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28Journal of Sustainable Development of Transport and Logistics
journal home page: https://jsdtl.sciview.net
Jayarathna, N. D., & Jayawardene, C. J. (2020). Clusters analysis application on transportation network. Journal of Sustainable Development of Transport and Logistics, 5(1), 28-36. doi:10.14254/jsdtl.2020.5-1.3.
Scientific Plafor.
ISSN 2520-2979
Clusters analysis application on transportation network
Nuwan Dhammika Jayarathna * , Chula J. Jayawardene **
* Faculty of Management, Humanities and Social Sciences, CINEC, CINEC Campus (Pvt) Ltd., Millennium Drive, IT Park, Malabe, Sri Lanka nuwan@cinec.edu
** Department of Mathematics, Faculty of Science, University of Colombo, College House, 94, Kumaratunga Munidasa Mawatha, Colombo 00700, Sri Lanka
open ^^access I d
Article history:
Received: January 13, 2020 1st Revision: February 05, 2020
Accepted: April 08, 2020
DOI:
10.14254/jsdtl.2020.5-1.3 AMS Mathematics Subject Classification (2010):
90C10, 90C05, 90C90
Abstract: 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.
Keywords: vehicle scheduling, minimizing transportation cost, Hamiltonian cycle, LINGO.
Corresponding author: Nuwan Dhammika Jayarathna E-mail: nuwan@cinec.edu
This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.
1. Introduction
Distribution systems can be defined as the sequential flow of procedures, systems, and activities which are designed and linked to facilitate and monitor the movement of goods and services from the source to the consumer. Essentially, distribution is about making products and services available to the end user when and where they need them. Often, you might hear the term 'channel of distribution' or 'marketing channel' with reference to distribution systems.
These two terms relate to a group of organizations or individuals who have an impact on the flow of products and services from the source of production to the end consumer. Since Sri Lanka is an agricultural country, its staple food is rice and curry. Therefore, vegetable and fruit consumption is usually very high among all Sri Lankans. In spite of the obvious variation in their production in different areas in the county, the demand for vegetables and fruits has remained constant, and is proportionate to the population density of each area. Provision of these goods to island-wide consumers is, therefore, a necessity. As the demand for these goods in different areas varies, the amount and frequency of delivering fresh fruits and vegetables need to be adjusted according to area demands. Delivery of those goods from the producer to the customer with a minimal price discrepancy in a cost-effective manner and via a minimally interrupted supply channel is called a fruit and vegetable distribution system. To make that a productive, cost effective process, the requirements of a neighborhood of a specific area of the country at a given time and the distance to that particular neighborhood need to be assessed. There should be a well-organized coordination between the economic centers and the peripheral warehouses. In Sri Lanka, the current distribution system operates in a manner where products are bought from the farmer by a middleman and delivered to the market or economic center by the middlemen. They are delivered to warehouses located in many areas of the country using trucks, and sold at a wholesale price, after which they are supplied to vendors and finally to the consumers at a retail price (see [2,4,5]). There are some problems that arise in the system due to a poor understanding of the requirements of fruits and vegetables in some areas, and the absence of a good transportation schedule, and this results in an excess or deficit in the supply. Further, due to incorrect transportation practices, a considerable postharvest loss occurs. To overcome those problems, there is a need for a proper distribution system in Sri Lanka's fruit and vegetable market.
2. Objectives of the research
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 the outlets in the provinces.
In this research, the final goal is to build an Internet Based System to solve this mathematical problem. The LINGO solver has been used in two ways for two major parts of this system.
1. Using the Hamiltonian Cycle to find the major paths to delivering vegetables and fruits from the Dambulla major hub to each warehouse in every district in Sri Lanka.
2. Using Excel, Access and Java software to build a computer-based system which delineates the manner in which all vegetables and fruits can be delivered to all vendors from all warehouses in Sri Lanka.
3. Literature review
Drezner et al. (2009) conducted a research of the central warehouse location problem revisited. The Purpose of the research was to find a central warehouse location with introducing optimum solutions. They have indicated that, most important and optimal solution is to minimize the transportation cost while finding best location of problems in the central warehouses. When finding locations of central warehouses, normally inventory cost is ignored. But warehouse location is considered by warehouse inventory problems. As well as location is considered very little when solving inventory problems. Optimum level of inventory cost is very conflicted in general. Numerical methods are given solution to inventory methods with optimized algorithms. They have taken some reasonable assumptions to overcome disturbances of this research. For the analyzing and solving
problems, they proposed four methods. First one is the back-order cost and they have taken second one as a most common method. It can be calculated back order cost by using service level of system and normally service level has been given to calculation. They have stated that it is very difficult process of estimating good will cost. As the third method, it can be defined as keeping high service level is the most influential rather than reducing the cost. It means objective of the third method is to increase the service level. Weber location problem is the last method of analysis and it is ignored inventory cost. They have mentioned that numerical result shows ideal location of new facility rather than existing location. Researchers have verified ideal location for a new facility by reducing inventory cost and transportation cost.
Sahoo and Pal (2012) conducted a research of truck allocation model using linear programming and queueing theory. Queueing theory is the special design of telephone system and it is being used for control traffic, in hospital management and it was designed computer system of time shared. When solving optimization problems in transport problems and operational research, linear programming is being taken. In linear programming problems, which is included a linear objective function, constrains and non-negative constrains but in nonlinear programming problems, which is including nonlinear objective function and constrains. Simplex method is given either basic feasible result or solution in an effective manner.
The researcher has introduced new truck allocation model with reducing wastage of time through increasing operational improvements and optimized route planning. Truck allocation model has been built using linear programming and Queueing theory assuming that single truck size.
Research of economic evaluation of a warehouse investment in central Europe has conducted by Machackova (2009). The Research was based on Nokian Heavy Tyres ltd and it was an ongoing project in 2009. The researcher has comprised eminent analysis of warehouse physical location in central Europe. The goal was to build a warehouse for Nokian Heavy Tyres in central Europe when comparing private warehouse and contract warehouse. The researcher has taken three alternatives under warehouse planning
Michael Haythorpe (2011) has carried out a research of Markov chain-based algorithms for Hamiltonian cycle problem. Research has embedded Hamiltonian cycle problem to Markov decision process. Hamiltonian cycle is famous for solving traveling salesmen problem. Optimization problems are applied by Hamiltonian cycle problem and Markov decision process. Through that he has developed new theoretical results with that optimization models. Methods have been conducted a path like branches of tree to find a Hamiltonian cycle. Researcher has considered three graphs. First one is the one or more Hamiltonian cycles which contained by Hamiltonian graphs and Second one is the non Hamiltonian cycles which conducted by Bridge graphs but it could be found out in polynomial time. Third one can be defined as neither all graphs those are neither Hamiltonian nor one connected which conducted by non Hamiltonian graphs. The researcher has tested travelling salesmen problems using these methods and proved optimized paths.
Andrew Chalaturnyk (2008) has conducted a research of a fast algorithm for finding Hamiltonian cycles. This thesis was done by researcher as an algorithmic study and it was applied with Hamiltonian cycle problem. He has used two methods for the research and first one is the Graph theory concept. In this concept he used basic terminology and graphical representation to prove the concept. Set of vertices and edges are composed for the graphs. Paths and cycles were applied for the concept and after checked connectivity for each path. Second one is the Multi path method and it was used to find Hamiltonian cycle.
4. Methodology and research techniques
Solving an optimization model is a comprehensive task that requires a great deal of time for calculation (see [1]). But these models have economic value especially when considering the supply chain optimization. As a result, many logistics solution providers have emerged to cater to the rising demand, and these custom-made solutions are highly paid for by companies. At the same time, software has also been developed to facilitate these mathematical models to yield accurate calculations.
By coding the objective function and all the constraints in a particular programming language, the solution can be obtained faster and without errors. LINGO is one popular software tool among
industrial professionals in transportation, logistics and finance for reliable modelling calculations. LINGO software facilitates optimization modelling in linear, nonlinear, quadratically constrained, second order cone, stochastic and integer models in an easier and faster way. It contains an integrated package that provides a powerful programming language for expressing optimization modelling and a fully functional software for building and editing problems.
4.1 Route analysis - Hamiltonian cycle
As a first step of the research is to find a route plan with optimal path is done by using lingo software. Lingo is software which is made for easy to solve liner and non linear optimization problems. Through that, Hamiltonian cycle sample model is adjusted to this research and it is solved by using Lingo software. Hamiltonian cycle is given optimal path to each main cluster. Adjusted Hamiltonian cycle sample problem is given bellow. After solving model, when value is showed 1, it is taken as a path.
MODEL:
! Traveling Salesman Problem for the cities of
New Facility, Colombo 01, Colombo 09, Colombo 11, Colombo 12, Colombo 13, Colombo 14, Colombo 15;
SETS: CITY / 1.. 8/: U; ! U( I) = sequence no. of city; LINK( CITY, CITY): DIST, ! The distance matrix; X; ! X( I, J) = 1 if we use link I, J; ENDSETS
Model Assumptions
We identified the fact that the objective of MDL is to reduce the transportation costs in delivering goods from its major hub through its minor hubs to its outlets in the provinces. Here the mathematical model for MDL was formulated by considering the following assumptions:
1) All districts of Sri Lanka are divided into four groups.
i. Cluster 1
ii. Cluster 2
iii. Cluster 3
iv. Cluster 4
2) Each district contains two warehouses. Locations of the warehouses and relevant distances will be applied to the model accordingly.
3) Each district contains three vendors. One vendor represents ten supermarkets in a certain area.
4) The volume capacity of trucks is assumed to be the same.
5. Analysis of the research
This research is based on building a cost optimization model which derives a suitable method for delivering vegetables and fruits from the Dambulla major hub through its minor hubs to its outlets in the provinces.
The final goal of this research is to build an Internet Based System to solve this mathematical problem. However, in order to satisfy these major points, the LINGO solver was used in two locations. Advanced analysis was carried out utilizing the following tasks.
Task 1
I. All districts of Sri Lanka were divided into four groups: Cluster 1, Cluster 2, Cluster 3, Cluster 4.
Figure 4.1: Position of Clusters
i ♦ i -Jaffna
Kilinochchi
N
4 Mullaittivu
,, Vavuniya Mannar J
Trincomalee
Anuradhapura
Plonnaruwa
Batticaloa
Puttalam
KurunegalaMata|c Kandy
P™PahaKaga"e Badutla
Colombo NuWaracliya
Monaragala
Kalutara Ratnapura
Galle Hambantota
Matara
Ampara
Table 4.1: Details of clusters
Index
Region
The districts contained
1
2
3
4
Cluster 1 Cluster 2 Cluster 3 Cluster 4
Anuradhapura, Vavuniya, Mannar, Jaffna, Kilinochchi, Mullaitivu, Trincomalee
Puttalam, Kurunegala, Kegalle, Colombo, Gampaha, Kalutara, Rathnapura, Galle, Matara Matale, Kandy, Badulla, Monaragala, Hambanthota, Nuwara Eliya
Polonnaruwa, Batticaloa, Ampara_
Task 2
Each district contains two warehouses and three vendors. A vendor represents ten supermarkets in a certain area. Locations of the warehouses and relevant distances will be applied to the model accordingly.
Task 3
Under this task, the Hamiltonian cycle was used to find the major paths related to each cluster which are used to deliver vegetables and fruits from the Dambulla major hub to each warehouse in every district in Sri Lanka.
Task 4
During this step, Excel, Access and Java software were used to build a computer-based system which delineates the manner in which all vegetables and fruits are delivered to each vendor from all warehouses in Sri Lanka.
Figure 4.2: Hamiltonian Path of Each Cluster
6. Advanced analysis
Route Analysis using Hamiltonian Cycles
The first step of the research is to find a route plan, where the optimal path is calculated using the LINGO software. LINGO is a software which facilitates the solution of linear and non-linear optimization problems. Through LINGO, the Hamiltonian cycle model is adjusted accordingly to suit this problem. The LINGO output will yield the Hamiltonian cycle related to the optimal path to each cluster.
Cluster 1: Dambulla, Anuradhapura, Vavuniya, Mannar, Jaffna, Kilinochchi, Mullaitivu, Trincomalee, Dambulla
Cluster 2: Dambulla, Puttalam, Kurunegala, Kegalle, Colombo, Gampaha, Kalutara, Rathnapura, Galle, Matara
Cluster 3: Dambulla, Matale, Kandy, Badulla, Monaragala, Hambanthota, Nuwara Eliya
Cluster 4: Dambulla, Polonnaruwa, Batticaloa, Ampara
After finding the optimal path pertaining to each cluster, the total vegetable run is calculated.
Table 4.2: Daily Vegetable Run in Km
Cluster
Daily Vegetable Run km
1 674
2 804
3 661
4 426
Total 2565
7. Getting started
A main issue of this research is to find a proper system to transport all vegetables from warehouses to the vendors under optimum conditions. According to the model, one person in each district was assigned to take all demand values of the corresponding district and update the system at a certain time each day, using a secure login protocol. Thus, according to the system, each responsible person of each district should update his data at a given time each day. In addition, route analysis has to be performed for each of the four clusters by this administrative officer.
The main administrative officer of this system who works for the Logistics Department at the Dambulla Economic center, refreshes the system inputs every hour.
Figure 1: Access Sheet - Demands of Vendors
; Win
• District • Venderljo Venderljtt* VendeßTo Vender2_Qt - Vender3_To Vender3_Qt • FirstJD Dat • Add Mew Field
| Ampara Townl 10 Townl 10 Town 1 10 Yes 2014/09/14
2 Ampara Town 2 15 Town 2 20 Town 2 15 2014/09/14
3 Ampara Town 3 20 Town 3 10 Town 3 15 2014/09/14
4 Ampara Town 4 24 Town 4 10 Town 4 0 2014/09/14
5 Ampara Town 5 10 Town 5 0 Town 5 0 2014/09/14
S Ampara Town 6 10 Town 6 0 Town 5 0 2014/09/14
7 Ampara Town 7 10 Town 7 0 Town 7 0 2014/09/14
8 Ampara Town 8 10 Town S 10 Town 8 10 2014/09/14
9 Ampara Town 9 10 Town 9 10 Town 9 10 2014/09/14
10 Ampara Town 10 10 Town 10 10 Town 10 10 2014/09/14
11 Anuradhapura Town 1 Î5 Townl 40 Townl 35 Yes 2014/09/14
12 Anuradnapura Town 2 40 Town 2 40 Town 2 35 2014/09/14
13 Anuradhapura Town 3 40 Town 3 40 Town 3 35 2014/09/14
14 Anuradhapura Town 4 40 Town 4 40 Town 4 35 2014/09/14
15 A'jrid'SCjr: "C..-5 40 Town 5 40 Town 5 30 2014/09/14
IS Anuradhapura Town 6 40Town6 20 Town 5 30 2014/09/14
17 Anuradhapura Town 7 35Town7 20 Town 7 30 2014/09/14
13 Anuradhapura Town 8 40 TownS 20 Town 10 30 2014/09/14
19 Anuradhapura Town 9 25 Town 9 20 Town 9 0 2014/09/14
20 Anuradhapura Town 10 20 Town 10 20 Town 10 0 2014/09/14
ZL Badulla Townl 10 Townl 10 Townl 0 Yes 2014/09/26
77 BaHnlb Tmun9 liTminl WTVwml n imi/m/ifi
Figure 2: Route Analysis (using Hamilton cycles)
Figure 3: Transportation Cost Matrix of Warehouses and Vendors
Figure 4: Solution set within a cluster and the Lingo output
Shipments
Warehouses VENAMP1 VENAMP2 VENAMP3 VENANU1 VENANU2 VENANU3
25 0 0 0 0 0
0 0 0 0 262 0
0 0 0 0 0 120
0 0 0 120 o 0
The LINGO software connected to the Excel sheet imports the entered data and analyzes them using a LINGO package. The analyzed data is then distributed to the respective users via a Java ODBC bridge (as an Access Database). The Java code for Database Connectivity to access using an Action Performed function is run by the main administrative officer at Dambulla.
This enables the responsible person of each district to have access to this system and find the optimal schedule for transport planning, along with quantities of shipment within designated clusters (see Figure 3 and Figure 4).
8. Conclusion and recommendation
This study is based on the Dambulla economic center. This is an initial step towards establishing a correct protocol to arrange a transport model to distribute the vegetables and fruits from this center in a cost-effective way. This model is flexible enough to be re-scheduled at any request. It helps to create a larger model for solving any type of transportation planning problem. In this study, the model is designed only for one vegetable or fruit at a time. But it can be extended to apply to more than one item in the same excel sheet. For that purpose, an advanced LINGO code should be introduced, and it is also necessary to maintain a sufficient database.
As the first task, we arranged the optimal path to distribute the vegetables and fruits to the minor hubs. This reduces fuel consumption and unnecessary waste of time. In addition, due to problems that may arise on the roads during transportation, it is necessary to have an alternative plan to distribute vegetables and fruits during such times. We recommend carrying out a pilot survey and gravity model to find the optimal locations where new warehouses can be built in each district. It is recommended to assign one person from each district to submit all sub vendors' requirements. By
arranging one person to manage more than one district, it is possible to reduce the cost incurred by
MDL in Dambulla.
Citation information
Jayarathna, N. D., & Jayawardene, C. J. (2020). Clusters analysis application on transportation
network. Journal of Sustainable Development of Transport and Logistics, 5(1), 28-36.
doi:10.14254/jsdtl.2020.5-1.3
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