1
Author: Huang, Yanhui Title: Applying Linear Programming Method in Six Sigma Approach to Develop a
Truck Planning Tool The accompanying research report is submitted to the University of Wisconsin-Stout, Graduate School in partial
completion of the requirements for the
Graduate Degree/ Major: MS Technology Management
Research Adviser: James Keyes, Ph.D.
Submission Term/Year: December, 2013
Number of Pages: 56
Style Manual Used: American Psychological Association, 6th edition
I understand that this research report must be officially approved by the Graduate School and that an electronic copy of the approved version will be made available through the University Library website
I attest that the research report is my original work (that any copyrightable materials have been used with the permission of the original authors), and as such, it is automatically protected by the laws, rules, and regulations of the U.S. Copyright Office.
My research adviser has approved the content and quality of this paper. STUDENT:
NAME Yanhui Huang DATE: December 16, 2013
ADVISER: (Committee Chair if MS Plan A or EdS Thesis or Field Project/Problem):
NAME Dr. James Keyes DATE:
---------------------------------------------------------------------------------------------------------------------------------
This section for MS Plan A Thesis or EdS Thesis/Field Project papers only Committee members (other than your adviser who is listed in the section above) 1. CMTE MEMBER’S NAME: DATE:
2. CMTE MEMBER’S NAME: DATE:
3. CMTE MEMBER’S NAME: DATE:
--------------------------------------------------------------------------------------------------------------------------------- This section to be completed by the Graduate School This final research report has been approved by the Graduate School.
Director, Office of Graduate Studies: DATE:
2
Huang, Yanhui. Applying Linear Programming Method in Six Sigma Approach to Develop a
Truck Planning Tool
Abstract
Six Sigma is a tool for business to achieve continuous improvement. The benefits of
implementing Six Sigma projects include cost reduction and productivity improvement. Six
Sigma uses the Define, Measure, Analyze, Improve and Control (DMAIC) methodology to solve
problems. In this study, the linear programming approach was used in the improve and control
phases of a Six Sigma project to find a truck scheduling tool for ABC Transportation Company
to reduce their shipping cost. The key cost variables and their probability distributions were
identified in the analyze phase. The study results showed that the new truck scheduling tool
would reduce the shipping cost significantly.
3
Acknowledgments
I would like to thank my husband, my son and other family members for their patience
and support during this project and throughout my studies. I would also like to thank ABC
Transportation Company for their support during this study. Finally, I would like to thank Dr.
Keyes and his assistant, Jamie Scholl, for their assistance and time.
4
Purpose of the Study............................................................................................................ 10
Methodology ....................................................................................................................... 12
Summary ............................................................................................................................. 14
Six Sigma ............................................................................................................................ 16
DMAIC Methodology ......................................................................................................... 17
Linear Programming............................................................................................................ 21
Development ....................................................................................................................... 22
Summary ............................................................................................................................. 25
Data Analysis – Determine the Probability Distributions of Cost Items................................ 31
Development of Linear Programming Model ....................................................................... 32
Solving the Linear programming Model .............................................................................. 34
Limitations .......................................................................................................................... 34
Summary ............................................................................................................................. 35
Results of Probability Distributions of Extra Cost Items ...................................................... 38
Linear Programming Model................................................................................................. 41
Summary ............................................................................................................................. 44
6
Appendix A: ABC Transportation Company 2012 Shipping Cost Summary .............................. 56
7
Table 1: Summary of Trucks Used for XYZ Electrical Business.................................................. 9
Table 2: Sample Truck Cost Record – Company Truck ............................................................. 27
Table 3: Sample Truck Cost Record – Rental Truck .................................................................. 28
Table 4: Sample Extra Cost Item Tracking Table – Company Truck ......................................... 30
Table 5: Sample Extra Cost Item Tracking Table – Rental Truck .............................................. 30
Table 6: Sample Overload Cost Probability Distribution - Overload vs. Overload Fine ............. 32
Table 7: Probability Distribution of Extra Costs for Rental Truck .............................................. 38
Table 8: Probability Distribution of Overload Weight vs. Overload Fine ................................... 39
Table 9: Probability Distribution of Overload Weight vs. Extra Fuel Cost ................................. 40
Table 10: Probability Distribution of Overload Weight vs. Late Delivery Penalty ..................... 41
Table 11: Actual Cost vs. Linear Programming Output Results for April 2012 Shipment .......... 44
8
Figure 1: Cause and Effect Matrix Example .............................................................................. 19
Figure 2: DMAIC Six Sigma Improvement Methodology ......................................................... 20
Figure 3: Chinese GDP Annual Growth Rate from Year 2008 to Year 2012 .............................. 23
Figure 4: Chinese Diesel Prices Historical Data from Year 2005 to Year 2012 .......................... 24
Figure 5: Sample Size Code ...................................................................................................... 28
Figure 6: Sample Master Table .................................................................................................. 29
Figure 7: Example of a Pareto Chart for Cost Items Analysis .................................................... 31
Figure 8: Linear Programming Variable Constraint Set ............................................................. 33
Figure 9: Linear Programming Objective Function .................................................................... 34
Figure 10: Pareto Analysis Results for Key Cost Items .............................................................. 37
Figure 11: Linear Programming Model Variable Constraint Set ................................................ 42
Figure 12: Linear Programming Model Objective Function ....................................................... 42
Figure 13: MS Excel Solver Output – Linear Programming Model Solution .............................. 43
Figure 14: The Relationship between the Current Study and Future Research Opportunities ..... 50
9
A transportation service provider, hereafter referred to as ABC Transportation Company
(ABC) to protect the confidentiality of the information provided, which was established in 1997.
Based in Guangdong Province, China, the company provides transportation services throughout
mainland China. At the end of 2012, ABC had four departments and 52 employees. The main
customer of ABC Transportation Company was XYZ Electrical (an actual company, the name
has been altered to protect confidentiality).
The trucks used to ship the XYZ electrical products came from three resources; trucks
owned by ABC, trucks owned by drivers who were partnering with ABC and trucks rented by
ABC from other transportation service providers. The shipping costs of renting trucks from
other transportation service providers were significantly higher than that of ABC owned trucks
or drivers that are partnered with the company. If possible, ABC wanted to use its own trucks
and trucks owned by drivers that are partnered with the company. The rental option was only to
be used when the first two options could not meet the customers’ needs. Table 1 summarizes the
capacity, job assignment priority and operation cost of ABC’s truck resources.
Table 1
Summary of Trucks Used for XYZ Electrical Business
Owner Number Job Priority Operation Cost Trucks owned by ABC 16 High Low
Trucks owned by sub-contractors 24 Medium Medium
Trucks rented Unlimited Low High
In the past, the majority of XYZ electrical products were shipped by trucks owned by
ABC and drivers partnered with ABC. Rental trucks were only used in emergency situations.
10
With the dramatic development of real estate in China (new residential buildings increased on
average 7.7% per year from 2008 to 2012), the demand of XYZ Electrical products also
increased significantly (Ruan, 2012). As a result, XYZ Electrical increased the shipment of its’
products which included items such as: Wiring devices, home automation systems, structured
cabling systems and door entry systems. In order to meet the increased demand, XYZ Electrical
asked ABC to ship higher volume to more destinations and more frequently. ABC was not
prepared for the increase in demand and found it had to use more rental trucks from other
providers.
Statement of the Problem
ABC experienced a high number of late deliveries, unbalanced truckloads, and increased
use of rental trucks from other transportation service providers. This reduced the company's
profits.
Purpose of the Study
The purpose of the study was to use Six Sigma methodologies to improve ABC’s truck
capacity planning and scheduling to reduce the shipping cost and increase the company’s profits.
ABC used a demand driving scheduling process in which the truck scheduling was based on
customer demand. After receiving the customers’ order, the operations department combined the
orders and assignments into truckloads sorted by destinations. Trucks were assigned based on
the total number of truckloads required. If there were not enough company trucks available, ABC
rented trucks from contract truck providers. This approach came with the following issues; such
as, not enough trucks carrying products to specific destinations and lack of demand forecasting.
This study used a Six Sigma approach to reduce the unbalanced scheduling issues, so the
capacity of company trucks could be optimized.
11
Six sigma methodology. Emphasize statistical tools to improve the established
processes (Reytblat, 2011).
DMAIC. Six Sigma problem solving steps: Define, Measure, Analyze, Improve, Control
(Hahn, & Hill, 1999).
Linear programming. The mathematic approach that is used to find optimized solutions
for the linear models with constraints (Moore & Weatherford, 2001).
Truckload. The total goods loaded to a single truck.
Overload. The load exceeds the designated truck capacity. This may cause delay of
delivery because the extra load can affect truck speed.
Target cost. The base cost of shipping one regular load truck to a certain destination.
The target cost is clean cost which means there are no overload fines and late delivery penalties.
Cost deviation. The difference between actual cost and target cost.
MIL-STD-105E. The acceptance sampling plan standard published by the Department
of Defense USA that emphasizes on verifying the accuracy of a population data set based on
sampling (Montgomery, 2009).
Pareto analysis. Used in identifying key problems (Montgomery, 2009).
Renminbi (RMB). Chinese currency, 1 RMB is equivalent to 0.16 US dollars.
Assumptions of the Study
Several assumptions were made throughout this study to find the optimized truck
schedule. First, ABC created a project team and provided sufficient resources to support the
project. The four team members represented company functions including; customer service,
scheduling, operation and accounting.
12
Secondly, the operation data used within this study was accurate and up to date. Data
from 12 months operation was used to optimize the truck schedule. It was expected that the
historical data used by the project team was accurate. Sample operational data was selected
based on MIL-STD-105E to verify the accuracy.
Thirdly, the optimization model was created from the previous 12 months’ operational
data. This study assumed that the customer demand would remain at the same level; therefore,
the customer would continue working with ABC and there would be no significant change in the
shipment volumes. In this case, ABC did not have to purchase extra trucks to increase its’
resource capacity.
Finally, the geographic destinations of the shipments would remain in the same area.
Since the optimization scheduling model inputs were based on data from the previous 12 months
of operation; it was very important to keep the truck routes constant so the model could be used
for future scheduling.
Methodology
The objective of this study was to use Six Sigma methodologies to provide a planning
tool that resulted in lower costs of operation. It was accomplished by optimizing the truck
overload scheduling to lower the shipping cost. Linear programming was employed in the Six
Sigma analyze and improves phases in this study. Linear programming models contain an
objective function and several linear constraints. In this research, the objective function was to
minimize the cost in each operation cycle. The linear constraints included the total overload
shipment volume and the overload weight allowance of each truck. The total shipping cost was
calculated based on the probability distributions of the key cost items.
13
The operational data was collected between January 2012 and December 2012. The data
included the following information:
1. Customers’ order data
1) Total shipment volumes
3) Destination of the shipments
4) Desired delivery dates
2. Truck availability
The truck availability data included; how many trucks were available at each date, how many of
them were ABC owned trucks, how many of them were driven by partners of ABC, how many
trucks were under regular maintenance and how many trucks were not available due to
emergency issues such as accidents or driver illnesses.
3. Rental truck cost
4. Actual shipment records
The actual shipment data included how each order was shipped, the delivery date and late
delivery penalties, overload fines, extra fuel costs and the actual costs of each order shipped.
The data were summarized by the following approach. First, the target cost was
determined for each destination area. Next, the deviations between the actual cost and target
costs were calculated. In the third step, the cost deviations were categorized into different cost
categories such as extra fuel costs caused by overload, overload fines, extra rental truck costs and
late delivery penalties.
14
Pareto analysis was performed to examine the summarized data. The purpose of Pareto
analysis was to identify the main cost items that resulted in high operation costs. The linear
programming model was established based on the finding from the Pareto analysis. The objective
of the linear programming model was to minimize the shipping costs. Microsoft (MS) Excel
Server was used to solve the linear programming model.
The truck scheduling plan was formulated based on the results of MS Excel Server
outputs. The impact to the total shipping cost was calculated based on the recommended truck
schedule and was compared to the historical actual costs to see if there was a significant
improvement opportunity.
Limitations of the Study
This research project focused on utilizing the trucks owned currently by ABC
Transportation Company. Options such as increased resource capacity (buying new trucks or
adding more partner driver trucks) were excluded. Second, the data used in this research only
reflected the historical operational costs of ABC Transportation. Hence, the proposed specific
solutions from this research may not generalize to other businesses. Third, the forecasting model
used in this research did not apply to situations such as new competition entering the business or
government policy changes.
Summary
This chapter addressed the background of the research project including the problems
ABC faced, the purpose of the study and objectives of the research. It also defined important
terms and the limitations of the study.
The next chapter explores the literature related to the Six Sigma DMAIC approach, linear
programming and the transportation business in China. More importantly, the next chapter will
15
review how to link the linear programming model to Six Sigma’s analyze and improve phases
and what benefits are associated with it.
16
ABC Transportation Company experienced operational efficiency problems, which has
led to higher costs, late deliveries and poor truck utilization. The company wanted to utilize a Six
Sigma approach to reduce their operational costs and to increase their profitability. This
literature review analyzed Six Sigma methodology and the reason for using Six Sigma in this
project. It also reviewed linear programming and the benefit of applying linear programming to
improve ABC’s operational efficiency. In addition, literature related to the Chinese
transportation market was reviewed to provide an understanding about the research project.
Six Sigma
Six Sigma is “A business improvement approach that seeks to find and eliminate causes
of mistakes or defects in business processes by focusing on outputs that are of critical importance
to customers” (Snee, 1999, p. 100).
The American Society for Quality (2013) defines Six Sigma as:
a fact-based, data-driven philosophy of quality improvement that values defect
prevention over defect detection. It drives customer satisfaction and bottom-line results
by reducing variation and waste, thereby promoting a competitive advantage. It applies
anywhere variation and waste exist, and every employee should be involved.
Six Sigma is a well-defined process that focuses on problem solving which maximized the return
on a company’s investments. Six Sigma was developed by Motorola in the 1980’s to improve
manufacturing processes quality and to enhance customer satisfaction (He, Tang & Chang,
2010). At the Six Sigma quality level, with a 1.5 standard deviation shift from the process target,
the manufacturing process produces 3.4 defective parts per million opportunities (Harry, 1998).
Beginning in the 1990’s, organizations such as General Electric (GE) and AlliedSignal
17
(Honeywell) used a Six Sigma approach to improve other aspects of operations such as reduced
cycle time, increased process yield, and enhanced resources efficiency (Evans & Lindsay, 2010).
The benefit of implementing Six Sigma projects include: Defect and cost reduction,
productivity improvements, cycle time reductions, customer relations improvements, and market
share increases (Pande, Roland & Cavanagh, 2000). Hahn & Hill (1999) reported that Motorola
saved $940 million over three years from Six Sigma projects. AlliedSignal (Honeywell) had an
estimated savings of $1.5 billion for the year 1997 from their Six Sigma initiative and GE
received $1.75 billion for 1998 and $2.5 billion for 1999 from its $1 billion investment in Six
Sigma improvement projects (Breyfoggle, 2003).
DMAIC Methodology
Six Sigma uses Define, Measure, Analyze, Improve and Control (DMAIC) methodology
to solve problems (Hahn & Hill, 1999).
The define phase is the first phase of the Six Sigma improvement process. In this phase,
the following tasks will be completed:
1. Define the stakeholders
The Six Sigma project Stakeholders included internal stakeholders and external stakeholders.
Internal stakeholders are within the organization such as top management team, functional
managers, and project team members. External stakeholders are outside the organization such as
customers, competitors, suppliers, and other intervener groups (Breyfoggle, 2003).
2. Analyze the impact of the Six Sigma project to the stakeholders
18
The impact of the project to each stakeholder would then be analyzed. The project that is found
most beneficial to the organization would be selected. The tools used during the define phase are
Suppliers, Inputs, Processes, Outputs, and Customers (SIPOC) analysis (Breyfoggle, 2003).
3. Form the Six Sigma project team
After the project was selected, a Six Sigma project team was formed and roles were assigned to
each team member (Breyfoggle, 2003).
4. Develop Project Plan
The project team developed a project plan during the define phase. This project plan included
the problem statement, project goal, project scope, project team, project resources needed and
project timeline (Breyfoggle, 2003).
5. Approval
After the Six Sigma project plan was approved by the project sponsor, the resources would be in
place and the project team could move to the measure phase (Breyfoggle, 2003).
A process has to be measured before it can be improved. The measure phase is intended
to identify the data that illustrates the state of the current process. The Six Sigma team had to
first identify the input and output variables for the process. The team then developed a data
collection procedure and sampling plan (Breyfoggle, 2003). The data collection tools included
checklists, check sheets and a control chart (Evans & Lindsay, 2010). The Six Sigma team set a
baseline based on the data collected to determine the root causes for corrective actions.
Breyfoggle (2003), created a cause and effect matrix that served as a tool to help the Six Sigma
team prioritize the process input variables shown in Figure 1. The cause and effect matrix is used
through the following steps:
19
2. Enter the effect value that each input variable has on the output variable.
3. The result values were calculated from the sum of the multiplication of effect value
and output priority.
4. The percentage impact of each input variable was calculated based on the
contribution of each input variable.
5. The results of the cause and effect matrix could help the Six Sigma team determine
which input variable affected the output variable the most.
Figure 1. Cause and Effect Matrix Example (Retrieved from Breyfoggle, 2003)
The analyze phase was the most important phase in the Six Sigma process (Eckes, 2003).
The improvement idea was generated based on the analyzed results. The recommendation for
improvement was made in this phase as well. The Six Sigma team used tools such as histograms,
Pareto analyses, experimental designs and statistical process control to find root causes for the
problem (Evans & Lindsay, 2010).
The improve phase is where the problem solution or corrective action was implemented.
The tools used in this phase included experimental designs and hypothesis testing (Evans &
Lindsay, 2010). This phase required multiple attempts until the project goals and objectives were
A B C D 4 2 3 1 Results
1 3 1 3 3*4+1*3+3*1=18 18/71=25.4% 2 5 7 5*2+7*3=31 31/71=43.6% 3 2 4 2*4+4*1=12 12/71=16.9% 4 2 2 2*2+2*3=10 10/71=14.1%
Total 18+31+12+10=71 100%
Process Input
20
reached. Once the team was able to show that the solution resulted in improvement, they could
move on to the control phase (Go Lean Six Sigma, 2013). Researchers recently used linear
programming as a mathematical and statistical tool in the Six Sigma analyze and improve phases
(Bobek, Imondi, Shott & Toobaei, 2012). The details about linear programming will be reviewed
later in this chapter.
The control phase is the last phase in the DMAIC procedure. The objective of this phase
is to sustain the achieved improvement in the improve phase. The Six Sigma team needed to
create a control plan to ensure the improved process maintained its ability to meet customers’
needs (Eckes, 2003). Statistical Process Control is often used in the control phase to monitor the
status of process.
Like Deming’s Plan-Do-Check-Act quality improvement cycle, Six Sigma DMAIC
procedure is a tool for business to achieve continued improvement (Evans & Lindsay, 2010). An
organization starts a new Six Sigma improvement after one project is completed. Figure 2 shows
the DMIAC methodology. Plan-Do-Check-Act is considered the foundation of DMAIC. There
are many similarities between Plan-Do-Check-Act and DMAIC.
Figure 2. DMAIC Six Sigma Improvement Methodology
21
Linear Programming
Linear programming is the process of finding the optimized outcome for a given set of
linear equations related to a specific situation (Moore & Weatherford, 2001). Many real world
problems lend themselves to linear programming modeling or can be approximated by linear
models. In general, a linear model contains three types of functions:
1. Linear objective function
This objective function defined the goal of the linear model. Each linear model can only have
one goal such as maximum profit or minimum cost, shortest processing time and largest amount
of products throughout (Moore & Weatherford, 2001).
2. Linear constraint set
The linear constraint set defined the situational constraints such as; number of resources
available, total amount of time an order has to be completed and machine hours between regular
maintenance. For linear programming models, all constraints have to be in linear functions
(Moore & Weatherford, 2001).
3. Variable constraint set
The variable constraint set indicated the variable range. Each variable must has its own
constraint defined in the constraint set (Moore & Weatherford, 2001).
Linear programming can be solved by using computer software such as MS Excel Solver.
However, not all the linear programming models can solve for optimized solutions under the
following three situations:
1. Infeasibility
The linear constraint set is unsolvable, which means there is no variable combination that meets
all constraints (Moore & Weatherford, 2001).
22
2. Unsoundness
The objective function had a result close to infinity (Moore & Weatherford, 2001).
3. Alternate solution
There was more than one variable combination that resulted in the same object function result
(Moore & Weatherford, 2001). In order to avoid the above situation, researchers often modified
the linear model to reach a unique optimized solution. Industry has had a long history of
applying linear programming to solve complex problems and find the optimized solutions in
production operation and services areas (Balbirer & Shaw, 1981). Linear programming was used
to find optimized solutions for complex situations; researchers recently started to use it as a
mathematical and statistical tool in the Six Sigma analyze and improve phases (Bobek et al.,
2012).
The Relationship Between Chinese GDP Growth and Residential Building Development
According to Dickinson (2012), GDP stands for Gross Domestic Product, which is the
market value of all goods and services produced within a country in a given period of time. From
1989 to 2012, the Chinese average GDP Annual Growth Rate was 9.2% (National Bureau of
Statistics of China, 2013a). Figure 3 shows the GDP annual growth rate from 2008 to 2012 in
China.
Investment in new residential building development contributed heavily to Chinese GDP
growth (Sahoo, Dash & Nataraj, 2010). The dramatic growth of new residential development
generated increased demand of raw materials, as well as the transportation of these materials.
ABC is one of the beneficiaries of this demand increase.
23
Figure 3. Chinese GDP Annual Growth Rate from 2008 to 2012 (National Bureau of Statistics of
China, 2013b)
Truck Transportation Operation in China
In general, there are two types of truck transportation service providers in the Chinese
market. They are government owned providers and private providers. ABC would be considered
as a private provider. Unlike the government owned providers, which have business from
government owned companies; ABC needs to sell its transportation service to customers and
produce a profit to stay in business.
At the beginning of each year, ABC and its’ customers negotiate a contract for the
transportation service. The key element of the contract is the unit price, which is the price that
customers pay for the shipment of a certain amount of goods to a certain destination within a
certain amount of time. Once this unit price is agreed upon by both parties; it normally would not
change until the next year unless one party decides to stop the business relationship. In addition,
the competition in the transportation market was getting stronger. There were 20% more private
truck transportation service providers in 2012 than 2011 in Guangdong Province (Guangdong
24
Bureau of Statistics of China, 2013). The operational costs of a private truck transportation
provider include the following five categories: fuel costs, toll costs, overload fines, late delivery
penalties and truck rental costs.
The first category is fuel costs, the diesel prices increased 80% from 2009 to 2012; Figure
4 shows the increase of fuel prices in China (National Development and Reform Commission,
2012). The second item is the toll costs. Vehicles have to pay toll costs while using these
highways because the highways were built by funding from banks. Chinese banks belong to the
Government, which defines the toll price. The Government will typically develop a long term
toll price to recover the invested costs of the highway system (Chen, 2012).
Figure 4. Chinese Diesel Prices Historical Data from 2005 to 2012 (National Development and
Reform Commission, 2012)
For instance, a truck would have to pay RMB 1,180 or $180 toll fee from Huizhou, Guangdong
Province to Wuxi, Zhejiang Province (around 1,400 kilometers).
25
The third cost item is the fine of overload. In order to offset the increasing fuel and
highway costs, many transportation providers reconfigure their trucks so they can overload
goods shipped on their trucks. A study showed that 100% of the Chinese trucks in Southern
China had been overloaded. Some trucks had overloaded the normal capacity, by as much as
800% (Chen, 2012). Most of the time, the overloaded trucks just pay a fine and continue to their
destination (Wei, 2012).
The fourth cost item is the late delivery penalties. Large amounts of overloaded trucks
slowed down the traffic and increased the probability of accidents, which resulted in late
deliveries. Customers charged late delivery penalties to the trucking firm. The transportation
company then needed to absorb the cost of the penalty.
The fifth cost item is renting from other transportation providers. In general,
transportation providers charge higher prices than company owned trucking costs. This price
may have even been higher than what customers were willing to pay to ABC.
Summary
This chapter covered the Six Sigma process improvement approach, the linear
programming method and the Chinese truck transportation business. The Six Sigma approach is
often used to reduce costs and increase operational efficiency. Linear programming can help the
organization determine the best operational variable combination, which leads to improved
profit. Given the operational challenge ABC faced, this research intended to use the above
approaches to help the company find a way to better utilize its resources and reduce their costs.
The next chapter will look at the methodology associated with Six Sigma process
improvement and linear programming resource optimization. It will go over the methods
26
employed to help ABC find their best operational strategy. The data collection and procedures
used in the research will also be covered.
27
ABC Transportation Company experienced a high number of late deliveries, unbalanced
truckloads, and increased use of rental trucks from other transportation service providers. This
reduced the company's profits. The objective of this study was to use Six Sigma methodologies
to provide a planning tool that resulted in lower cost of operation. Linear programming was used
in the Six Sigma analyze and improved phases in this study. The linear programming model
contained an objective function and several linear constraints. In this research, the objective
function was to minimize the cost deviation in each operation cycle. The linear constraints
included the total overload weight and the truck overload capacity.
Data Collection
The shipping cost records were collected for 2012. The cost records included shipping
destination, date shipment requirement received, delivery date, total overload weight and total
cost. The cost records were entered into an MS Excel file. An identification number was
assigned to each record. There were two types of shipping cost records. The first type of
shipping cost records were the shipping costs for the trucks owned by ABC and their sub-
contractors. Table 2 shows an example of this type of record.
Table 2 Sample Truck Cost Record – Company Truck
ID 10 Destination Target Cost Date Order Received Delivery Date Total Overload Weight Total Cost Rental Truck?
Wuxi City RMB 5,000 or $840 01/15/2012 01/30/2012 7 Ton RMB 6,400 or $1,060 No
28
The second type of shipping cost records were the shipping costs for the rental trucks. An
example of rental truck shipping costs is shown in Table 3.
Table 3
Sample Truck Cost Record – Rental Truck
ID 12 Destination Target Cost Date Order Received Delivery Date Total Overload Weight Total Cost Rental Truck?
Wuxi City RMB 5,000 or $840 01/15/2012 01/31/2012 10 Ton RMB 8,200 or $1,360 Yes
Data Verification
The accuracy of the truck cost records were checked before this data was analyzed. MIL-
STD-105E sampling plan defined by the U.S. Department of Defense was used to determine the
sample size (Montgomery, 2009). In the first step, Sample Size Code Letter was determined
from the MIL-STD-105E standard shown in Figure 5.
Figure 5. Sample Size Code (Montgomery, 2009)
29
Secondly, the total number of samples that needed to be checked was identified from the
MIL-STD-105E Master Table shown in Figure 6. The acceptance level was also determined
from the Master Table. In the third step, the researcher used the MS Excel random number
generator to determine which record would be selected for verification. Finally, the selected
sample records were checked to verify if the truck cost record data met the accuracy standard. If
the verification results showed that the data accuracy met the MIL-STD-105E standard, the data
set could be used for analysis. If the verification results show the data accuracy met the MIL-
STD-105E standard, a 100% double check of the shipping cost records had to be done to ensure
all the errors in the data set were corrected before any data analysis was conducted.
Figure 6. Sample Master Table (Montgomery, 2009)
Data Analysis – Pareto Analysis for High Cost Items
Pareto analysis was used to analyze data to determine the key cost items that affected
truck cost. ABC established target cost for each destination. The target cost was the base cost of
30
shipping one regularly loaded truck. The target cost was a clean cost, which means there were no
overload fines, no extra fuel costs and no late delivery penalties. Table 4 shows an example of
how the extra cost items were collected for the company owned trucks.
Table 4
Sample Extra Cost Item Tracking Table – Company Truck
ID 10 Extra Cost Destination Target Cost Date Order Received Delivery Date Total overload Total Cost Rental Truck? Extra Cost from Rental Extra Fuel Cost Extra Toll Cost Overload Fine Late Delivery Penalty Other Extra Cost
Wuxi City RMB 5,000 or $840 01/15/2012 01/30/2012 7 Ton RMB 6,400 or $1,060 No 0 RMB 620 or $100 0 RMB 660 or $110 RMB 100 or $17
0 RMB 620 or $100 0 RMB 660 or $110 RMB 100 or $17 RMB 20 or $3
Table 5 shows how the extra cost items were collected for rental trucks. For rental
trucks, the rental company had to pay extra fuel costs, extra toll costs, overload fines and late
delivery penalties.
Table 5
Sample Extra Cost Item Tracking Table – Rental Truck
ID 12 Extra Cost Destination Target Cost Date Order Received Delivery Date Total Overload Weight Total Cost Rental Truck? Extra Rental Cost
Wuxi City RMB 5,000 or $840 01/15/2012 01/31/2012 10 Ton RMB 8,200 or $1,360 Yes
RMB 3,200 or $520
31
A Pareto chart was developed to determine the top contributing extra cost items. Figure 7
shows an example of a Pareto chart which ranked extra cost items from the highest to lowest
contribution. The actual results will be shown in Chapter IV. The key contribution cost items
were used as decision variables for the linear programming model.
Figure 7. Example of a Pareto Chart for Cost Items Analysis
Data Analysis – Determine the Probability Distributions of Cost Items
As mentioned in Chapter II, most Chinese transportation service providers overloaded the
weight capacity of their trucks to reduce shipping cost. The consequences associated with
overloaded trucks were extra costs including; possible overload fines, extra fuel costs and
potential late delivery penalties. However, since there were different random factors such as
number of traffic control agencies on duty that might affect the values of extra cost items (e.g. a
truck overloaded by five tons to Wuxi City had to pay an overload fine of RMB 660 or $110 for
one trip and RMB 850 or $140 for another), it was necessary to understand the probability
distribution of the extra cost items. In this study, the researcher determined the probability
distribution of the extra cost items based on the frequency of occurrences in the truck record
data. Table 6 shows an example of the cost probability distributions between overload and
32
overload fine. The probability distributions for other key cost items such as the probability
distributions between overload and late delivery penalty, overload and extra fuel cost will also be
determined using the same methodology. The results of probability distributions for the key cost
items will be shown in Chapter IV.
Table 6
Overload (Ton) Overload Fine Probability
Under 5 RMB 500 or $80
RMB 740 or $120
RMB 800 or $130
RMB 740 or $120
RMB 800 or $130
RMB 800 or $130
RMB 1,000 or $160
Development of the Linear Programming Model
Linear programming was used during the improve phase of the DMAIC process to
determine the truck scheduling policy. As mentioned in Chapter II, linear programming has a
history of being implemented as a tool to help business sectors determine the optimized
utilization of their resources. The linear programming model was built through the following
steps:
33
The variables in this model were the overload weights of truckloads for each shipment. These
variables were defined as V1 to Vn, which stands for the total overload weight of each truck.
2. Variable Constraint Set
The first set of variable constraints was the overload weights of each truck; the overload weights
should not contain negative numbers. The second constraint was the total overload weight
volume. This volume will be greater than or equal to the total shipment overload volume.
The third constraint was the overload constraint. Even though it was common in the Chinese
transportation market that trucks were overloaded, each transportation service provider
established a maximum overload weight allowance that a truck could be overloaded for safety
concerns. ABC had its’ own limit for how much weight a truck could handle for different
destinations. Based on the above constraint regulations, the following constraint set was
established. The constraint set is shown in Figure 8.
Figure 8. Linear Programming Variable Constraint Set
3. Linear Objective Function
The objective of this research project was to reduce the shipping cost for ABC Transportation.
Based on this, the objective function for linear model was established to minimize the total cost
as shown in Figure 9.
34
Solving the Linear programming Model
The linear programming model was developed using MS Excel Solver, which would
solve the model and return the best combination of values for V1 through Vn. The results will
be shown in Chapter IV.
The project team used one month’s historical data to validate if this approach would
reduce the shipping costs. The truck costs developed through the linear programming model was
compared with the previous year’s costs to determine if there was a need to modify the model.
Limitations
As pointed out in Chapter I, there were several limitations for this study. First, the
project team only analyzed 12 months of operational data for this analysis, which implied that
the economic growth impact might not have been addressed in the linear programming.
The second limitation of this study was the probability distributions of extra cost items.
They were based on past experiences. With changes of road conditions such as new highways,
the parameters in the linear programming models might have to be modified to reflect the current
conditions. While the project provided a framework for optimized truck scheduling, it was
limited to the costs that were current at the time of the research.
The same limitation applied to the probability distribution of overload fines. While the
team tried to calculate the probability distributions of overload fines, the accuracy of these
35
probabilities was limited to the information provided by the truck cost records during the
research study period.
The fourth limitation of this study was the lack of forecasting for future demand. Given
that residential building development was growing at a fast pace in China, there is a higher
probability that the demand from customers may increase in the near future. This trend was not
addressed in the linear programming model.
Summary
This chapter covered the research methodology for evaluating the shipping costs of ABC
Transportation. Pareto analysis was used to determine the key extra cost items. The probability
distributions of extra cost items were also identified.
Next, this chapter covered how to use the parameters generated from the data analysis to
establish the linear programming model. The objective function of the linear programming
model was to minimize the total extra cost. The parameters were used in the objective function
as well as the linear programming constraints. Verification was done based on one month of
operational data. A new policy was established to ensure the improved performance was
sustained.
Finally, the limitations of the study were given. The main concern of this study was the
accuracy of the probability distribution for the extra cost items. These distributions may change
due to the fast development of the Chinese economy. The linear programming model parameters
would have to be updated if these changes become significant.
The next chapter will review the results of this study. The linear programming model
outcome will be discussed in detail in the next chapter as well. Truck scheduling policy related to
the linear programming model output will also be explained.
36
ABC Transportation Company experienced a high number of late deliveries, unbalanced
truckloads, and increased use of rental trucks from other transportation service providers. This
has increased the company’s shipping costs and reduced their profits. The goal of this study was
to use Six Sigma methodologies to provide a truck capacity and schedule planning tool that
would help ABC lower its shipping cost.
To accomplish the goal, linear programming was used in the Six Sigma analysis and
improves phases in this study to develop a truck capacity and scheduling plan. The research was
conducted through the following phases. First, the shipping cost records for 2012 were collected
and verified for accuracy. Pareto analysis was conducted in the second step to determine the key
cost variables that affected the shipping costs. Third, the probability distributions of the key cost
variables (extra rental cost, overload fines, late delivery penalties and extra fuel costs) were
determined. In the fourth step, key variables found from the second step and their probability
distributions identified in the third step were used to build the linear programming model.
Lastly, the results of linear programming model from MS Excel Solver were used to improve
ABC’s truck capacity planning.
Results of Data Verification
There were total of 816 truck cost records collected for this study. According to MIL-
STD-105E standard Sample Size Code Letter table showed in Chapter III Figure 5, the sampling
plan letter code was letter K. The total number of samples needs to be checked with letter code
K was 125 based on MIL-STD-105E Master Table showed in Figure 6 in Chapter III. The master
table also indicated that the acceptance level of this verification should be 0 which meant if there
was no error in 125 samples, the data set would be considered as accurate. The researcher
37
selected 125 shipping records from the 816 data set and verified the accuracy of them. The result
showed that all of them were correct. The data set was considered accurate and could be used
for analysis.
Results of Pareto Analysis
Pareto analysis was used to identify the key cost items that affected the total truck cost.
These variables were programmed into the linear programming model.
The input cost items for the Pareto analysis were, extra fuel cost caused by overloaded
trucks, overload fines, late delivery penalties, extra cost of rental trucks and extra toll costs
caused by overload. The cost items of 816 shipping records were summarized (summary results
shown in Appendix A). The Pareto chart shown in Figure 10 was created based on the data
summary results.
Figure 10. Pareto Analysis Results for Key Cost Items
The results of Pareto analysis showed that the extra toll costs only contributed 1.1% to
the total cost, which meant it would not be considered as a key variable when making the truck
planning tool. The other four cost items (extra rental, overload fine, extra fuel cost and late
38
delivery penalty) made significant contributions to the total cost and were included in the linear
programming model.
Results of Probability Distributions of Extra Cost Items
The Pareto analysis indicated that there were four cost items that significantly affected
ABC’s shipping cost. These four cost items were extra cost of rental truck, extra fuel cost,
overload fine and late delivery penalty. The probability distributions of each cost item were
needed to build the linear programming model. In this research project, the probability
distributions were determined by frequency count.
ABC Transportation Company incurred extra costs to use rental trucks. The extra costs
rental companies charged varied depending on the market. According to the frequency count
result, ABC used 280 rental trucks in 2012. ABC paid RMB 4,500 or $725 for 168 of them,
RMB 4,800 or $770 for 98 of them and RMB 5,200 or $840 for the rest 14 of the rental trucks.
Based on this frequency count outcome, the probability distribution of extra charge per truck was
calculated and summarized in Table 7.
Table 7.
Extra Charge by Rental
168/280 = 60%
98/280 = 35%
14/280 = 5%
The Pareto analysis results shown in Figure 8 indicated that there were three key cost
items associated with using overloaded company owned trucks: Extra fuel costs, overload fines
and late delivery penalties.
39
A frequency count approach was used to determine the probability distribution between
overload weights and overload fines. For example, the 2012 shipping cost records showed that
there were 75 trucks that had overload weights between two to three tons. Among these 75
trucks, 15 trucks (20%) were charged with RMB 300 or $50 overload fine, 30 trucks (40%) were
charged with RMB 400 or $65 overload fine and the remaining 30 trucks (40%) were charged
with RMB 600 or $80 overload fine. This probability distribution was used in the linear
programming model to calculate the overload fines of trucks that had been overloaded by
between two to three tons. Table 8 shows the probability distribution between overload weight
(ton) and overload fines.
Overload Weight (Ton) Overload Fine Probability
1
2-3
4-5
6-7
100%
20%
40%
40%
20%
45%
20%
15%
15%
50%
25%
10%
40
The same approach was used to determine the probability distribution between overload
weight and extra fuel costs. Table 9 shows the probability distribution between overload weight
and extra fuel costs.
Overload Weight (Ton) Extra Fuel Cost Probability
1
2
3
4
5
6
7
45%
55%
60%
40%
30%
40%
30%
40%
50%
10%
15%
20%
30%
35%
35%
30%
35%
20%
35%
35%
10%
41
Table 10 shows the probability distribution between overload weight and late delivery
penalties. The probabilities were calculated from frequency count results.
Table 10
Overload Weight (Ton) Late Delivery Penalty Probability
2-3
4-5
6-7
Linear Programming Model
The key cost items and their probability distributions were used to build the linear
programming model. The company’s maximum overload weight allowances were also
determined. For ABC’s company owned trucks, the maximum overload weight allowance is
seven tons. The maximum overload weight allowance for rental trucks is 10 tons. The linear
constraint set of the linear programming model is shown in Figure 11.
42
Figure 11. Linear Programming Model Variable Constraint Set
The goal of this research was to find a scheduling tool to reduce the shipping cost. In
order to achieve this goal, the linear objective function was used to minimize the total shipping
cost as shown in figure 12.
Figure 12. Linear Programming Model Objective Function
Results of Linear Programming Output
MS Excel Solver was used to solve the linear programming model. The objective
function of the linear model was to minimize the total extra costs. The total extra costs were the
summary of extra fuel costs, overload fines, late delivery penalties and extra rental costs. The
output of MS Excel solver provided the specified overload value (ton) of each truck. Figure 13 is
a screenshot of a MS Excel Solver output.
For this particular week, ABC had to ship 108 tons of overloaded products. The linear
programming solution made the following recommendations:
43
1. The output showed that company trucks V1 through company trucks V10 had final
values greater than zero. This indicated that the company had to use 10 company
trucks.
2. The overload value of each company truck was the final value from the output.
3. The output showed that the final values of rental trucks V1 through V5 were greater
than zero, which indicated that ABC had to use five rental trucks.
4. The overload value of each rental truck was the final value from the output.
5. The total overload amount was 108 tons, which equals the customer requirement.
Figure 13. MS Excel Solver Output – Linear Programming Model Solution
44
6. The total cost of the week was RMB 58,450 or $9,430 based on this truck capacity
planning.
Results of One Month Historical Data Comparison
A pilot test was conducted by using four weeks of historical data from April 2012 with
the linear programming approach. The results in Table 11 show that the total truck costs under
this new planning approach would have been RMB 240,739 or $38,828, which was 15.2% less
than the actual truck cost (RMB 284,025 or $45,810) of that month. The new approach reduced
the truck cost significantly.
Table 11
Actual Cost vs. Linear Programming Output Results for April 2012 Shipment
Cost Item Actual Cost
Output (April, 201)
Extra Rental Cost
Extra Fuel Cost
Late Delivery Penalty
Summary
This chapter began by showing the results of truck cost data verification. It showed that
the data used in this research was accurate. The chapter also went over the results of Pareto
analysis, which was used to identify the key cost items. These items were used as decision
variables to build the linear programming model. After the key cost items were decided, the
probability distributions between the overload and the key cost items were identified. The
probability distributions were used in the linear programming model for truck cost calculations.
45
MS Excel Solver was used to solve the linear programming model. The company’s operation
team used the linear programming model solution to lead the truck capacity planning. The pilot
test results showed that this approach would reduce the shipping cost for ABC Transportation
Company. The next chapter will draw conclusions from the study and make recommendations.
The opportunities for future research will also be discussed in the next chapter.
46
Chapter V: Discussion
Six Sigma is a tool used to achieve continued improvements. The benefits of
implementing Six Sigma projects include; cost reduction and productivity improvement. Six
Sigma uses Define, Measure, Analyze, Improve and Control (DMAIC) methodology to solve
problems. In this study, a linear programming approach was used during the improve and
control phases of a Six Sigma project to develop a truck scheduling tool for ABC Transportation
Company.
Chapter I introduced the background of ABC Transportation Company and the
challenges of truck scheduling they were facing. ABC was unable to effectively plan for truck
scheduling which resulted in high shipping costs. The goal of this study was to use linear
programming methodology and Six Sigma approach to help ABC Transportation Company
create a truck scheduling tool. This chapter also covered the assumptions of the study.
Chapter II was a literature review of Six Sigma approach, linear programming
methodology, Chinese economic development and the truck transportation service in China. The
chapter covered Six Sigma DMAIC and why it could help an organization reduce costs and
improve operational efficiency. It also described linear programming in depth and how an
organization may benefit from using such a technology.
Chapter III covered the methodology for this study regarding collection and analysis of
historical data, built a linear programming model and provided truck scheduling tools for ABC
Transportation. The 2012 truck cost records were collected for this study. These records were
verified by MIT-STD-105E for accuracy. Pareto analysis was then performed to determine the
key cost variables that affected the truck shipping costs. The probability distributions of the key
cost variables were identified based on frequency count. A linear programming model was built
47
with the key cost variables and their probability distributions. The objective of the linear
programming model was to minimize the total shipping cost. Chapter III concluded with the
discussion of the limitations of the study.
In Chapter IV, the results of data verification, Pareto analysis, probability distributions of
key cost variables and the linear programming output were presented. The linear programming
output was used as ABC’s truck scheduling tool. The one month pilot test result was conducted
and the shipping costs from the linear programming output were compared with the actual cost.
The comparison results showed that the cost based on the proposed scheduling tool was
significantly lower than the actual cost, which meant the new scheduling tool could reduce
ABC’s shipping cost.
This chapter draws conclusions from this research project followed by recommendations
that are made for ABC Transportation Company. Opportunities for future research will be
discussed at the end.
Limitations
This study was limited to the ABC Transportation Company’s 2012 operation records so
the economic growth impact factor could not be identified. The second limitation of this research
was the probability distributions of the key cost variables were also determined only by 2012
operation data which means the changes of road conditions, fuel price and administration
policies would not be reflected.
Results
There were 816 shipping cost records in 2012. The data verification results showed that
these records were accurate and could be used in this research project.
48
The results of Pareto analysis showed that there were four cost items that had significant
contributions to the total shipping cost. These four key cost items included extra rental cost, extra
fuel cost, overload fine and later delivery penalties. The probability distributions for these key
cost items were identified based on frequency count.
The linear programming objective function took into account the above key cost items
and probability distributions and summed them for the total shipping cost. The goal of this
research was to find a scheduling tool to reduce the shipping cost. In order to achieve the
research goal, the linear objective function was set up to minimize the total shipping cost. The
linear constraint functions in this research include total overload shipment weight and maximum
overload allowance of each truck. The variables in the linear programming model were the
overload weights of each truck.
The linear programming model was solved by MS Excel Solver. In order to test if the
outcome of the linear programming model could help ABC Transportation Company reduce its
shipping cost, a one month pilot test was conducted. The shipping costs were calculated from
linear programming output and were compared with the actual shipping costs for that month.
The comparison showed that the linear programming model reduced the shipping cost
significantly.
The pilot test results indicated that the linear programming model could help the ABC
Transportation better schedule its truck capacity to reduce shipping cost. This would increase
the company’s profit level.
Conclusions
The literature review demonstrated that Six Sigma DMAIC approach could reduce an
organizations operational cost. It showed that organizations can benefit from successful Six
49
Sigma projects. Linear programming can help an organization determine the optimized capacity
planning and resource scheduling. The literature review also showed the challenges and
opportunities that Chinese transportation providers are facing.
A goal of this study was to focus on providing a truck scheduling tool that ABC
Transportation Company could use to reduce the shipping cost. This goal was accomplished
through Six Sigma DMAIC approach. The key cost variables and their probability distributions
were identified in the analyze phase. Linear programming was used in the improvement phase to
minimize the total cost.
The findings in this study correlate to the literature review. For ABC transportation
Company, there would be a significant cost savings with the use of linear programming
scheduling tool.
Recommendations
Based from the results of this study, the following recommendations are being made for
ABC Transportation Company. First, the company should start using the new scheduling tool
from this research project. This new tool will help the company reduce the shipping cost.
Next, it is being recommended that ABC Transportation Company overload the trucks from
rental companies to their full overload weight limit. The linear programming output showed that
the overload weights for rental trucks equaled their overload limit. It is believed that this
strategy will reduce the risks of high overload fines, high late delivery penalties and high fuel
costs to the rental company. As part of this study, it is also recommended that ABC needs to
negotiate with the rental companies for a fixed price rental agreement to avoid rental cost
increases. Third, ABC should keep updating the linear programming model with the most current
50
shipping cost records. It is recommended that ABC update the probability distributions of key
cost variables so the linear programming model would reflect the current road situation.
Finally, a future recommendation would be for ABC transportation Company to
continually apply the Six Sigma approach to search for additional opportunities to reduce the
shipping cost and improve their operation effectiveness.
Opportunities for Future Research
In the research project, ABC Transportation Company used linear programming model as
a truck scheduling tool to determine the overloaded weight of each truck. The results of the pilot
test showed that this could reduce the shipping cost for ABC significantly. There are future
research opportunities that linear programming model could help ABC improve its operation.
Figure 14 shows the future research project opportunities that ABC Transportation
Company may use to improve its operation.
Figure 14. The Relationship between the Current Study and Future Research Opportunities
First, the linear programming model in this study was built based on two sources, the key
cost variables from the Pareto analysis and the probability distributions of these key variables.
Third Level
Linear Programming Model Adding external cost variables to help ABC establish its business
strategic plan.
First (current) Level Linear Programming Model Focusing on truck overload scheduling to reduce ABC’s
shipping cost.
Second Level Linear Programming Model Adding other internal cost variables to reduce ABC’s
the total operation cost.
51
An additional study focusing on the key variable probability distributions may be needed. The
higher the accuracy of the probability distributions, the closer the linear programming model
reflects the actual operational situation. This will increase the confidence level of using the
linear programming outputs.
Secondly, this project only focused on using linear programming model as a truck
scheduling and capacity planning tool to determine the overload weight of each truck. It might
be worthwhile in the future research projects to evaluate ABC Transportation Company’s total
cost, which include other cost items such as purchasing trucks for the company, maintenance
cost for company owned trucks and salaries and benefits of company owned truck drivers. This
would allow the linear programming model to represent the company’s operational costs more
accurately.
Thirdly, a future study might be conducted to evaluate ABC Transportation Company’s
business model. The literature review indicated that the competition of the Chinese truck
transportation service market is getting stronger. ABC should perform a strengths, weakness,
opportunities and threats (SWOT) analysis and reevaluate their business model to determine if
they need to change their strategic plan to become a marketing company and outsource the truck
shipping services. A linear programming model could be used in this type of evaluation. The
external factors that impact the operational costs could be used in building the linear
programming model. The output of the linear programming model would help the management
team figure out what business model will bring the most financial benefit to the company.
Another research opportunity could be the deeper evaluation of the linear programming
outputs. Future researchers may use linear programming sensitivity analysis to evaluate different
what-if truck scheduling situations in the linear programming outputs. However, in order to
52
perform this type of evaluations, more powerful linear programming software such as LINGO®
will be needed for this type of analysis.
53
References
American Society for Quality. (2013). Six Sigma learning resources & information. Retrieved
from http://www.asq.org/learn-about-quality/six-sigma/overview/overview.html
Balbirer, S., & Shaw, D. (1981). Application of linear programming to bank financial planning.
Journal on the Practice of Operations Research, 11(5), 77-83.
Bobek, A., Imondi, C., Shott, T., & Toobaei, M. (2012). Heterogeneous project scheduling for
optimal Six-Sigma cost reduction using linear programing. Technology Management for
Emerging Technologies (PICMET), 2012 Proceedings of PICMET '12, 35-42. Retrieved
from http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6304257&url=http %3A
%2F%2Fieeexplore.ieee.org%2Fiel5%2F6296788%2F6304012%2F06304257.pdf%3Far
number%3D6304257
Breyfoggle III, F. W. (2003). Implementing Six Sigma – Smarter solutions using statistical
methods. Hoboken, NJ: John Wiley & Sons.
Chen, Z (2012). Inspection result shows 100% trucks were overloaded. Retrieved from
http://news.dayoo.com/guangzhou/201008/12/73437_13564655.htm
articles/2011/01/02/gdp_a_brief_history#sthash.1tF4JHfh.dpbs
Eckes, G. (2003). Six Sigma for everyone. Hoboken, NJ: John Wiley & Sons, Inc.
Evans, J., & Lindsay, W. (2010). Managing for quality and performance excellence.
Independence, KY: South-Western Cengage Learning.
Go Lean Six Sigma. (2013). DMAIC – The 5 phases of lean Six Sigma. Retrieved from
Guangdong Bureau of Statistics of China. (2013). The new registration transportation company
data. Retrieved from http://www.gdstats.gov.cn/tjgb/default.htm
He, Y., Tang, X., & Chang, W. (2010). Technical decomposition approach of critical to quality
characteristics for product design for Six Sigma. Quality & Reliability Engineering
International, 26(4), 325-339.
Harry, M. (1998). Six Sigma: A breakthrough strategy for profitability. Quality Progress, 31(2),
60-64.
Hahn, H., & Hill, W. (1999). The impact of six sigma improvement: A glimpse into the future of
statistics. The American Statistician, 53(2), 208-215.
Montgomery, D. C. (2009). Introduction to statistical quality control. Hoboken, NJ: John Wiley
& Sons.
Moore, J., & Weatherford, L. (2001). Decision modeling with Microsoft Excel. Upper Saddle
River, NJ: Prentice Hall.
National Bureau of Statistics of China. (2013a). Chinese GDP historical data. Retrieved from
http://www.stats.gov.cn/was5/web/search?channelid=288041&andsen=GDP
National Bureau of Statistics of China. (2013b). Chinese GDP historical data. Retrieved from
http://data.stats.gov.cn/search/keywordlist2;jsessionid=7AC6D61E4F733BDEEAC898F
E1B06E958?keyword=GDP
from http://www.ndrc.gov.cn/hgjj/t20090114_256217.htm
Pande, P., Roland, N., & Cavanagh, R. (2000). The Six Sigma way: How GE, Motorola, and
other top companies are honing their performance. Hoboken, NJ: McGraw-Hill.
55
http://www.isixsigma.com/new-to-six-sigma/
http://www.chinanews.com/estate/2011/08-09/3245733.shtml
Sahoo, P., Dash, R., & Nataraj, G. (2010). Infrastructure development and economic growth in
China, IDE Discussion Paper, 261, 68-70.
Snee, R. D. (1999). Why should statisticians pay attention to Six Sigma? Quality Progress,
32(9), 100.
Wei, X. (2012). Drivers purchase “Monthly Pass” for overloaded trucks. Retrieved from
ABC Transportation Company 2012 Shipping Cost Summary
Extra Rental Cost, Overload Fine, Extra Fuel Cost and Late Delivery Penalty in 2012
Month
Jan-12 99,658 16,070 70,616 11,380 57,100 9,200 51,446 8,290
Feb-12 103,688 16,720 68,672 11,070 56,854 9,170 51,464 8,300
Mar-12 99,903 16,110 70,040 11,290 56,824 9,160 52,869 8,520
Apr-12 99,400 16,030 71,045 11,460 62,480 10,080 51,100 8,240
May-12 103,084 16,620 69,401 11,190 56,280 9,070 51,711 8,340
Jun-12 101,895 16,430 69,901 11,270 56,754 9,150 51,066 8,230
Jul-12 102,004 16,450 68,807 11,090 57,049 9,200 51,756 8,340
Aug-12 102,995 16,610 68,861 11,100 57,720 9,300 51,330 8,270
Sep-12 101,913 16,430 70,183 11,310 58,243 9,390 52,085 8,400
Oct-12 100,656 16,230 70,868 11,430 58,509 9,430 51,870 8,360
Nov-12 99,896 16,110 71,137 11,470 57,951 9,340 52,131 8,400
Dec-12 102,404 16,510 70,564 11,380 56,778 9,150 52,155 8,410
Total 1,217,496 196,370 840,095 135,490 692,542 111,700 620,983 100,150
Extra Rental Overload Fine Extra Fuel Cost Late Penalty
List of Figures
Chapter I: Introduction
Statement of the Problem
ABC experienced a high number of late deliveries, unbalanced truckloads, and increased use of rental trucks from other transportation service providers. This reduced the company's profits.
Purpose of the Study
Assumptions of the Study
Limitations of the Study
Chapter II: Literature Review
ABC Transportation Company experienced operational efficiency problems, which has led to higher costs, late deliveries and poor truck utilization. The company wanted to utilize a Six Sigma approach to reduce their operational costs and to increase the...
Six Sigma is “A business improvement approach that seeks to find and eliminate causes of mistakes or defects in business processes by focusing on outputs that are of critical importance to customers” (Snee, 1999, p. 100).
The American Society for Quality (2013) defines Six Sigma as:
a fact-based, data-driven philosophy of quality improvement that values defect prevention over defect detection. It drives customer satisfaction and bottom-line results by reducing variation and waste, thereby promoting a competitive advantage. It app...
Six Sigma is a well-defined process that focuses on problem solving which maximized the return on a company’s investments. Six Sigma was developed by Motorola in the 1980’s to improve manufacturing processes quality and to enhance customer satisfactio...
DMAIC Methodology
Six Sigma uses Define, Measure, Analyze, Improve and Control (DMAIC) methodology to solve problems (Hahn & Hill, 1999).
Figure 1. Cause and Effect Matrix Example (Retrieved from Breyfoggle, 2003)
DMAIC Methodology and Continues Improvement
Figure 2. DMAIC Six Sigma Improvement Methodology
Figure 3. Chinese GDP Annual Growth Rate from 2008 to 2012 (National Bureau of Statistics of China, 2013b)
Truck Transportation Operation in China
Chapter III: Methodology
ABC Transportation Company experienced a high number of late deliveries, unbalanced truckloads, and increased use of rental trucks from other transportation service providers. This reduced the company's profits. The objective of this study was to us...
Data Collection
The shipping cost records were collected for 2012. The cost records included shipping destination, date shipment requirement received, delivery date, total overload weight and total cost. The cost records were entered into an MS Excel file. An iden...
Table 2
The second type of shipping cost records were the shipping costs for the rental trucks. An example of rental truck shipping costs is shown in Table 3.
Table 3
Data Verification
Data Analysis – Determine the Probability Distributions of Cost Items
Chapter IV: Results
Results of Data Verification
There were total of 816 truck cost records collected for this study. According to MIL-STD-105E standard Sample Size Code Letter table showed in Chapter III Figure 5, the sampling plan letter code was letter K. The total number of samples needs to b...
Results of Pareto Analysis
Pareto analysis was used to identify the key cost items that affected the total truck cost. These variables were programmed into the linear programming model.
The input cost items for the Pareto analysis were, extra fuel cost caused by overloaded trucks, overload fines, late delivery penalties, extra cost of rental trucks and extra toll costs caused by overload. The cost items of 816 shipping records were ...
Figure 10. Pareto Analysis Results for Key Cost Items
Chapter V: Discussion
Results
There were 816 shipping cost records in 2012. The data verification results showed that these records were accurate and could be used in this research project.
The results of Pareto analysis showed that there were four cost items that had significant contributions to the total shipping cost. These four key cost items included extra rental cost, extra fuel cost, overload fine and later delivery penalties. Th...
The linear programming objective function took into account the above key cost items and probability distributions and summed them for the total shipping cost. The goal of this research was to find a scheduling tool to reduce the shipping cost. In ...
The linear programming model was solved by MS Excel Solver. In order to test if the outcome of the linear programming model could help ABC Transportation Company reduce its shipping cost, a one month pilot test was conducted. The shipping costs wer...
The pilot test results indicated that the linear programming model could help the ABC Transportation better schedule its truck capacity to reduce shipping cost. This would increase the company’s profit level.
Conclusions
The literature review demonstrated that Six Sigma DMAIC approach could reduce an organizations operational cost. It showed that organizations can benefit from successful Six Sigma projects. Linear programming can help an organization determine the o...
A goal of this study was to focus on providing a truck scheduling tool that ABC Transportation Company could use to reduce the shipping cost. This goal was accomplished through Six Sigma DMAIC approach. The key cost variables and their probability ...
The findings in this study correlate to the literature review. For ABC transportation Company, there would be a significant cost savings with the use of linear programming scheduling tool.
Recommendations