Chapter 7: Transportation Models
description
Transcript of Chapter 7: Transportation Models
![Page 1: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/1.jpg)
Chapter 7: Transportation Models
Skip Ship Routing & Scheduling (pp. 212-214)
• Service Selection
• Shortest Path
• Transportation Problem
• Vehicle Routing & Scheduling
– One route: TSP
– Multiple routes: VRP
• Consolidation
![Page 2: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/2.jpg)
Service Selection (Mode Selection)
• Most important factors:– Dependability (on-time delivery).
– Cost.
– Safety.
– Tracking.
• Different modes have different costs and characteristics.
• Lowest transportation cost is not always best.
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Service Selection Tradeoff
• Transportation Cost vs. Inventory Cost.
• Shorter transit time: Higher transportation cost.
Fewer days held Lower inventory cost.
• Usually, Shorter transit time Smaller vehicles. More frequent trips Higher transportation cost.
Fewer units held Lower inventory cost .
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Service Selection for Competing Suppliers
One buyer purchases 1000 cwt from each of two competing suppliers: A and B. Both use rail transport, but could use truck transport. Supplier profit = $20/cwt - transport cost.
Transport Cost Delivery TimeRail $2/cwt 6 daysTruck $5/cwt 3 days
Buyer offers to switch 100 cwt to supplier A from B for each day decrease in delivery time. For supplier A:
Sales ProfitRail (current) 1000 cwt 1000 cwt ($20/cwt - $2/cwt) = $18,000
Truck 1300 cwt 1300 cwt ($20/cwt - $5/cwt) = $19,500
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Service Selection for Competing Suppliers
What if supplier B also switches to truck?
Buyer should give each equal business:
Sales ProfitSupplier A 1000 cwt 1000 cwt ($20/cwt - $5/cwt) = $15,000
Supplier B 1000 cwt 1000 cwt ($20/cwt - $5/cwt) = $15,000
So both suppliers are worse off than before! ($15,000 profit vs. $18,000 using rail)
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Shortest Path Model
• Network includes:– Nodes: cities, customers, demand points
– Arcs or Links: Transportation links
– Number for each link to represent travel cost, time or distance.
A F
D
B
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C
3
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9
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Shortest Path Problem
• Given:– A network with a specified origin and destination.– The distance (or travel time or cost) for each link.
• Determine the shortest path from the origin to the destination.
• Solution: Labeling algorithm (one of many)– Nodes are labeled as "solved" or "unsolved". – Solved = shortest path from the origin to that node is
known.
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Shortest Path Labeling Algorithm
1. The origin is a solved node. All others are unsolved.
2. For each solved node, find the one unsolved node that is nearest and calculate the minimum total distance (origin to solved node + solved node to nearest unsolved node).
3. Make the unsolved node with the smallest total distance a solved node.
4. Repeat steps 2 and 3 until the destination is a solved node.
5. Trace the shortest path.
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Shortest Path Example 1
A F
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B
EC
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• Find the shortest path from A to F.
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20
A F
D
B
EC
30
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518
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C
A F
D
B
EC
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A C
A F
D
B
EC
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 C
A F
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B
EC
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 C D 26
A F
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EC
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26
A F
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EC
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A B C
A F
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B
EC
30
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B C
A F
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B
EC
30
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*
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C
A F
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B
EC
30
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*
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C D 26
A F
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EC
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518
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1612*
*
*
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Shortest Path Example 1
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C D 26 D 26 C-D
A F
D
B
EC
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*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B C D
A F
D
B
EC
30
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*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 D E 31
A F
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EC
30
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*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31
A F
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EC
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1612*
*
*
*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B D E
A F
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B
EC
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1612*
*
*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 E F 47
A F
D
B
EC
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1612*
*
*
*
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 F 44 D-F E F 47
A F
D
B
EC
30
20
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6
17 10
518
27
1612*
*
*
*
* *
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Trace Shortest Path Backwards
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 F 44 D-F E F 47
A-C-D-F
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Check Answer
A F
D
B
EC
30
20
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6
17 10
518
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1612
A-C-D-F Length = 20+6+18 = 44
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Shortest Path Example 2
• Find the shortest path from A to K.
A K
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B
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A K
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C
0
![Page 31: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/31.jpg)
A K
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A C
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8
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![Page 33: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/33.jpg)
A K
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B C
0
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![Page 34: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/34.jpg)
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B C E
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 15 C F 10 E H 9 H 9 E-H
0
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path B C E H
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path B D 15 C F 10 F 10 C-F E I 14 H D 12
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B C E H F
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B D 15 C I 15 E I 14 H D 12 D 12 H-D F I 14
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path C E H F D
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path C I 15 E I 14 H K 14 K 14 H-K
F I 14 D J 15
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Shortest Length = 14
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Trace Shortest Path Backwards
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B D 15 C I 15 E I 14 H D 12 D 12 H-D F I 14 C I 15 E I 14 H K 14 K 14 H-K
F I 14 D J 15
![Page 44: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/44.jpg)
Trace Shortest Path Backwards
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 15 C F 10 E H 9 H 9 E-H
A-C-E-H-K
![Page 45: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/45.jpg)
Check Answer
A-C-E-H-K Length = 4+4+1+5 = 14
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Shortest Path Example 3
• Find the shortest path from A to K.
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![Page 47: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/47.jpg)
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E
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First 3 steps are same as Example 2!
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B C E
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 13 C I 14 E H 13
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Tie for minimum distance
Select both!
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 13 D 13 B-D C I 14 E H 13 H 13 E-H
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D G
JF
I12
16
8
5
4
4
Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path C D E H
0
4
6
8
13
13
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A K
H
E4
63
16
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B
C
D G
JF
I12
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path C I 14 D G 29 E I 14 H K 25
0
4
6
8
13
13
Tie for minimum distance
Select both!
![Page 53: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/53.jpg)
A K
H
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16
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B
C
D G
JF
I12
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Nearest Total MinimumSolved Unsolved Distance Nearest Distance Path C I 14 I 14 C-I D G 29 E I 14 I 14 E-I H K 25
0
4
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8
13
13
There are two equal shortest paths from the origin to I!
![Page 54: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/54.jpg)
Example 3 Answer
A-C-E-I-F-J-K
A-C-I-F-J-K
Length = 4+4+6+4+5+1 = 24
Length = 4+10+4+5+1 = 24
A K
H
E4
63
16
7
5
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12
10
B
C
D G
JF
I12
16
8
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4
4
![Page 55: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/55.jpg)
Shortest Path Software in LogWare
• ROUTE module.
• For each node, enter:– Node number and name.
– X and Y coordinates if desired.
• For each link (arc), enter:– “From node” number.
– “To node” number.
– Cost.
– Save data.
• Click Solve to get shortest paths from node 1 to all other nodes.
![Page 56: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/56.jpg)
LogWare
![Page 57: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/57.jpg)
ROUTE Module in LogWare
Otherwise, click “Open file” and open Rfl01.dat.
If possible, click “Add row”; then enter data.
![Page 58: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/58.jpg)
ROUTE Module: Edit as desired
Now, Delete and Add rows and edit data.
Save before solving.
![Page 59: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/59.jpg)
ROUTE Module: Solution
![Page 60: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/60.jpg)
Transportation Problem
• Given:– m origins (sources for product flows). – n destinations (sinks for product flows).– Supply at each origin.– Demand at each destination.– Shipping cost per unit of product from each origin to
each destination.
• Determine the minimum total cost shipping pattern to satisfy demand. – We will solve using TRANLP module of LogWare.
![Page 61: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/61.jpg)
Transportation Problem Example
• 3 origins (sources) and 4 destinations (sinks)
Origin Supply Destination Demand
1 300 cwt. 1 400 cwt.
2 900 cwt. 2 300 cwt.
3 800 cwt. 3 700 cwt.
4 600 cwt.
Shipping
cost ($/cwt): D1 D2 D3 D4
O1 3 3 4 2
O2 2 4 3 7
O3 2 5 1 5
![Page 62: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/62.jpg)
Transportation Problem Example
• 3 origins (sources) and 4 destinations (sinks)
300 O1
D4 600
D3 700
D2 300
D1 4003
342
24
37
5
152
800 O3
900 O2
![Page 63: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/63.jpg)
Transportation Problem Example
• A feasible solution: flows are in blue.
300 O1
D4 600
D3 700
D2 300
D1 4003
342
24
37
5
152
800 O3
900 O2
300
100
300
500
200
600
Cost = 300x3+100x2+300x4+500x3+200x5+600x5 = 7500
![Page 64: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/64.jpg)
Solving Transportation Problems
• Place data in Transportation Matrix.
From/To T1 T2 T3 T4 Supply
F1 3 3 4 2 300
F2 2 4 3 7 900
F3 2 5 1 5 800
Demand 400 300 700 600
Enter data into TRANLP and solve.
1.Open a file.
2. Change Problem label and specify number of rows and columns.
3. Enter data (use Backspace to erase entries).
4. Save data.
5. Click Solve.
![Page 65: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/65.jpg)
TRANLP in LogWare
If possible, enter “No. of rows” and “No. of columns”.
If not, then click “Open file” and open TRAN01.dat.
![Page 66: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/66.jpg)
File TRAN01.dat
Now, enter “No. of rows” and “No. of columns”.
Then, edit data.
Save before solving.
![Page 67: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/67.jpg)
TRAN01.dat Solution
Solution.
Click “Report” for more...
![Page 68: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/68.jpg)
TRANLP OutputProblem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 1,400.00 200 Totals 3,400.00 900 Source capacity = 900 Slack capacity = 0
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 2,000 Slack required = 2,000Total cost = 5,200.00
![Page 69: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/69.jpg)
TRANLP OutputProblem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 1,400.00 200 Totals 3,400.00 900 Source capacity = 900 Slack capacity = 0
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 2,000 Slack required = 2,000Total cost = 5,200.00
Optimal Cost
Optimal flows
![Page 70: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/70.jpg)
Optimal Solution
• Optimal solution: flows are in blue.
300 O1
D4 600
D3 700
D2 300
D1 4003
342
24
37
5
152
800 O3
900 O2
300
400
300
200700
100
Cost = 300x2+400x2+300x4+200x7+700x1+100x5 = 5200
![Page 71: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/71.jpg)
TRANLP OutputProblem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 1,400.00 200 Totals 3,400.00 900 Source capacity = 900 Slack capacity = 0
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 2,000 Slack required = 2,000Total cost = 5,200.00
slack capacity=0 means all is sent from every source
Total allocated = Slack required means each destination receives what it needs.
![Page 72: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/72.jpg)
Transportation Problem
• In last problem total supply = total demand.– Each origin sends all it has.– Each destination receives all it demands.
• Other possibilities:– Total Supply > Total Demand
• Some origins will keep some of the supply.
– Total Supply < Total Demand
• Some destinations will not receive all they demand.
![Page 73: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/73.jpg)
TRANLP Output #2Problem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 .00 0 Totals 2,000.00 700 Source capacity = 900 Slack capacity = 200
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 1,800 Slack required = 1,800Total cost = 3,800.00
What is happening here?
![Page 74: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/74.jpg)
TRANLP Output #2Problem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 .00 0 Totals 2,000.00 700 Source capacity = 900 Slack capacity = 200
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 1,800 Slack required = 1,800Total cost = 3,800.00
Total allocated = Slack required means each destination receives what it needs.
Supply > Demand
slack capacity=200 means 200 is left at origin 2
![Page 75: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/75.jpg)
TRANLP Output #3Problem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 1,400.00 200 Totals 3,400.00 900 Source capacity = 900 Slack capacity = 0
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 2,000 Slack required = 2,200Total cost = 5,200.00
What is happening here?
![Page 76: Chapter 7: Transportation Models](https://reader036.fdocuments.in/reader036/viewer/2022081503/568159df550346895dc72b10/html5/thumbnails/76.jpg)
TRANLP Output #3Problem label: Example OPTIMUM SUPPLY SCHEDULE ----------- Cell ------------ Unit Cell Units Source name Sink name cost cost allocated F1 T1 3.00 .00 0 F1 T2 3.00 .00 0 F1 T3 4.00 .00 0 F1 T4 2.00 600.00 300 Totals 600.00 300 Source capacity = 300 Slack capacity = 0
F2 T1 2.00 800.00 400 F2 T2 4.00 1,200.00 300 F2 T3 3.00 .00 0 F2 T4 7.00 1,400.00 200 Totals 3,400.00 900 Source capacity = 900 Slack capacity = 0
F3 T1 2.00 .00 0 F3 T2 5.00 .00 0 F3 T3 1.00 700.00 700 F3 T4 5.00 500.00 100 Totals 1,200.00 800 Source capacity = 800 Slack capacity = 0
Total allocated = 2,000 Slack required = 2,200Total cost = 5,200.00
Total allocated < Slack required means some destination(s) did not receive what they need. Can not tell which one(s) without input data.
Supply < Demand