Monitoring delivery chains in a supply chain
using multivariate control charts
Alireza Faraz and Cédric Heuchenne
Quantom Department, HEC Management School, University of
Liège, Belgium.
Erwin Saniga
Department of Business Administration, University of Delaware,
Delaware, USA.
Earnest Foster
Department of Business Administration, Penn State University,
Pennsylvania, USA
Supply Chain Management
Supply chain management (SCM) includes all activities required to provide the
final customers with quick, reliable, high quality and economic services and/or
products.
All activities related to the delivery of products to customers in a supply chain are
included in delivery chains.
Delivery chains, as the final link in supply chains, play an important role in business
Quality and Delivery chains
Customer's voice in recent years has caused organizations strive to register the
quality of their products as a commercial advertisement in customers’ mind.
Quality before: meeting the design standards.
Quality Today: Good Performance and
Reliability Lower price, lower maintenance
costs, good aftersales services and even ontime deliveries are associated with the term of
quality.
Objective: Developing a scheme to help
companies provide the customers with the
better processes of timely and uninterrupted
delivery of goods and services.
Example:
pizza shop A
Badge: delicious and excellent pizzas made of the
high quality crops, but unusual delivery times.
VS
pizza shop B
Badge: Hate Late. On time deliveries,
but good not excellent pizzas .
What is a delivery chain?
A delivery chain is represented by a network of delivery links.
Network links corresponding to transportation segments, say
Delivery Segments:
Depot to truck,
truck to truck,
truck to rail,
rail to rail switching,
Delivery Actions:
Loading
transporting
Unloading
Obligatory waiting times
…
Monitoring delivery chains in a supply chain
The usefulness of control charts is that management can distinguish common cause
variation from special cause variation and therefore avoid unnecessary “fire fighting”
of variation inherent to the system.
A study has shown that supply chain
managers can over-react to random
variations in logistics data (Lurie and
Swaminathan, 2009).
The consequences of over-reaction
(Deming , 1986): increased management
costs and increased variability.
State of Art
Improving the supply chain efficiency by quality management:
Forker et al (1997), Kuei et al (2001), Trent (2001), Flynn and Flynn (2005) and
Matthews (2006)
The importance of using control charts to the supply chain of Motorola and
Rolle Royce companies: Ramos et al (2007)
Research Highlights:
 Using control charts for monitoring Delivery chains has not been addressed
in the literature.
 Generally there are several production and delivery sites and a variety of
different methods of transportation of goods and services which complicated
the task. We propose to consider delivery chains as a multivariate process.
 we emphasis on applying economic solutions which reduce the operational
costs and improve the customer satisfaction.
Forming Delivery Chains to a
Multivariate Process
First a DC is developed after optimizing an OR
model which minimizes delivery costs while
considering the some constraints like: customer
demands, production and delivery capacities,
number of available trucks and …. .
The delivery times can be represented by a
vector, in which each component represents a
delivery elapsed time from the origin to
customers.
For example the total elapsed time to deliver
goods from production site 1 to customers’
location 1 includes O1A, AB, BC and CD1
branches in which the four segment times add up
to form the total delivery time.
Forming Delivery Chains to a Multivariate Process
The Model assumptions
Monitoring delivery chains in a supply chain by multivariate control charts
Monitoring a delivery processes usually follows four steps:
1.
2.
3.
4.
In control period,
Out of control period,
Time to take a sample and interpret the results,
Time to find and repair an assignable cause.
ATC
AATS

Average time of a Cycle:
In control Time
Since assignable causes follow a Poisson distribution, the expected in control time is
1

The expected time of occurrence within the interval
Given the occurrence of the assignable cause between the jth and (j+1)th
amples:
( j 1) h
 
 t

(
t

jh
)
e
dt

jh
( j 1) h
 t

e
dt

jh
1  (1  h)e h

 (1  e h )
AATS
The expected time until an out of control signal is triggered, which is given by:
h
AATS 

1 
Time to Take (j+n) th Sample and Interpret Results
It is assumed that the time is proportional to the sample size and has a
proportionality constant E.
Time to find the assignable cause
The time to find and repair the assignable cause is constant, here denoted
by T .
Calculating Cycle Cost
C0 = Cost of delays per hour while the process is in control,
C1 = Cost of delays per hour while the process is out of control,
S = cost of sampling
Y= Cost of finding an assignable cause,
W= Cost of investigating a false alarm.
Expected False Alarms

  i[e
i 0
 ih
e
  ( i 1) h
e  h
] 

h
(1  e )
The expected cost per cycle is:
In control
Delay cost per hour
Out of control
Delay cost per hour
E[C ] 
1
C0 ( )  C1 ( AATS  E  T )

 e h
E[T ]
Y  W
S
h
(1  e )
h
Cost of finding an assignable cause, Cost of investigating a false alarm.
E[T ] 
1

 AATS  E  T
sampling Cost
Due to the renewal reward assumption, the expected delay cost per hour is E[A] =
E[C]/ E[T]
E ( A)  the expected cost per hour =
h
1  (1   h)e   h
 C1 (

 E T)
h

1 
 (1  e )

h
1 1  (1   h)e
h


E

T
h

 (1  e )
1 
C0
 e h 
S 1 1  (1   h)e   h
h
W


Y


(


E

T)
h 
h
h 
 (1  e )
1 
 1 e 
1 1  (1   h)e   h
h


E

T
h

 (1  e )
1 
Where
min E ( A)
s.t :
  0.005
k 0
h  0.5(0.5)7
E = The expected time to plot and chart the sample, T= The expected time to
discover and repair the assignable cause, C0 and C1 = the cost of delivery delays
while the process is in control and out of control, respectively. W = the cost of
investigating false alarms, Y = the cost of locating and repairing an assignable
cause and S = the sampling and testing cost.
Genetic Algorithm:
A Case Study: TNT & Tabarok Industrial Group (TIG)
Monitoring delivery chains in a supply chain by multivariate control charts
The most important goods: Saffron, Pistachio, Olive, Date, Compotes, Conserves,
Juices, French, Ketchup and Mayonnaise sauces , Oil, Onion, Potato, Corns, Rice,
Tea and three years durable Tomato paste with 1000 tones capacity in a day.
 There are two depots
wholesalers customers.
and
three
 After crossing the local routes with
trucks (DAS 1 and 2), the products are
transited to Tehran (DAS 3) and then to
Tabriz (DAS 4) by trains. The goods are
then delivered to three customers
located in Urmia , Mahabad and Tabriz
by trucks (DAS 5, 6 and 7).
 The goods are then distributed to more
than 5400 retail stores.
The TNT delivery chain with its elapsed time variables
The data collection system
Monitoring delivery chains in a supply chain by multivariate control charts
;
The in-control delivery process mean vector and covariance matrix are
unknown and so are estimated as follows by latest 60 initial samples (m = 60)
when the deliveries were satisfactory.
52 
50 
 
 49 
ˆμ 0   
51 
 49 
 
 48 
 2.98 2.52 1.63 4.45 3.88 2.72 


2.37
4.18
3.73
1.85
2.31



2.13 3.38 2.68 1.98 
ˆ


2.10
2.15
3.41



1.72 4.06 


2.21


Monitoring delivery chains in a supply chain by multivariate control charts
This benefit is achieved only by establishing an ESD T2 control scheme on the delivery
process
Advantages of the monitoring delivery :
1- When the control chart indicates that unacceptable delays have occurred,
the manager may implement previously constructed re-routing plans that may
involve temporarily using alternate rail and truck segments to reduce delays.
2-The logistics manager will not over-react to the long shipment times while
they do not exceed control limits. This will avoid costs associated with expediting
the orders and increasing variability due to over-correction.
3-The resulting statistically stable delivery process decreases inventory holding
costs and to provide customers with statistically determined delivery standards.
Future Application:
Company: The GM North America
Deliveries chain: Transporting vehicles
form Detroit Michigan to the Texas and
Pennsylvania destinations.
DASs: They all begin and end with truck
transportation
modes
and
have
rail
transportation modes in the middle.
Colleagues:
Prof. Cédric Heuchenne
HEC Management School, University of Liège,
Belgium.
DANNA JOHNSON Prof. Erwin Saniga
Department of Business Administration, University
of Delaware, USA.
Prof. Earnest Foster
Department of Business Administration, Penn State
University, USA
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References:
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