute of Industrial Economics of the National Academy of Sciences (Ukraine), ANTONOVA A. O., PhD in Technical Sciences, Associate Professor, Associate Professor of Air Transportation Management Department of National Aviation University (Ukraine), ZAMIAR ZENON Doctor of Technical Sciences, Professor, Vice-Rector the International University of Logistics and Transport in Wroclaw (Poland)
IDENTIFICATION OF AIR TRANSPORT ECOLOGICAL COMPONENT LEVEL IN THE CONTEXT OF ENSURING SUSTAINABLE DEVELOPMENT OF THE NATIONAL ECONOMY 38 - 53
TADEUSZ POPKOWSKI, PhD eng., Professor, The International University of Logistics and Transport (Wroclaw, Poland), BUGAYKO D. O. PhD in Economics, Associate Professor, Acting Director International Cooperation and Education Institute, Instructor of ICAO Institute of National Aviation University (Ukraine) MODERN CHALLENGES OF DANGEROUS AND EXTRAORDINARY GOODS
TRANSPORTATIONS 54 - 61
A®
This work is licensed under a Creative Commons Attribution 4.0 International License
SAVCHENKO L.V. PhD of Technical Sciences, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine), Davydenko V.V., PhD of Economics, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine) EFFICIENCY OF DIGITAL COMMUNICATIONS IN THE LOGISTICS BUSINESS: EVALUATION INDICATORS _____________________________________________________________________________________________________________________________________________________________________________________________ 62 - 73
KOULIK V^. PhD (Economics), Professor, Professor of Logistics Department National Aviation University (Ukraine), Honored Worker of National Education of Ukraine, Honorary employee of aviation transport of Ukraine (Ukraine), ZAHARCHUK A.P. Assistant of the Logistics Department of National Aviation University (Ukraine)
PROBLEMS OF MANAGEMENT IN THE SYSTEM OF SPIRAL DYNAMICS OF SUPPLY CHAINS 74 - 82
MOLCHANOVA K.M. Senior lecturer at the Department of Logistics National Aviation University (Ukraine), TRUSHKINA N.V. PhD (Economics), Associate Professor, Senior Research Fellow, Regulatory Policy and Entrepreneurship Development Institute of Industrial Economics of the National Academy of Sciences of Ukraine (Ukraine), KATERNA O.K. PhD (Economics), Associate Professor, Associate Professor at the Department of Foreign Economic Activity Enterprise Management National Aviation University (Ukraine)
DIGITAL PLATFORMS AND THEIR APPLICATION IN THE AVIATION INDUSTRY 83 - 98
EVENTS AND SCIENTIFIC CONFERENCES
Marcin PAWÇSKA - THE JUBILEE INAUGURATION OF THE 2020/2021 ACADEMIC YEAR at
The International University of Logistics and Transport in Wrociaw............................................ 99 - 105
Yevhen KRYKAVSKYY, Nataliya HAYVANOVYCH - XIII International Scientific and Practical Conference "MARKETING AND LOGISTICS IN THE SYSTEM OF MANAGEMENT" at Lviv Polytechnic National University........................................................................................................ 106 - 108
Mariia HRYHORAK, Lidiia SAVCHENKO, Oksana OVDIIENKO - LOGISTICS - RELEVANT, GLOBAL, VIRTUAL AND REAL!...................................................................................................................... 109 - 111
UDC 656.029.4: 656.135 DOI: https://doi.org/10.46783/smart-scm/2020-3-6
JEL Classification: R40, R22, O18. Received: 22 October 2020
Savchenko L.V. PhD of Technical Sciences, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine)
ORCID - 0000-0003-3581-6942
Researcher ID - Q-5323-2018
Scopus author id: 57208225385
Davydenko V.V., PhD of Economics, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine)
ORCID - 0000-0002-8419-4636
Researcher ID -
Scopus author id: -
MODELS OF ZONING OF URBAN TERRITORY FOR RATIONAL DELIVERY IN THE MICROCONSOLIDATION SYSTEM
Lidia Savchenko, Volodimir Davydenko. "Models of zoning of urban territory for rational delivery in the microconsolidation system". Urban logistics (or city logistics) is developing rapidly due to the strong growth of e-commerce. Accordingly, the last-mile urban logistics faces a significant number of orders that need to be fulfilled in a dense urban development, environmental constraints and permanent congestion. One of the possible systems of rational city delivery is the use of a network of consolidation centers at the micro level. Such a network provides for a two-tier system of urban delivery -1) from the central warehouse or warehouses to the network of microconsolidation centers; 2) from microconsolidation centers to end consumers. This scheme is especially relevant in the presence of restrictions on the movement of trucks or heavy vehicles in certain areas of the city, as well as in significant congestion and the problem of parking trucks when unloading at the location of the client.
Methods (research methodology). To create a rational delivery network through a microconsolidation system, the primary task is to determine the delivery zones (or geographical clusters) - their number, size, location. To solve this problem, optimization models are proposed based on several minimization criteria -delivery distance, time, cost and integrated distance-time criterion.
Results. The result is the optimization models creation, based on those it is possible to divide urban consumers into several delivery zones. Delivery routes are planned within each zone of the respective centroid and minimize the cost of last-mile logistics. Delivery of goods to the centroids can be carried out by light or medium trucks, and within the zones should be dominated by delivery of environmentally friendly modes of transport (motorcycle or moped, bicycle, car, on foot delivery with the possibility of public transport usage).
Conclusion. Thus, the article provides a mathematical apparatus for obtaining territorial zoning of existing customers of the city in order to minimize the cost (distance, time or their combination) for delivery within each zone.
Perspectives. A perspective study may be an analysis of the costs of operating a network of urban consolidation centers and the delivery of goods from the central warehouse or warehouses to this network.
Accordingly, the task of minimizing the total costs of the city freight delivery system should be solved, taking into account economic, environmental and social aspects.
Keywords: city logistics, zoning of territory, zoning (territorial clustering) of clients, models of optimal territorial zoning, city consolidation, two-level (two-tier) system of urban delivery.
Лiдiя Савченко, Володимир Давиденко. "Модел зонування м'кькоi територи для рац'юнально) доставки у систем'1 мтроконсолдацн'". Мська логстика стр'мко розвиваеться завдяки потужному зростанню електронно)'торг'1вл'1. BidnoeidHO, м'1ська логстика останньо)'милi стикаеться 3i значною к'льк'/стю замовлень, яку потрiбно виконувати в умовах щльно)' мкько)' забудови, еколог'чних обмежень та перманентних затор'т. Однкю з можливих систем рацонально)' мкько')' доставки е застосування мережi консолiдацiйних центр'1в на мiкрорiвнi. Така мережа передбачае двор'вневу систему м'1сько)'доставки - 1) вiд центрального складу чи склад'1в до мережi мiкроконсолiдацiних центр'1в; 2) з мiкроконсолiдацiйних центр'т до кнцевих споживач'т. Особливо така схема е актуальною при iснуванн обмежень щодо руху вантажного транспорту або взагалi транспортних засоб'в у певних районах мста, а також при значних заторах та проблемою у паркуваннi вантажнихавтомоблв при вивантаженн б'ля м'\сця розташування клкнта.
Для створення рац'юнально)' мережi доставки через систему мiкроконсолiдацi)' первинною задачею е визначення зон доставки (або географ'1чних кластерiв) - )х к'лькост'1, розм'1р'1в, розташування. Для виршення цезадачiпропонуються оптимiзацiйнiмодел'1,заснован на деклькох критер'шхм'т'1м'1зацИ- вiдстанiдоставки, часу, вартост'1 та '¡нтегрованого критерю в'дстань-час.
Результатом роботи е створення оптимiзацiйних моделей, на основi яких можливо розбити мкьких споживач'1в на декльказон доставки. Маршрути доставки плануютьсяусередин кожно)'зони вiд в'1дпов'1дного центро)ду та дозволяють м'т'1м'1зувати витрати на лог'1стику останньо)' мил'1. Доведення товар'1в до центро)д1'в може здйснюватися легкими або середшми вантажними автомоблями, а всередин зон мае превалювати доставка еколог'чно дружнiми видами транспорту (мотоцикл чи мопед, велосипед, легковий автомобль, пша доставка з можлив'1стю залучення громадського транспорту).
Таким чином, стаття надае математичний апарат для отримання територ'юльного зонування наявних клкнт'1в м'1ста з метою мМм'вацП витрат (в'1дстан'1, часу або )х комб'тацИ) на доставку усередин кожно)' зони. Перспективним дослiдження може бути анал'з витрат на функ^онування мережi консолiдацiйних центр '1в та на довезення товар '1в з центрального складу чи склад'т до це мережi. В'1дпов'1дно, мае бути виршеназадача м'т'1м'1зац1)'загальних витрат на систему мкько')' доставки з урахуванням економ'чних та екологiчно-соцiальних аспект'т.
Кпючов'1 слова: мкька лопстика, зонування територи, зонування (територiальна кластеризащя) ^етчв, моделi оптимального територiального зонування, мкька консол^афя, дворiвнева система мкькоТ' доставки.
Лидия Савченко, Владимир Давиденко. "Модели зонирования городской территории для рациональной доставки в системе микроконсолидации". Городская логистика стремительно развивается благодаря мощному росту электронной торговли. Соответственно, городская логистика последней мили сталкивается с большим количеством заказов, которую нужно выполнять в условиях плотной городской застройки, экологических ограничений и перманентных пробок. Одной из возможных систем рациональной городской доставки будет применение сети консолидационных центров на микроуровне. Такая сеть предполагает двухуровневую систему городской доставки -1) от центрального склада или складов в сети микроконсолидациних центров; 2) с микроконсолидацийних центров до конечных потребителей. Особенно такая схема актуальна при существовании ограничений движения грузового транспорта или вообще транспортных средств в определенных районах города, а также при значительных пробках и проблемой в парковке грузовых автомобилей при выгрузке у места расположения клиента.
Для создания рациональной сети доставки через систему микроконсолидации первичной задачей является определение зон доставки (или географических кластеров) - их количества, размеров, расположения. Для решения этой задачи предлагаются оптимизационные модели,
основанные на нескольких критериях минимизации - расстояния доставки, времени, стоимости и интегрированного критерия расстояние-время.
Результатом работы является создание оптимизационных моделей, на основе которых возможно разбить городских потребителей на несколько зон доставки. Маршруты доставки планируются внутри каждой зоны соответствующего центроиду и позволяют минимизировать затраты на логистику последней мили. Доведения товаров до центроидов может осуществляться легкими или средними грузовыми автомобилями, а внутри зон должно превалировать доставка экологически дружественными видами транспорта (мотоцикл или мопед, велосипед, легковой автомобиль, пешая доставка с возможностью привлечения общественного транспорта).
Таким образом, статья предоставляет математический аппарат для получения территориального зонирования существующих клиентов города с целью минимизации затрат (расстояния, времени или их комбинации) на доставку внутри каждой зоны. Перспективным исследования может быть анализ расходов на функционирование сети консолидационных центров и на подвоз товаров с центрального склада или складов в сети. Соответственно, должна быть решена задача минимизации общих затрат на систему городской доставки с учетом экономических и экологически социальных аспектов.
Ключевые слова: городская логистика, зонирование территории, зонирования (территориальная кластеризация) клиентов, модели оптимального территориального зонирования, городская консолидация, двухуровневая система городской доставки.
Introduction. The urgency of clustering (or zoning) of the urban area is relevant to the need to model and build rational routes of vehicles, monitoring of freight and passenger flows between different districts or neighborhoods of the city. During clustering, a certain area of the city is considered as a whole with a certain demand for goods, supply for other areas, with a known number of consumers, shops, vehicles, and so on.
At clustering (zoning) of the territory of the city the following purposes can be set:
- modeling of logistics flows for the rational organization of traffic, construction of routes, assessment of bottlenecks in transport infrastructure, etc.;
- systematization of urban planning (obtaining zones with approximately the same indicators for the application of certain rules, technologies, restrictions, etc.);
- organization of cargo delivery, customer service of the city (division of the city into zones for customer service within each zone).
Urban logistics (or city logistics) is developing rapidly due to the strong growth of e-commerce. Accordingly, the last-mile urban logistics faces a significant number of orders that need to be fulfilled in a dense urban development, environmental
constraints and permanent congestion. One of the possible systems of rational city delivery is the use of a network of consolidation centers at the micro level. Such a network provides for a two-tier system of urban delivery - 1) from the central warehouse or warehouses to the network of microconsolidation centers; 2) from microconsolidation centers to end consumers. This scheme is especially relevant in the presence of restrictions on the movement of trucks or heavy vehicles in certain areas of the city, as well as in significant congestion and the problem of parking trucks when unloading at the location of the client.
Analysis of the latest research. The issue of clustering or cluster analysis is reflected in a significant number of mathematical methods and models for dividing a certain set into several groups [1, 2, 3, 4]. Widespread use of clustering (or grouping, separation) methods proves to some extent the universality of this approach and existing methods.
In modern city logistics, grouping of customers by geographical zones is widely used, with the possible assignment of drivers of a certain car or group of cars, couriers to each zone. This method of planning allows
drivers and couriers to thoroughly study the service area and establish contacts with receivers, which generally speeds up the delivery process and increases customer satisfaction [6]. However, mathematical methods and models of geographical clustering for the needs of creating a rational distribution system are missing. Against this background, it should be noted a significant number of software products for urban delivery [7-11], which optimize the process of building rational routes, but do not allow to divide them into territorial zones to minimize delivery costs within each zone.
When dividing the territory into transport areas (zones or clusters), the number and size of such areas depend on the size of the city and population. When setting the boundaries of transport areas, it is recommended to adhere to the following principles:
- use of lines of natural and artificial obstacles (rivers, railway lines, etc.);
- observance of administrative zoning of the territory;
- accounting for functional zoning of the city;
- preservation of existing building blocks;
- prevention of formation of transport areas of elongated configuration [5].
The problem of an urban area clustering and possible tasks that can be set for zoning of city customers are considered in [16]. The authors [18] consider possible ways of interaction of participants of the process of city delivery, in particular, with the use of city consolidation centers of different levels.
Accordingly, with a significant number of studies on clustering, in particular territorial, there is a shortage of theoretical and practical information on the rational division of customers into groups for further planning of optimal routes within each group of relevant centroids (for urban logistics - from microconsolidation centers).
Formulation of the purpose of the study. Given the lack of research on territorial clustering to divide city customers into zones and further delivery through a network of
microconsolidation centers, the aim of the article is to obtain basic mathematical models for grouping city customers into delivery zones by minimizing delivery costs within the respective zones.
Presentation of the main research. 1. General approaches to clustering that can be used in the city customers zoning for delivery through a network of microconsolidation centers. Clustering (or cluster analysis) is the task of breaking a set of objects into groups called clusters. From a mathematical point of view, clustering helps to identify a set of closely related (by a certain criterion) objects in a certain set of such objects. Within each group should be "similar" elements, and the elements of different groups (clusters) should be as different as possible. The main difference between clustering and classification is that the list of groups is not clearly defined and is determined during cluster analysis.
The application of cluster analysis in general is based on the following stages:
1. Selection of objects for clustering.
2. Defining the criteria by which objects will be evaluated.
3. Calculation the degree of similarity between objects.
4. Application of a certain method of cluster analysis to create groups of similar objects (clusters).
5. Obtaining and analyzing the results of the analysis. If necessary - adjusting the model.
The first task that is recommended to be performed before starting the cluster analysis is to assess the overall clustering tendency of the available data.
Hopkins statistics are one indicator of a trend toward grouping. To calculate it, several pseudo-data sets are created, randomly generated based on a distribution with the same standard deviation as the original data set. For each observation i with n calculate the average distance to k nearest neighbors: w, between real objects and q, between artificial objects and their nearest real neighbors. Then Hopkins statistics
Z Wi
variation W(Ck) = Z (X -Mk)2. If the data
H =_
ind n
i=1
Z q+Z wi
i=i
i=i
greater than 0.5 would correspond to the null hypothesis that q, and w, are similar, and the grouped objects are randomly distributed and homogeneous. A value of Hind <0.25 with 90% confidence indicates an existing tendency to group the data.
Clustering with a known number of clusters.
Partitioning algorithms [4] decompose a set of data consisting of n observations into k groups (clusters) with previously unknown parameters. The search for centroids - the most distant from each other the centers of condensation of points Ck with minimal scatter within each cluster. The separation algorithms include:
- method of k-means McKueen (k-means clustering; MacQueen, 1967), in which each of the k clusters is represented by a centroid;
- division around k medoids or PAM (Partitioning Around Medoids; Kaufman, Rousseeuw, 1990), where the medoid is the center of gravity, the coordinates of which are shifted to the nearest of the original data objects;
- CLARA algorithm (Clustering Large Applications) - a method very similar to PAM and used to analyze large data sets.
The most common clustering algorithm is the method of k means. It performs clustering as follows:
1. Assign the number of groups (k) into which the data should be divided. Randomly, k objects of the source set are selected as the initial centers of the clusters.
2. Each element is assigned a group number on the nearest centroid, ie on the basis of the smallest Euclidean distance between the object and the point Ck.
3. List the coordinates of the centroids ^k of all k clusters and calculate the intra-cluster
set includes p variables, then ^k is a vector of averages with p elements.
4. The general intragroup scatter is
minimized Wtotal = (Ck) ^ min, for
k
which steps 2 and 3 are repeated many times until the group assignments stop changing or the specified number of iter.max iterations is reached.
It is convenient to perform clustering using the programming language R. The maximum number of iterations for minimizing Wtotal, set by the function kmeans () by default, is iter.max = 10 [5].
Clustering by the method of k means is a very simple and efficient algorithm. However, the results of clustering are sensitive to the initial choice of group centers. A possible solution to this problem is to repeatedly execute the algorithm with the choice of different primary centroids.
Partition into (approximately) identical clusters.
For urban zoning, obtaining the same clusters makes sense if the clustering objects are customers with certain geographical coordinates. Then the cluster can be a set of such clients, the number of which allows one delivery route, while fully loading the vehicle or courier. Thus, it is possible to get areas of the city with approximately the same number of customers in each of them.
An example of clustering with the same cluster size is proposed in R [3].
Evaluation of clustering quality.
After receiving a cluster solution, the question usually arises as to how stable and statistically significant it is. There is an empirical rule here - a stable group must be preserved when changing clustering methods: for example, if the results of hierarchical cluster analysis have a coincidence of more than 70% with clustering by the method of k means, then the assumption of stability is accepted. Other
methods and criteria for assessing the quality of clustering validation results can be studied in [4].
2. Models of urban area zoning for rational delivery in the microconsolidation system.
In conditions of city delivery freight companies have to deal with an array of
customers located in different parts of the city. When planning delivery routes often appeal to clustering of territory, which for the city is called zoning. In this case, we mean the division of the city into zones (clusters) in order to reduce transport costs (Fig. 1).
Figure 1 - Terminals (consolidation centers) as centroids [12]
Accordingly, the main criteria used for urban zoning are the distance of the route and the time of transportation. The time criterion is necessary in urban conditions, especially when delivered during morning and evening traffic jams. At this time, the minimum distance does not mean the minimum transport costs. Sometimes increasing the distance even twice allows, on the one hand, to speed up delivery, on the other hand, to reduce transport costs.
Consider the general mathematical formulation of the problem of zoning the urban area.
It is necessary to divide the urban area into zones to minimize delivery costs (Fig. 2).
For zoning of the territory, information is required on:
- the needs of the points of the territory (demand);
- location of points.
The location of the points can be seen on the map, and then set their Cartesian coordinates.
The problem of optimal zoning of the urban territory can be solved with the following criteria:
- minimum delivery distance;
- minimum delivery time;
- minimum shipping cost;
- integrated criterion.
Sometimes the optimal solution is getting a minimum of distance, time, and cost simultaneously. However, in conditions of congestion, toll roads and other limiting undesirable phenomena, one criterion should be selected and based on it, the search for an optimal solution should be made. If necessary, it can be used an additional solving of the problem to determine alternative solutions with different criteria for the problem.
Figure 2 - Solutions based on the concept of multi-tier distribution systems Source: based
on [14, 15].
1. Criterion of minimum distance. The simplest way to determine the distance is the formula
R(U J') = V(x - xj )2 +(y - yj )2
(1)
where x, x, y, yj - Cartesian coordinates of the points in the zone.
That is, the so-called Cartesian distance. Concequently, the objective function (minimization of the sum of all distances between all point of all zones) is
n n
OFd = Z Z R(i> j) ^ min (2)
i=1 j=1
or
OFd =X tyííX^X/Hy^j ^ min
(3)
i=i j=i
However, the transport network does not always have a direct path between points.
For obtaining more accurate data on the distance, it can be used any tools for laying routes in real time, in particular, Google Map.
If distribution routes are supposed to be used for the delivery to the customers of the zone, the length of the tour/route (L) can be calculated with:
L = 2/0 + lcc (n -1), (4)
where lo - average length of the first and last trip of the delivery tour (route), km;
lcc - average distance between customers on a typical delivery tour (route), km;
n - number of clients/customers included in a zone.
Value lcc could be obtained as an atithmetic average of the distances between the points of the zone:
n n
Z Z R(i, j)
l = i=1 j=1
(5)
The objective function becomes
OFd = 2ml0 + lcc ( n -1) ^ min (6)
where m - number of routs during the shift (or working day).
One of the constraints to take into consideration is the number of parcels that one delivery vehicle/means can transport in a route from the point of view of vehicle capacity both in terms of weight and volume capacity:
ni = min { INT {Q I q}, INT { VI v}},
(7)
where the INT function gives the number to the nearest smaller integer;
Q - weight capacity of a means of delivery, kg;
q - average weight of a parcel, kg;
V - volume capacity of a means of the delivery, m3;
v - average volume of a parcel, m3.
The maximum number of routes per shift is calculated as the ratio of the duration of the shift and the time of a route on this shift:
mmax = rounddown{t/T} = rounddown
U tprep +
lcc (2 + n -1)
V (t )
+ nt
1c
(8)
where the rounddown function rounds numbers down;
t - duration of a shift (working day), h. The minimal number of routes per one working shift is a ratio of the number of delivery points and capacity of delivery means:
mmin = roundup{n/nx}, (9)
where roundup function rounds numbers up.
OFd = 2mlcc + lcc (n -1) = lcc (2m + n -
For the resulting objective function, the variable will be the distance between the route points R(i, j), which can be calculated using Cartesian coordinates.
2. Criterion of minimum time.
Minimizing delivery times is usually more important than minimizing distance. This is due to the ever increasing "cost" of time in business. For delivery services, delivery times
While solving the optimal solution equations (8) and (9) are the limitations of the model. Real number of the routes must be not less than mmin and not grater than mmax.
If we assume that each zone will be served from the so-called centroid, then the distance of zero run can be taken as the distance between route points (lo = lcc). Then the objective function will look like:
(2m + n -1) X R(i, j)
i=1 j=1
----> min (10)
n
have a direct impact on significant cost items such as wages and depreciation. The side of customers waiting for an order should also be taken into account. In case of failures in delivery time, there is a risk of the need for redelivery if the client did not wait for the courier. In this case, losses are incurred twice, supplemented by reputational losses for the delivery service company.
1)=
The delivery time should be calculated taking into account the time of day (availability and intensity of congestion), as well as the number of customers on the route and the time for servicing these customers.
In distribution route, the travel time could be calculated as:
T(t) = tprep + 2t0 + Tcc (t) + Tc = tprep +[2/0 + ( n -1) lcc ]/v(t) + ntic,
(11)
where tprep - preparatory-final time for delivery tour/route, h;
to - time to travel from the sender's base to the first customer and to return from the last customer to the sender's base by mode I during the working shift j, h;
Tcc(t) - travel time between successive customers, h;
Tc - time spent at customers' delivery points, h;
V(t) - average speed, km/h;
t1c - average time spent at customer's delivery point, h.
The speed depends on the time of day, due to the different level of traffic/congestion, as well as on the type of delivery vehicle/means used [17].
OFt = Ë Ë T(i' J) ^ min (12)
i=1 J=1 And finally, if consider l0=lrc:
(2m + n -1) ¿ R(i, j)
OFt = mtprep +-77^-+ nt1c ^ min (13)
nV (t )
3. Criterion for minimum delivery cost.
With the possibility of calculating direct financial costs on the route, automation and simplicity of this process, it is possible to solve the zoning problem according to the criterion of total costs in monetary terms. Naturally, this criterion is the most acceptable and allows to immediately see the delivery costs. However, the calculation of transportation costs is a rather difficult task, given the constantly changing conditions on the route (different speeds, number of stops, time spent at customers' delivery points, etc.). Therefore, in practice, this criterion is rarely used.
In any case, the objective function for the shipping cost criterion looks like
n n
OFs =Z Z S(i, j) ^ min (14)
i=i j=i
where S (i,j) - transport costs for movement between points i and j.
4. Integrated criterion.
It is often convenient to use an integrated criterion. For this, it is usually taking several local criteria and assign them weights (significance coefficients), showing their mutual significance in the integrated criterion. It is most convenient to use the values of the weights from 0 to 1 with the condition that the sum of the weights of the local criteria is 1. For example, for the distance criterion, the significance coefficient can be taken as 0.3, and for the time criterion - 0.7.
The most rational approach to determining the significance factors is based on the calculation of the cost of a typical transportation. Further, the components of this cost are divided into two groups: 1) depent on the distance of the route; 2) depent on delivery time. If some component of the
cost price depends on both distance and time (for example, often the driver's salary consists of two parts - depent on the distance traveled and hours of work), it should be divided into the groups depending on the actual proportion.
with condition wd + wt = 1 .
It should be noted that modern alternatives to a warehouse can be used as a consolidation center, with a small size and weight of packages requiring delivery (Fig. 3), namely:
1. Unattended delivery systems at the customer's home include the use of:
After receiving the abovementionned groups of cost components, the total cost of each group is calculated and the share of each group in the total cost is determined. This specific weight should be used as the coefficients of significance in the integrated criterion:
(15)
- Reception boxes;
- Delivery boxes;
- Controlled access systems.
2. Unattended delivery systems away from the customer's home include:
- Pick-up points;
- Collection points;
- Locker banks.
OF, = Z Z(wd ' D(i, j) + w, • T(i, j)) - min
i=1 j=1
Security cameras
Base module of 53 lockers, extendable
Electronic system to open the relevant locker
Option: Banner with backlight
(7) Standard locker module (op Media equipment
Small boxes: 30 x 380 x 640 mi
Medium boxes: 190 x 380 x 640 rr Large boxes: 410 x 3S0 x 640 rr
Source: InPost
Comfortable durable LCD screen and keypad Dual Language Stereo speakers En a rgy efficient
. Consumers choose M deliveries from selected ' e-retailers, logistics 1 companies and postal operators to be made to APM
Щ*
Text message and email notification
including a delivery code and location
Parcel is collected by
consumer at the selected АРМ
Figure 3 - Principle of working of Automated parcel machine [13]
Conclusions. Assessing the current state of scientific and practical developments in the field of urban zoning to build an effective system of goods delivery to residents, construction sites, business environment, food facilities, etc. it is necessary to state some detachment of theoretical materials from
practice. It is obvious that the need of business for high-quality, fast and inexpensive software solutions for planning a rational city delivery is growing. This is confirmed by a wide range of companies offering such solutions on the market of both Ukraine and other countries. Also noticeable
is the dynamic development of existing programs in parallel with the development of cloud technologies, blockchain, and other solutions that simplify and clarify the process of transactions of participants in logistics processes, transmission and analysis of information, data processing in real time.
Thus, clustering (or zoning) of the urban territory on a territorial basis helps in the implementation of rational logistics solutions in customer service of the city. Considering the city as a set of neighborhoods with a certain number of delivery customers in each allows to make rational delivery routes and provide a reliable level of logistics service by
minimizing delays and errors in the implementation of last-mile logistics. Such a delivery scheme is possible in the presence of a network of microconsolidation centers located in each defined area of the city. The environmental and social aspects of the solution are reinforced by the use of environmentally friendly vehicles or on foot delivery within each zone. Thus, the rational division of the city into delivery zones in combination with the principle of microconsolidation will reduce 1) the load on the city road network, 2) harmful emissions into the city atmosphere and 3) accidents and noise pollution in densely populated areas.
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