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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
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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
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 4-4
Manufacturer Storage with Direct Shipping (Fig. 4.6)
Manufacturer
Retailer
Customers
Product Flow
Information Flow
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In-Transit Merge Network (Fig. 4.7)
Factories
Retailer
Product Flow
Information Flow
In-Transit Merge by Carrier
Customers
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Distributor Storage with Carrier Delivery (Fig. 4.8)
Factories
Customers
Product Flow Information Flow
Warehouse Storage by Distributor/Retailer
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Distributor Storage with Last Mile Delivery (Fig. 4.9)
Factories
Customers
Product Flow
Information Flow
Distributor/Retailer Warehouse
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Manufacturer or Distributor Storage with Customer Pickup (Fig. 4.10)
Factories
Retailer
Pickup Sites
Product Flow Information Flow
Cross Dock DC
Customer Flow
Customers
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 4-9
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
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 4-11
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!
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
4-12
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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?
4-13
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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
4-14
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Distance Measures – Euclidean
X
Y
PerthSydney
(x1 , y1 ) (x2 , y2 )
Distance from Perth to Sydney by plane
( ) ( )2122
1212 yyxxD −+−=
4-15
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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 )
4-16
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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?
4-17
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Rectilinear Distance
It is also called “Manhattan Distance”
Rectilinear distance is commonly used to measure movement inside warehouses
4-18
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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
4-19
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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
Dallas, TX Gainesville, GA Tacoma, WA
Lakeland, FL Denver, CO
Nine 1.04
Summit, NJ Alhambra, CA Chicago, IL
Dallas, TX Gainesville, GA Tacoma, WA
Lakeland, FL Denver, CO Oakland, CA
Ten 1.04
Summit, NJ Alhambra, CA Chicago, IL
Dallas, TX Gainesville, GA Tacoma, WA
Lakeland, FL Denver, CO Oakland, CA
Mansfield, OH
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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?
4-24
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
4-25
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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
4-26
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
4-27
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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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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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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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Y
25 60 100 35 85 125
½ Total Weight = 430/2 = 215
Therefore, X = 6
Also evaluate in the reverse direction!
4-31
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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
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125 210 310
345
370
430
From the bottom-up
Therefore, Y = 2
Solution does not change for top-down!
4-32
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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)
4-33
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
MiniMax Objective, Rectilinear Distance
( )ii yYxXMin −+−=max Z
P1
P2
P3
P4 P5
P6
P7
P8 P9 We will discuss a Linear Programming Algorithm
4-34
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Linear programming for Rectilinear MiniMax
( )ii yYxXMinimize −+−=max Z
Ω= ZMinimize
Subject to:
ii yYxX −+−≥Ω
Two ways to open each absolute value
4-35
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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 −−=
4-36
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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 −+−=
4-37
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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4-38
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
4-39
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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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
4-41
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 4-42
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
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
4-43
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