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Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
18
ROUTE FIRST-CLUSTER SECOND METHOD FOR PERSONAL
SERVICE ROUTING PROBLEM
MELİKE KÜBRA EKİZ1
*
, MUHAMMET BOZDEMİR2,
BURCU ÖZCAN TÜRKKAN1
1Departman of Industrial Engineering, University of Kocaeli, Kocaeli, 41001, Turkey
2Department of Industrial Engineering, Konya Technical University, Konya, 42250, Turkey
Abstract: The Vehicle Routing Problem (VRP), which has many sub-branches, is a difficult
problem that cannot be solved using classical methods. This study includes a case study for
Service Routing Problem, which is one of the sub-branches of VRP. The case study is a
problem of determining service routes for staffs of a company. In this context, we first
assigned the employees to the stations, and then we reached a solution using the route first-
cluster second heuristic method. We used the Genetic Algorithm (GA) to improve the route
and compared the results by creating different scenarios in clustering methods.
Keywords: vehicle routing problem, clustering methods, service routing problem
1. INTRODUCTION
Logistic term provide that is deliver to customers when a product or service is produced in companies. Nowadays,
the term of logistics has become more important because of the development of technology, the increase of
competition and the expansion of e-commerce services. With the increase of technological activities, the position
of the products at that moment, the times of access to the customer or supplier etc. situations can be monitored
more easily. The main reason for the increase in the competition between companies and firms is that the logistics
costs constitute a large part of the companies' budget. Therefore, the objectives such as minimizing the duration,
distance or cost of the routes used in the transportation of the product to the customer or supplier, and maximizing
the occupancy rates of the vehicles used arise. Also e-commerce services are preferred nowadays, therefore
increasing the usage rates of e-commerce companies increases the importance of logistics concept day by day.
In this context, the problem of routing, which is a part of the term of logistics, has been discussed. First of all, the
problem that was introduced to the literature as a Traveling Salesman Problem (TSP) has as the only tool
assumption. The problem of dealing with a large number of vehicles and single warehouses is included in the
literature as a Multiple Travelling Salesman Problem (mTSP) [1].
The Vehicle Routing Problem (VRP), which was first discovered by Dantzig and Ranser [2], is the problem of
minimizing the travel distance or duration of vehicles with a large number of capacities. For VRP, optimal results
were obtained with mathematical models proposed in the literature. With the addition of new constraints to the
problem over time, the size of it increased and became a combinatorial and turned into an np-hard. Also, with the
addition of these constraints, different VRPs emerged. For example; VRP with time windows, pick-up and
delivery, simultaneous pick-up and delivery etc.
*
Corresponding author, email melike.ekiz@kocaeli.edu.tr
© 2019 Alma Mater Publishing House
Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
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Mathematical models for VRP, which contain many constraints in real life problems such as personnel or school
service, garbage, medical waste collection, bread and milk distribution, are not sufficient and an optimal or suitable
solution cannot be obtained. Therefore, artificial intelligence applications and heuristic – meta-heuristic methods
are frequently used in order to obtain suitable solutions for VRP in the np-hard class. In our study, the personnel
service problem, which has become an important problem for the companies, has been discussed.
In this study is proceeding as follows. In chapter 2, we mention the VRP and its subgroups which that have different
constraints. In chapter 3, we mention literature review of VRP with time windows, service and school service
routing problems which are subgroups of VRP related to our problem. In chapter 4, the Genetic Algorithm (GA),
which is one of the meta-heuristic methods used in the solution of our problem, is included. In addition, we mention
clustering algorithms used to the route obtained in this chapter. In chapter 5, we have implemented the case study
and steps. In Chapter 6, we mention the case study and lastly we report the conclusions in chapter 6.
2. VEHICLE ROUTING PROBLEM (VRP)
VRP is the problem of determining the routes required to return to the warehouse by determining the objective
function in the form of the minimization of total transportation distance or transportation time, provided that the
fleet of vehicles in a central warehouse has a certain homogeneous or heterogeneous capacity. The assumptions of
the classical VRP model are as follows:
- Routes start in the warehouse and end there;
- The capacity of the vehicles is homogeneous;
- Demands are deterministic;
- Every demand point must be met once and the entire demand must be met (demands cannot be divided).
The classic VRP model is given below. Here, i and j represent nodes and also 0 and k represents the warehouse
and vehicle, respectively. M, N and Q are number of vehicles, number of customers and vehicle capacity,
respectively. Also parameters of VRP, cij is transportation cost from node i to node j and qi is demand of node i
(customer).
Decision variables:
xijk=1 if vehicle of k visits from node i to node
0 otherwise
yi=
sub-tour qualifying decision variable
Min Z= cij xijk
M
k=1
N
j=0
N
i=0 (1)
xijk =1, j=1,…,N
M
k=1
N
i=0 (2)
xipk
N
i=0 -xpjk=0, k=1,…,M;p=0,…,N
N
j=0 (3)
qixijk
N
j=0 ≤
Q, k=1,…,M
N
i=1 (4)
x0jk
N
j=1 =1, k=1,…,M (5)
yi-yj+N xijk
≤
N-1, i≠j=1,…,N
M
k=1 (6)
xijk
0,1, i=j=1,…,N;k=1,…,M (7)
yi
free (8)
Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
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where the objective function defined in equation (1) is to minimize the cost. equation (2) assures that each node i
is assigned to at least node j with any k. equation (3) ensured that a tour between the nodes. Equation (4) is the
capacity constraint and equation (5) allows each vehicle to leave the warehouse once. Equation (6) provides sub-
round qualifying and finally, we give integrality constraints which define the nature of the decision variables.
Different varieties are formed and divided into sub-groups by adding different constraints to VRP over time. Some
of these subgroups are listed below:
- VRP with mixed vehicle capacity;
- VRP with multiple warehouse;
- VRP with indeterminate demand;
- VRP with pick-up and delivery;
- VRP with simultaneous pick-up and delivery;
- Time-dependent VRP;
- School bus routing problem;
- VRP with time window.
3. LITERATURE REVIEW
In this section of the study, we discussed the study of VRP with capacity constrained, time window and school
service routing problem, which are the subgroups of VRP models which are the closest to the problem we
discussed. In the personnel transportation problems, VRP with capacity restricted model can be preferred due to
the fact that the vehicle has a certain capacity [3]. In addition, due to the time window in the personnel
transportation problem, the VRP with time windows has also been utilized. The VRP with time windows is divided
into two subgroups: VRP with hard and flexible time windows. In the case of the VRP with a hard time window,
vehicles arriving at the node before the earliest start-up time must remain on that node until the specified time
window, and vehicles that arrive after the latest start time cannot start the service. In the VRP with flexible time
window, there is a penalty cost for vehicles that cannot reach the service within the specified time window.
Koç and Karaoğlan [4] developed a mathematical model for multi-use and time-window VRP and applied to
existing test problems in the literature. Unlike VRP, the VRP with time window includes the concepts of early
start time (ai) and late start time () of vehicles. The node with the [
ai] time window should be serviced in
this range. The difference between VRP and multi-use VRP is that a vehicle can take a new route after completing
the route. Ünlü, Uçar, Akkuş and Şen [5] conducted a multi-vehicle dynamic routing application with time window
for cargo companies.
Atmaca [6] carried out by using the data of a cargo company, the VRP model was simultaneously studied. The
results were compared with the current status of the cargo company in terms of the number of vehicles, vehicle
occupancy rate, and route lengths. In the study conducted by Hezer and Kara [7], VRP with simultaneous pick-up
and delivery was applied to sample test problems by using Bacterial Foraging Optimization Algorithm. The results
of the proposed model are compared with insertion based heuristic algorithm. Çetin and Gencer [8] proposed a
mathematical model by combining the VRP model with the exact time window and the simultaneous pick-up and
delivery. The objective function of many VRPs in the literature has been taken as the minimization of the received
path or cost while the objective function is taken as the minimization of the delays. Cetin and Gencer [9] proposed
a VRP model which is taking into account the situations where vehicle capacities are not equal or the vehicle types
are not the same and with simultaneous pick-up and delivery with exact time windows. Koç and Karaoğlan [10]
suggested a mathematical model for the problem, which is called time-dependent VRP, when the speed of the
vehicles varied between the nodes.
Bozyer, Alkan, and Fığlalı [11] mentioned that mathematical models would be insufficient if the size of the VRP
problem increased and they proposed a heuristic method which is based on before clustering after then routing.
Şahin and Eroğlu [12] have addressed the problem of limited capacity VRP and have studied with the heuristic
and meta-heuristic methods that are available in the literature. Düzakın and Demircioğlu [13] examined the models
and heuristic methods developed by VRP in their studies. Güvez, Dege and Eren [14] determined the positions of
health institutions on the digital map and calculated their distance to each other and worked on the collection of
medical wastes with the lowest cost using the integer programming model. Onder [15] handled the multi-
warehouse VRP and implemented an application on bread distribution.
Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
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For school service routing problems, nodes (stops) are usually determined for students using a clustering algorithm.
In school service problems, the number of schools and accordingly the ringing time is important. If the vehicles
serve more than one school, the ring time of each school is important. Gündoğar and Akıl [16] examined routing
problems and considered the problem of routing of service vehicles as a scheduling problem. Uzun and Tezel [17]
used the heuristic method for each individual to benefit from the service in his / her time window in the use of
rehabilitation service of disabled individuals. Uzumer and Eren [18] has optimized the school service routing
problem with the linear program model. Ünsal and Yiğit [19] mentioned that both the fuel and the cost will be
contributed by the optimal route of service vehicles, and the time spent in the service and the walking distance will
be reduced by the personnel who use the vehicles. In order to benefit from the developing technology and to
facilitate the routing problem, data were obtained from GSP, GIS and firstly nodes were determined by using K-
means clustering algorithm. In determining the most suitable route for service vehicles, GA which is one of the
artificial intelligence techniques is used.
4. DESCRIPTION OF THE PROBLEM AND METHODS
In our study, we determined a problem which is a own service vehicles to be able to provide the most appropriate
service to their staff in the morning and in the evening. In this context, the purpose of the company is to minimize
the factors such as route and cost. It also wants the vehicles to reach the company in time and to minimize the time
spent by the personnel in the service. The request of the company in the routing problem is the smallest walking
distance to the designated nodes (stops) by clustering.
In our study, we used route first—cluster second method for the service routing problem. In this context, the
problem was first thought to be TSP and the first route was created with the nearest neighbor algorithm. The first
route using the GA was improved and the nodes were assigned to the vehicles by controlling their capacity using
3 different clustering methods. Below, we will first talk about the GA used to improve TSP and then 3 different
clustering methods.
4.1. Genetic Algorithm (GA)
Individuals in nature struggle with each other to have resources such as food, shelter and water. The lives of the
victors in the struggles are longer and their genes are transferred to the next generations. Thus, weak individuals
are eliminated. The good characteristics from different individuals will merge over time and better individuals will
emerge. The GA based on this basic logic is a heuristic method that does not guarantee us the best solution, but in
a short time it gives good solution which is near to best solution. Steps of GA are as follows:
-A random group of all possible solutions in the search space is selected and coded as a series of solutions. Then,
a random process is performed to create the starting population.
-The fit value is calculated for each set of solutions. The calculated fit value indicates the quality of the solution.
-A group is selected by means of a selection mechanism. Selected group are subjected to crossing and mutation
processes and new generations are created.
-The above procedures are continued until the stop criterion is established. The most appropriate individual is
chosen as the solution.
In the following part of the study, the tournament selection method and linear crossing and placement mutation
method are mentioned which we used in the case study.
Tournament Selection Method: Two sequences are randomly selected from the whole generation. As a result of
the struggle between these two series, whoever is better wins and gets a point. All individuals in the generation
have the right to participate in the tournament twice. Those who succeed in both tournaments will print their name
to the list.
Linear Crossing: Firstly, a random gene site is determined, and the genes of the mother and father are assigned to
two children according to the location. Remaining genes in children are completed in a way not to repeat by mother
and father.
Placement Mutation: A randomly determined gene from the population is placed in another random position within
the same population.
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After multiplication, crossing and mutation processes, an infinite number of generations are formed. The stop
criterion is determined to stop an infinite number of these generations. The number of iterations is generally used
as a stop criterion.
4.2. Clustering Methods and Distance Functions
Clustering methods divide assets into different groups according to their similarities. It is desired that these groups
have the most similarity among themselves, while the similarity between the other groups is desired to have the
least similarity [20]. K-Means, K-Medoids and K-Modes clustering algorithm were used in the study. The
important issue in clustering methods is the distance functions. In this context, Euclidean, Manhattan and Square
Euclidean distance functions are included in this study.
4.2.1. K-Means Clustering Algorithm
The K-Means clustering algorithm performs grouping by the number of sets determined by looking at the similarity
of each asset in the data set. The stages of K-Means clustering algorithm are as follows [21]:
-Determining the number of clusters (determining the number of k) and separating the data into k sets;
-Assignment of the assets in the cluster to the closest cluster in terms of value (the value is calculated with the
distance function);
-Step 2 is repeated until no asset is out.
4.2.2. K-Medoids Clustering Algorithm
The K-Medoids clustering algorithm, which has many variants in the literature, has been developed due to the fact
that K-Means clustering algorithm. K-Medoids is better than K-Means clustering algorithm in terms of non
sensitive to outliers, execution time and reduces noise [22]. The stages of K-Medoids clustering algorithm are as
follows [23]:
-Random k elements are selected and these elements are determined as cluster center;
-New entities are added to the cluster and those that contribute the most to the cluster development are selected
and are assigned as a central;
-Step 2 is repeated until no asset is out.
4.2.3. K-Modes Clustering Algorithm
The stages of the K-Modes clustering algorithm, a variant of the K-Means clustering algorithm, are as follows:
-Random k beginning mode is selected;
-Objects in the cluster are displaced if the mode of assets is closest to which cluster center;
-Cluster modes are updated after each displacement;
-Steps 2 and 3 are repeated until the displacement of the objects in the cluster is finished.
5. CASE STUDY
In order to solve the problem of personnel service, the method was applied to route first-cluster second. In order
to improve the route, GA was chosen from artificial intelligence algorithms. We have developed a software for
improving the route for GA. First of all, 20 initial solutions were created with the nearest addition heuristic.
Tournament Selection Method was applied in the selection of the initial solutions. Generally, those who have 1
point in the tournament selection method should be eliminated. However, because of the diversity in the cluster,
we have included even get 1 point fields in the generation set. We preferred the linear crossing method to multiply
the individuals in the generation set.
A total of 2000 crossings were performed with 1000 iterations. The mutation operator was used to ensure genetic
diversity. A random decimal number of 0 to 1 was generated for each mutation operator to apply the mutation
operator. If the random decimal number is between 0 and 0.1, a mutation is performed. We checked the fit values
within the generation clusters that were formed as a result of the selection, crossing and mutation process. The
population cluster with the lowest fit value is considered a solution space. After determining the solution space,
different scenarios were created according to the strategies formed according to clustering methods and distance
functions. We have developed a software for applying the method developed for the solution of the personnel
service problem to the existing data. This software uses Microsoft Access 2016 database program, C #
programming language on Visual Studio.Net 2015 platform and GMap.NET library.
Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
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We created the total number of people who will use the personnel service is 93. The stops were determined
according to the proximity status of the regions where these 93 people live. We have established a route with 39
passenger stops and a destination company so a total of 40 stops. There are two different types of vehicles with
capacities 27 and 16. The results obtained with the scenarios created by setting the number of clusters to k= 4 are
given in Table 1.
Table 1. Results of scenarios created with clustering methods and distance functions.
Clustering Method
Distance Function
Result (km)
K-means
Euclidean
178.6593
K-Medoids
Euclidean
178.6593
K-Modes
Euclidean
178.6593
K-means
Manhattan
227.3776
K-Medoids
Manhattan
227.3776
K-Modes
Manhattan
178.6593
K-means
Square Euclidean
178.6593
K-Medoids
Square Euclidean
178.6593
K-Modes
Square Euclidean
178.6593
As a result of the scenarios, there were 2 different results, the best of which was 178.6593 km. The Euclidean and
Square Euclidean distance function produced good results, but the Manhattan distance function did not produce
good results in K-means and K-medoids methods. According to the best results, it has been assigned 3 service
units with a capacity of 27 and 1 service units with a capacity of 16 people. As one of the best solutions, route
lengths, number of staff and occupancy rate of services obtained by K-medoids clustering method and Euclidean
distance function are given in Table 2. The average occupancy rate of services is 96.3%. This ratio can be said to
be quite good.
Table 2. Results of K-medoids clustering method and Euclidean distance function.
Cluster
Route Length
Number of Staff
Occupancy Rate of Service
0
42.6223
26
96.3%
1
64.176
27
100%
2
15.6218
24
88.88%
3
56.2392
16
100%
6. CONCLUSIONS
In this study, first of all, it was followed route first-cluster second heuristic method for service routing problem.
We created scenarios using 3 different clustering algorithms; K-means, K-medoids and K-modes and 3 different
distance functions; Euclidean, Manhattan, Square Euclidean. According to these scenarios, the route length is
determined by the developed software and the total route length is calculated. Different scenarios produce the best
distance according to the clustering method and distance function.
The best result has 178.6593 km total route lengths and 96.3% average occupancy rate of services. According to
the best results, it has been assigned 3 service units with a capacity of 27 and 1 service units with a capacity of 16
people. We chose as one of the best solution which formed K-medoids clustering algorithm and Euclidean distance
function. In this solution, 4 clusters were created and a service was assigned to each cluster. The occupancy rates
of the services are 96.3, 100, 88.88, 100% respectively.
As a result of this study, it is not possible to comment that a specific clustering method and distance function give
the best results. However, in general, the best results in clustering methods were obtained with the Square
Euclidean and Euclidean distance functions.
Journal of Engineering Studies and Research – Volume 25 (2019) No. 2
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