TransportationMode SelectionRoute Selection

Shortest Path Minimum Spanning Tree Transportation Assignment TSP Route Sequencing Tanker Scheduling

Mode SelectionShipRailTruckPlane

Fas ter

Cheaper

More V

ariable

Mode that minimizes Total CostTransportation CostInventory Costs

Source Pipeline Destination - including safety stock

CostsTransportation Cost

Cost per unit UnitsCost per unit

$CWT (based on origin destination freight weight)

$Time (leased dedicated transportation)

InventoryAt the plant

12 ldquocycle quantityrdquoAt the warehouse

12 ldquocycle quantityrdquo Safety stock depends on lead time variability

In the pipeline Annual Volume Days in Transit Days per year

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Mode SelectionShipRailTruckPlane

Fas ter

Cheaper

More V

ariable

Mode that minimizes Total CostTransportation CostInventory Costs

Source Pipeline Destination - including safety stock

CostsTransportation Cost

Cost per unit UnitsCost per unit

$CWT (based on origin destination freight weight)

$Time (leased dedicated transportation)

InventoryAt the plant

12 ldquocycle quantityrdquoAt the warehouse

12 ldquocycle quantityrdquo Safety stock depends on lead time variability

In the pipeline Annual Volume Days in Transit Days per year

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Mode that minimizes Total CostTransportation CostInventory Costs

Source Pipeline Destination - including safety stock

CostsTransportation Cost

Cost per unit UnitsCost per unit

$CWT (based on origin destination freight weight)

$Time (leased dedicated transportation)

InventoryAt the plant

12 ldquocycle quantityrdquoAt the warehouse

12 ldquocycle quantityrdquo Safety stock depends on lead time variability

In the pipeline Annual Volume Days in Transit Days per year

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

CostsTransportation Cost

Cost per unit UnitsCost per unit

$CWT (based on origin destination freight weight)

$Time (leased dedicated transportation)

InventoryAt the plant

12 ldquocycle quantityrdquoAt the warehouse

12 ldquocycle quantityrdquo Safety stock depends on lead time variability

In the pipeline Annual Volume Days in Transit Days per year

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

InventoryAt the plant

12 ldquocycle quantityrdquoAt the warehouse

12 ldquocycle quantityrdquo Safety stock depends on lead time variability

In the pipeline Annual Volume Days in Transit Days per year

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Example (page 187)

Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30

ModeRate

($unit) Time Std Dev in LTShipment

Size (units) TransportPlant

InventoryWarehouse Inventory

Safety Stock Pipeline Total

Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Route SelectionGetting From A to BUnderlying Network

Roads Airports Telecommunication links

Costs of using each linkFind the cheapest (shortest) path

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Example (page 192)

9084 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Shortest Path ModelA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate

nodesNo ldquonegative cyclesrdquo

Tree of Shortest PathsFind shortest paths from Origin to

each nodeSend n-1 units from origin Get 1 unit to each destination

Shortest Path ProblemA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Tree of Shortest PathsFind shortest paths from Origin to

each nodeSend n-1 units from origin Get 1 unit to each destination

Shortest Path ProblemA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Shortest Path ProblemA B C D E F G H I J

A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -

A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total To - - - - - - - - - - Balance - - - - - - - - - -

Net (1) - - - - - - - - 1

A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -

Total - - - - - - - - - - -

A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -

Distances

Route Chosen

Costs Incurred

Limits

Minimum Spanning TreeFind the cheapest total cost of edges

required to tie all the nodes together90

84 84

126

15048

348

6613890

120 132

12660

13248

156

AE

D

C

B

J

H

G

F

I

Greedy AlgorithmConsider links from cheapest to most

expensiveAdd a link if it does not create a

cycle with already chosen linksReject the link if it creates a cycle

Whatrsquos the difference Shortest Path Problem

Riderrsquos version Consider the number of riders who will

use itSpanning Tree Problem

Builderrsquos version Consider only the cost of construction

Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)

PROTRAC Engine Distribution

500

800 700

500

400

900

200

Belgium

Germany

Netherlands

The Hague

Amsterdam

Antwerp

Nancy

Liege

Tilburg

Leipzig

Miles

100500

500

800

700500

200

400

900

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

Greedy AlgorithmConsider links from cheapest to most

expensiveAdd a link if it does not create a

cycle with already chosen linksReject the link if it creates a cycle

Whatrsquos the difference Shortest Path Problem

Riderrsquos version Consider the number of riders who will

use itSpanning Tree Problem

Builderrsquos version Consider only the cost of construction

Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)

PROTRAC Engine Distribution

500

800 700

500

400

900

200

Belgium

Germany

Netherlands

The Hague

Amsterdam

Antwerp

Nancy

Liege

Tilburg

Leipzig

Miles

100500

500

800

700500

200

400

900

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

Whatrsquos the difference Shortest Path Problem

Riderrsquos version Consider the number of riders who will

use itSpanning Tree Problem

Builderrsquos version Consider only the cost of construction

Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)

PROTRAC Engine Distribution

500

800 700

500

400

900

200

Belgium

Germany

Netherlands

The Hague

Amsterdam

Antwerp

Nancy

Liege

Tilburg

Leipzig

Miles

100500

500

800

700500

200

400

900

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)

PROTRAC Engine Distribution

500

800 700

500

400

900

200

Belgium

Germany

Netherlands

The Hague

Amsterdam

Antwerp

Nancy

Liege

Tilburg

Leipzig

Miles

100500

500

800

700500

200

400

900

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

PROTRAC Engine Distribution

500

800 700

500

400

900

200

Belgium

Germany

Netherlands

The Hague

Amsterdam

Antwerp

Nancy

Liege

Tilburg

Leipzig

Miles

100500

500

800

700500

200

400

900

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

Transportation CostsTo Destination

From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42

Unit transportation costs from harbors to plants

Minimize the transportation costs involved in

moving the engines from the harbors to the

plants

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

A Transportation ModelPROTRAC Transportation Model

Unit Cost FromTo Leipzig Nancy Liege Tilburg

Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$

Shipments FromTo Leipzig Nancy Liege Tilburg Total Available

Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500

Total Cost FromTo Leipzig Nancy Liege Tilburg Total

Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$

Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs

Direct from plant to customer

Via DC

A Network ModelUnit Shipping Costs

Plant to DC DC 1 DC 2

Plant to Customer Customer 1 Customer 2

Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$

DC to Customer Customer 1 Customer 2

DC 1 20$ 120$ DC 2 20$ 120$

Shipments

Plant to DC DC 1 DC 2 Total Out

Plant to Customer Customer 1 Customer 2 Total Out

Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100

Total In 200 280 Total In - 100

DC to Customer Customer 1 Customer 2 Total Out

DC 1 200 - 200 DC 2 200 80 280

Total In 400 80

Net FlowsNet Flow

Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100

Arc Capacities

Plant to Customer Customer 1 Customer 2

Plant to DC DC 1 DC 2

Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200

DC to Customer Customer 1 Customer 2

DC 1 200 200DC 2 200 200

Incurred Costs

Plant to Customer Customer 1 Customer 2 Total Out

Plant to DC DC 1 DC 2 Total Out

Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$

Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$

Transportation Costs ($ 000Ton)

Transportation Capacities (Tons)

Minimum Cost Network Flow Problem

A Network ModelUnit Shipping Costs

Plant to DC DC 1 DC 2

Plant to Customer Customer 1 Customer 2

Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$

DC to Customer Customer 1 Customer 2

DC 1 20$ 120$ DC 2 20$ 120$

Shipments

Plant to DC DC 1 DC 2 Total Out

Plant to Customer Customer 1 Customer 2 Total Out

Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100

Total In 200 280 Total In - 100

DC to Customer Customer 1 Customer 2 Total Out

DC 1 200 - 200 DC 2 200 80 280

Total In 400 80

Net FlowsNet Flow

Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100

Arc Capacities

Plant to Customer Customer 1 Customer 2

Plant to DC DC 1 DC 2

Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200

DC to Customer Customer 1 Customer 2

DC 1 200 200DC 2 200 200

Incurred Costs

Plant to Customer Customer 1 Customer 2 Total Out

Plant to DC DC 1 DC 2 Total Out

Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$

Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$

Transportation Costs ($ 000Ton)

Transportation Capacities (Tons)

Minimum Cost Network Flow Problem

Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers

Bad NewsWhatrsquos Missing

Single Homogenous Product Linear Costs No conversions or losses

Homogenous Product

Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale

Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Bad NewsWhatrsquos Missing

Single Homogenous Product Linear Costs No conversions or losses

Homogenous Product

Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale

Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Homogenous Product

Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale

Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale

Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

The RulesExactly like Linear Models exceptSome decision variables

restricted to Binary - 0 or 1 Yes or No True or

False Integers

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Steco Warehouse LocationStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

A Linear ModelIgnore leasing for now -- all warehouses

are openObjective Minimize Total CostDecision Variables

Number of trucks from each warehouse to each customer each month

Constraints Enough trucks to each customer Not too many trucks from each warehouse

Recognize this

Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary

New Constraints Effective Capacity depends on whether or

not warehouse is open Warehouse A effective capacity is

0 if we do not lease the warehouse200 if we do

This is Linear

An Integer ModelStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost

Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary

New Constraints Effective Capacity depends on whether or

not warehouse is open Warehouse A effective capacity is

0 if we do not lease the warehouse200 if we do

This is Linear

An Integer ModelStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost

Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

An Integer ModelStecos Warehouse Location Model

Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity

Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300

Decisions YesNo 1 2 3 4

Total Trucks From

Effective Capacity

Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0

Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60

Lease Cost To 1 To 2 To 3 To 4

Total Truck Cost

Total Cost

Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$

Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$

Monthly Trucks FromTo

Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single

sourcingAssigning workers to tasks

ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs

Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to

depotMinimize travel cost

ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to

minimize the time to complete the work and get back to the depot

ExtensionsIf the ldquocustomersrdquo involve transportation

Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved

Construct routes for the 7 drivers at the North Metro Service center

If the vehicle has capacity LTL deliveries

If we intersperse pickups and deliveriesIf there are time windows on service

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs

Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to

depotMinimize travel cost

ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to

minimize the time to complete the work and get back to the depot

ExtensionsIf the ldquocustomersrdquo involve transportation

Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved

Construct routes for the 7 drivers at the North Metro Service center

If the vehicle has capacity LTL deliveries

If we intersperse pickups and deliveriesIf there are time windows on service

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to

depotMinimize travel cost

ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to

minimize the time to complete the work and get back to the depot

ExtensionsIf the ldquocustomersrdquo involve transportation

Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved

Construct routes for the 7 drivers at the North Metro Service center

If the vehicle has capacity LTL deliveries

If we intersperse pickups and deliveriesIf there are time windows on service

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to

minimize the time to complete the work and get back to the depot

ExtensionsIf the ldquocustomersrdquo involve transportation

Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved

Construct routes for the 7 drivers at the North Metro Service center

If the vehicle has capacity LTL deliveries

If we intersperse pickups and deliveriesIf there are time windows on service

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

ExtensionsIf the ldquocustomersrdquo involve transportation

Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved

Construct routes for the 7 drivers at the North Metro Service center

If the vehicle has capacity LTL deliveries

If we intersperse pickups and deliveriesIf there are time windows on service

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Basic TSPData issues

Estimate distance by location Calculate point to point distances Calculate point to point costs

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

HeuristicsCluster first Route Second

Build delivery zones with approximately equal work

Route a vehicle in each zoneClustering Approaches

Assign most distant blocks first Sweep Space-filling curve

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos

X = 165 = 1000010 124+023+022+021+020+12-1 +02-2

Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2

Space Filling Number - interleave bits (XY) = 10010000011101

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

PropertiesEvery pair (XY) has a unique point

(XY)Every point on the line corresponds

to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close

together (XY) and (XrsquoYrsquo) tend to be close together

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes

Give first 1Nth of customers to first route

Give second 1Nth of customers to second route

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

RoutingEach route visits the customers in

order of their values

defines a route on the plane that visits every point We visit the customers in the same order as that route

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Route FirstBuild a single large routeAssign each vehicle a segment of the

route

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

2-Interchange

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

2-Interchange

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

2-Interchange

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

2-Interchange

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Route Sequencing

Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034

10 1056 1425

Tanker Scheduling

Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61

ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production

• Transportation
• Mode Selection
• Mode that minimizes Total Cost
• Costs
• Inventory
• Example (page 187)
• Multi-Modal Systems
• Route Selection
• Example (page 192)
• Shortest Path Model
• Applicability
• Tree of Shortest Paths
• Shortest Path Problem
• Minimum Spanning Tree
• Greedy Algorithm
• Whatrsquos the difference
• Transportation Problem
• PROTRAC Engine Distribution
• Transportation Costs
• A Transportation Model
• Crossdocking
• A Network Model
• Good News
• Bad News
• Homogenous Product
• Linear Costs
• Integer Models
• The Rules
• Steco Warehouse Location
• A Linear Model
• Making Discrete Decisions
• An Integer Model
• Special Case
• ldquoApplicationrdquo
• Traveling Salesman Problem
• Example
• Extensions
• Basic TSP
• Heuristics
• Space-Filling Curve
• Properties
• Clustering
• Routing
• Route First
• Routing Heuristics
• 2-Interchange
• Slide 47
• Slide 48
• Slide 49
• Route Sequencing
• Tanker Scheduling
• Consolidation