ihe890_040711

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

IHE 890 Engineering Supply Chain Systems

Instructor: Pratik J. Parikh, Ph.D.

April 7, 2011

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 4-2

Outline  Design Options for a Distribution Network

 E-Business and the Distribution Network

 Facility Location Models


Design Options for a Distribution Network

 Manufacturer Storage with Direct Shipping  Manufacturer Storage with Direct Shipping and In-

Transit Merge  Distributor Storage with Carrier Delivery  Distributor Storage with Last Mile Delivery  Manufacturer or Distributor Storage with Customer

Pickup  Retail Storage with Customer Pickup  Selecting a Distribution Network Design


Manufacturer Storage with Direct Shipping (Fig. 4.6)

Manufacturer

Retailer

Customers

Product Flow

Information Flow


In-Transit Merge Network (Fig. 4.7)

Factories

Retailer

Product Flow

Information Flow

In-Transit Merge by Carrier

Customers


Distributor Storage with Carrier Delivery (Fig. 4.8)

Factories

Customers

Product Flow Information Flow

Warehouse Storage by Distributor/Retailer


Distributor Storage with Last Mile Delivery (Fig. 4.9)

Factories

Customers

Product Flow

Information Flow

Distributor/Retailer Warehouse


Manufacturer or Distributor Storage with Customer Pickup (Fig. 4.10)

Factories

Retailer

Pickup Sites

Product Flow Information Flow

Cross Dock DC

Customer Flow

Customers


Comparative Performance of Delivery Network Designs (Table 4.7)

Information

Facility & Handling

Transportation

Inventory

Returnability

Order Visibility

Customer Experience

Product Availability

Product Variety

Response Time

Manufacturer storage with pickup

Distributor storage with last

mile delivery

Distributor Storage with Package

Carrier Delivery

Manufacturer Storage with In-Transit Merge

Manufacturer Storage with Direct

Shipping

Retail Storage with Customer

Pickup

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Performance of Delivery Networks for Different Product/Customer Characteristics (Table 4-8)

Low customer effort

High product variety

Quick desired response

High product value

Many product sources

Very low demand product

Low demand product

Medium demand product

High demand product

Manufacturer storage with

pickup

Distributor storage with last mile delivery

Distributor Storage with Package Carrier

Delivery

Manufacturer Storage with In-Transit Merge

Manufacturer Storage with

Direct Shipping

Retail Storage with

Customer Pickup

+2

+2

+2

+2

+2

+2

+2 +2 +2

+2

+1

+1

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+1

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+1

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+1

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-1 -1

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-2 -2

-2

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-2 -2

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E-Business and the Distribution Network

 Impact of E-Business on Customer Service  Impact of E-Business on Cost  Using E-Business: Dell, Amazon, Peapod, Grainger

 Self reading!


Where should we locate the DC? What factors are important?

 Geographical Feasibility   Population

–  Appropriate labor –  Support

 Regulations   Tax Incentives  Modes of Transportation  Competitor’s locations

 Customer locations   Supplier locations

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Remember this ….

 Models do not make decisions, people do   Start at the macro level and work down to the micro level

–  Continuous models (infinite number of possibilities with approx data) –  Discrete models (finite number of choices with exact data)

  Limiting assumptions: –  Distance surrogate to represent transportation cost –  Continuous model: can we really locate anywhere with similar fixed costs? –  Discrete model: how to pick sites? which factors are important?

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Facility Location Models

 Continuous, Single-Facility –  Mini-Sum Model – minimize the sum of the weighted distances –  Mini-Max Model – minimize the maximum distance

 Continuous, Multi-Facility –  Location-allocation problem

 Discrete, Single-Facility  Discrete, Multi-Facility

–  p-center and p-median

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Distance Measures – Euclidean

X

Y

PerthSydney

(x1 , y1 ) (x2 , y2 )

Distance from Perth to Sydney by plane

( ) ( )2122

1212 yyxxD −+−=

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Distance Measures – Rectilinear

!

" #

$

What if we are in a grocery store?

What is the shortest distance between A and B?

(x2 y2 )

(x1 y1 )

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Rectilinear Distance

!

" #

$

(x1 , y1 )

(x2 , y2 )

xABd

yABd

yAB

xABAB ddD +=

2121 yyxxDAB −+−=

Where else do we find this type of structure?

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Rectilinear Distance

It is also called “Manhattan Distance”

Rectilinear distance is commonly used to measure movement inside warehouses

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Distance Measures – Great Circle Distance

How would we calculate the fuel consumption of an ocean-bound vessel going from L.A. to Taipei? (You do not need to provide the equation, just the concept.)

Can we use any of the previously mentioned norms?

Geometry on the surface of a sphere Great Circle Distance

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Location Objectives

What are we trying to accomplish when we choose the location of a facility?

Are the objectives the same for different types of facilities?

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DC

Store

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 22

# WH LT (Days) 2006 BEST WAREHOUSE LOCATIONS (Source: Chicago Consulting)

One 2.28 Bloomington, IN

Two 1.48 Ashland, KY Palmdale, CA

Three 1.29 Allentown, PA Palmdale, CA McKenzie, TN

Four 1.20 Lancaster, PA Palmdale, CA Chicago, IL

Meridian, MS

Five 1.13 Summit, NJ Palmdale, CA Chicago, IL

Dallas, TX Macon, GA

Six 1.08 Summit, NJ Pasadena, CA Chicago, IL

Dallas, TX Macon, GA Tacoma, WA

Seven 1.07

Summit, NJ Pasadena, CA Chicago, IL

Dallas, TX Gainesville, GA Tacoma, WA

Lakeland, FL

Eight 1.05

Summit, NJ Pasadena, CA Chicago, IL


Lakeland, FL Denver, CO

Nine 1.04

Summit, NJ Alhambra, CA Chicago, IL


Lakeland, FL Denver, CO Oakland, CA

Ten 1.04

Summit, NJ Alhambra, CA Chicago, IL


Lakeland, FL Denver, CO Oakland, CA

Mansfield, OH


Cost-based objective

•  Fixed cost of the facility •  Operating cost (rental, equip, etc.) •  Transportation cost •  Labor cost •  Inventory cost •  and others

•  From a cost standpoint, we wish to minimize the sum of all these costs!

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Other objectives - minisum

Minimize the total cost of transportation

Minimize the sum of transportation costs to

all customers

Minisum Objective

Does demand matter?

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Or - minimax

What type of relationship with the users do we want here?

Is coverage a key word?

We would like to Minimize the maximum distance to any given customer

Minimax Objective

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What about “obnoxious” facilities? (Maximin)

Would you like to live close to these facilities?

Our objective now is to stay away

We would like to Maximize the minimum distance of any customer to the facility Maximin Objective

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Location algorithms pursue an objective under a certain way to measure distance

Minisum

Minimax

Euclidean Rectilinear

Center of gravity models

Coverage circle models

Linear Programming

Models

Median models

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Rectilinear MiniSum

Σ i

Min f(x,y)= wi (|X-xi| + |Y-yi|)

Σ i

f1(X)= wi |X-xi| Σ i

f2(Y)= wi |Y-yi| +

f(X,Y) = f1(X) + f2(Y)

The problem is entirely separable into two problems (X and Y)

Weight/pull of customer i --- may be demand!

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Algorithm - solve for X first Rectilinear Minisum

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X

Y

1. On each X coordinate of a customer, write the total weight

25 60 100 35 85 125

x y w3 10 605 2 1006 5 351 8 257 1 859 0 125

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Algorithm - solve for X first

2. Come from left to right and place on each line the accumulated weights

25 85 185 220 305 430

x y w3 10 605 2 1006 5 351 8 257 1 859 0 125

Rectilinear Minisum

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X

Y

25 60 100 35 85 125

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Algorithm - solve for X first

3. Where the accumulated weight reaches or surpasses half the total weight, stop! (optimal location)

x y w3 10 605 2 1006 5 351 8 257 1 859 0 125

25 85 185 220 305 430

Rectilinear Minisum

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X

Y

25 60 100 35 85 125

½ Total Weight = 430/2 = 215

Therefore, X = 6

Also evaluate in the reverse direction!

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Algorithm – now solve for Y Rectilinear Minisum

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Yx y w3 10 605 2 1006 5 351 8 257 1 859 0 125

125 85

100

35

25

60

125 210 310

345

370

430

From the bottom-up

Therefore, Y = 2

Solution does not change for top-down!

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Comments on the optimal solution

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Rectilinear MinisumThe optimal facility will always be on the X coordinate of an existing customer -- the same holds true for the Y coordinate

But it will not necessarily coincide with a customer

The median condition also holds (less than half of the customer demand lies to either side)

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MiniMax Objective, Rectilinear Distance

( )ii yYxXMin −+−=max Z

P1

P2

P3

P4 P5

P6

P7

P8 P9 We will discuss a Linear Programming Algorithm

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Linear programming for Rectilinear MiniMax

( )ii yYxXMinimize −+−=max Z

Ω= ZMinimize

Subject to:

ii yYxX −+−≥Ω

Two ways to open each absolute value

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LP-Based Algorithm LP model has special characteristics that allow for a simplified solution

1. Let’s find constants c1 to c5

{ } iyxc ii ∀+= ; min1

{ } iyxc ii ∀+= ; max2

{ } iyxc ii ∀+−= ; min3

{ } iyxc ii ∀+−= ; max4

{ }34125 ,max ccccc −−=

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LP-Based Algorithm

2. The objective function value is c5/2

( ) ( )53131*

1*1 ,

21 , cccccYX ++−=

25cZ =

3. The optimal solutions are located in the segment that goes from (X1*, Y1*) to (X2*, Y2*)

( ) ( )54242*

2*2 ,

21 , cccccYX −+−=

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Let’s try one

xi yiP1 0 1.8P2 5.7 3.6P3 6.7 8P4 8.5 1.6P5 8 0.8P6 3.6 9.8P7 9.5 8.5P8 9 0.5P9 5.2 0.5

P1

P2

P3

P4 P5

P6

P7

P8 P9 0

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Objective function value is …

xi yiP1 0 1.8P2 5.7 3.6P3 6.7 8P4 8.5 1.6P5 8 0.8P6 3.6 9.8P7 9.5 8.5P8 9 0.5P9 5.2 0.5

{ } iyxc ii ∀+= ; min1

{ } iyxc ii ∀+= ; max2

{ } iyxc ii ∀+−= ; min3

{ } iyxc ii ∀+−= ; max4

{ }34125 ,max ccccc −−=

= 0+1.8 = 1.8

= 9.5+8.5=18

= -9+0.5=-8.5

= 9.8-3.6=6.2

= 16.2

Minimax objective, z = c5/2 = 16.2/2 = 8.1

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Optimal locations are …

xi yiP1 0 1.8P2 5.7 3.6P3 6.7 8P4 8.5 1.6P5 8 0.8P6 3.6 9.8P7 9.5 8.5P8 9 0.5P9 5.2 0.5

( ) ( )53131*

1*1 ,

21 , cccccYX ++−=

( ) ( )54242*

2*2 ,

21 , cccccYX −+−=

P1

P2

P3

P4 P5

P6

P7

P8 P9 0

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6

8

10

2 4 6 8 10

= ½(10.3,9.5) = (5.15, 4.75)

= (5.9, 4) 4-40

Comments

P1

P2

P3

P4 P5

P6

P7

P8 P9 0

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2 4 6 8 10 •  What if there is a physical barrier at and around the optimal location?

•  Rectilinear paths through this area not feasible

•  Calculate the objective function at a few points around this area and pick the least cost solution

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Summary of Learning Objectives  What are the key factors to be considered when

designing the distribution network?  What are the strengths and weaknesses of various

distribution options?  MiniSum and MiniMax models for facility location


Con$nue LP Formula$on

Ω= ZMinimizeSubject to:

ii yYxX −+−≥Ω

Subject to:

ii yYxX −+−+≥Ω

ii yYxX −++−≥Ω

ii yYxX +−−+≥Ω

ii yYxX +−+−≥Ω

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ihe890_040711

Documents

p9 p1 p2

p5 p8 p4

distribution

c1 c3

total weight

xi

maximum distance

rectilinear