Alireza Faraz and Cédric HeuchenneAlireza Faraz and Cédric HeuchenneQuantom Department, HEC Management School, University of

Liège, Belgium.

Erwin SanigaErwin Saniga Department of Business Administration, University of Delaware,

Delaware, USA.

Earnest FosterEarnest Foster Department of Business Administration, Penn State University,

Pennsylvania, USA

Monitoring delivery chains Monitoring delivery chains in a supply chain using in a supply chain using

multivariate control charts multivariate control charts

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

Quality before: meeting the design standards.

Quality Today: Good Performance and Good Performance and Reliability Reliability Lower priceLower price, lower maintenance lower maintenance costscosts, good aftersales servicesgood aftersales services and even on-on-time deliveries time 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.

Customer's voice in recent years has caused organizations strive to register the quality of their products as a commercial advertisement in customers’ mind.

pizza shop BBadge: Hate Late. On time deliveries, but good not excellent pizzas .

pizza shop ABadge: delicious and excellent pizzas made of the high quality crops, but unusual delivery times.

VS

Example:

What is a delivery chain?

A delivery chain is represented by a network of delivery linksa network of delivery links. Network links corresponding to transportation segments, say Delivery Segments: Delivery Segments: Depot to truck, truck to truck, truck to rail, rail to rail switching,

Delivery Actions: Delivery Actions: LoadingtransportingUnloadingObligatory waiting times…

Monitoring delivery chains in a supply chain

The usefulness of control charts is that management can distinguish common cause management can distinguish common cause variation from special cause variation and therefore avoid unnecessary “fire fighting” variation from special cause variation and therefore avoid unnecessary “fire fighting” of variation inherent to the systemof 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.

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)

State of Art

Research Highlights:

Using control charts for monitoring Delivery chains has not been addressed has not been addressed in the literaturein 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 processconsider 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. In control period,2. Out of control period,

3. Time to take a sample and interpret the results,4. Time to find and repair an assignable cause.

AATSAATSATCATC

Average time of a Cycle:

1

In control TimeSince assignable causes follow a Poisson distribution, the expected in control time is

The expected time of occurrence within the interval Given the occurrence of the assignable cause between the jth and (j+1)th

samples:

)1(

)1(1)(

)1(

)1(

h

h

hj

jh

t

hj

jh

t

e

eh

dte

dtejht

The expected time until an out of control signal is triggered, which is given by:

AATS

1

hAATS

Time to Take (j+n) th Sample and Interpret ResultsIt is assumed that the time is proportional to the sample size and has a

proportionality constant E.

Time to find the assignable causeThe 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

( 1)

0

[ ](1 )

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hi

ei e e

e

0 1

[ ]

1( ) ( )

[ ]

(1 )

h

h

E C

C C AATS E T

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e h

The expected cost per cycle is:Out of control Delay cost per hourIn control

Delay cost per hour

Cost of finding an assignable cause, Cost of investigating a false alarm. sampling Cost

1[ ]E T AATS E T

01

( ) the expected cost per hour =

1 (1 )( )1 (1 )

1 1 (1 )(1 ) 1

1 1 (1 )( )

1 (1 ) 1

1 1 (1 )(1 ) 1

h

h

h

h

h h

h h

h

h

E A

C h h eC E T

eh e h

E Te

e S h e hW Y E T

e h e

h e hE T

e

WhereE = 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.

7)5.0(5.0

0

005.0

:.

)(min

h

k

ts

AE

Due to the renewal reward assumption, the expected delay cost per hour is E[A] = E[C]/ E[T]

Genetic Algorithm:

A Case Study: TNT & Tabarok Industrial Group TNT & Tabarok Industrial Group (TIG)(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 and three wholesalers customers.

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

0

52

50

49ˆ

51

49

48

μ

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 1.98ˆ2.10 2.15 3.41

1.72 4.06

2.21

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.

;

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

Savings: 1285 $

1285 $ daily = 154200$

154200$

annually.

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 AmericaDeliveries 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.

ColleaguesColleagues: Prof. Cédric HeuchenneProf. Cédric HeuchenneHEC Management School, University of Liège, Belgium. DANNA JOHNSON Prof. Erwin Saniga DANNA JOHNSON Prof. Erwin Saniga Department of Business Administration, University of Delaware, USA.

Prof. Earnest FosterProf. Earnest Foster Department of Business Administration, Penn State University, USA

Refe

rence

s:

• Forker LB, Mendez D, Hershauer JC. TQM in the SCM: what is its impact on performance? Int J Prod Res 1997; 14: 91-118.

• Kuei C, Madu CN. Identifying critical success factors for supply chain quality management. Asia Pacific Management Review 2001; 6:409-423.

• Trent R. Applying TQM to SCM. Supply Chain Management Review 2001; 70-78.• Flynn BB, Flynn EJ. Synergies between supply chain management and quality management:

emerging applications. Int J Prod Res 2005; 43:3421-3436.• Matthews C. Linking the SCM to TQM. Quality Progress 2006; 39:29-35.• Ramos JC, Asan SS, Majetic J. Benefits of applying quality management techniques to support

supply chain management. Int Logistic and Supply Chain Congress 2007; November 8-9, Istanbul, Turkey.

• Saniga EM. Economic statistical control chart designs with an application to X-and R charts. Technometrics 1989; 31:313–320.

• Sullivan JH, Woodal WH. A comparison of Multivariate Quality control charts for individual observations. Journal of Quality Technology 1995; 27.

• Lorenzen TJ and Vance LC. The economic design of control charts: a unified approach. Technometrics 1986; 28:3–11.

• Mason RL, Young JC. Multivariate statistical process control with industrial applications. ASASIAM, Philadelphia, PA 2002.