Case Problem : Distribution System design

Abhishek SaxenaPGDMA 1101

Case Overview• Darby Company• Product : Electric Power Meter

SN Production Plant Per unit Production Cost

Capacity

1. El Paso $10.50 30,000

2. San Bernardino $10.00 20,000

Distribution Centers :1. Fort Worth2. Santa Fe3. Las Vegas

…

Per unit Shipping Cost (in $) from Production plant to Distribution centers

Plant Fort Worth Santa Fe Las Vegas

El Paso 3.20 2.20 4.20

San Bernardino

------ 3.90 1.20

No shipments are allowed from the San Bernardino to Fort Worth

Quarterly Demand Forecast

Customer Zone Demand(Meters)

Dallas 6300

San Antonio 4880

Wichita 2130

Kansas City 1210

Denver 6120

Salt Lake City 4830

Phoenix 2750

Los Angeles 8580

San Diego 4460

Shipping Cost ($) Customer Zones

Fort Worth Santa Fe Las Vegas

Dallas 0.3 5.2 ---San Antonio 2.1 5.4 ---Wichita 3.1 4.5 ---Kansas City 4.4 6.0 ---Denver 6.0 2.7 5.4Salt Lake City

--- 4.7 3.3

Phoenix --- 3.4 2.4Los Angeles --- 3.3 2.1San Diego --- 2.7 2.5

(Distribution Centres)

• In current distribution system, demand at the

Dallas, San Antonio, Wichita, and Kansas City customer zones is satisfied by shipments from the Fort Worth.

• In same way, the Denver, Salt Lake City and Phoenix customer zones are served by Santa Fe and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution centre.

1. El Paso

2. San Bernar

dino

5. Las Vegas

3. Ft. Worth

4. Santa

Fe

6. Dallas

12. Phoenix

14. San Diego

7. San Antonio

13. Los Angeles

9. Kansas City

8. Wichita

11. Salt Lake City

10. Denver

20,000

4880

2130

1210

8580

2750

4460

6120

4830

6300

30,000

3.2

0.3

3.1

4.4

2.7

4.7

3.4

2.5

2.1

2.2

4.2

3.9

1.2

2.1

X(1,3) Shipping Cost from 1 to 3

X(1,4) Shipping Cost from 1 to 4

X(1,5) Shipping Cost from 1 to 5

X(2,4) Shipping Cost from 2 to 4

X(2,5) Shipping Cost from 2 to 5

X(3,6) Shipping Cost from 3 to 6

X(3,7) Shipping Cost from 3 to 7

X(3,8) Shipping Cost from 3 to 8

X(3,9) Shipping Cost from 3 to 9

Decision variables

X(4,10) Shipping Cost from 4 to 10

X(4,11) Shipping Cost from 4 to 11

X(4,12) Shipping Cost from 4 to 12

X(5,13) Shipping Cost from 5 to 13

X(5,14) Shipping Cost from 5 to 14

Decision variables

Constraints…

SupplyX(1,3) + X(1,4) + X(1,5) <=30000

X(2,4) + X(2,5) <= 20000

X(1,3) -- X(3,6) -- X(3,7) -- X(3,8) -- X(3,9) = 0

X(1,4) + X(2,4) -- X(4,10)-- X(4,11)-- X(4,12) = 0

X(1,5) + X(2,5) -- X(5,13) -- X(5,14) = 0

Shipment

Constraints…

X(3,6) = 6300

X(3,7) = 4880

X(3,8) = 2130

X(3,9) = 1210

X(4,10) = 6120

X(4,11) = 4830

X(4,12) = 2750

X(5,13) = 8580

X(5,14) = 4460

Demand

Question .01

If the company does not change its current distribution strategy, what will its costs for the following quarter ?

Objective : To minimize the total cost of shipping

Min. Z = sum product(shipping cost, Units shipped)

Suppose that the company is willing to consider dropping the distribution center limitations: that is, customers would be served by any of the following distribution centers which costs are available. Can costs be reduced? By how much?

Question .02

1. El Paso

2. San Bernar

dino

5. Las Vegas

3. Ft. Worth

4. Santa

Fe

6. Dallas

12. Phoenix

14. San Diego

7. San Antonio

13. Los Angeles

9. Kansas City

8. Wichita

11.Salt Lake City

10.Denver

4880

2130

1210

8580

2750

4460

6120

4830

6300

20,000

30,000

3.2

2.2

4.2

3.9

1.2

0.3

3.1

4.4

6.05.2 5.4

4.56.0

2.74.7

3.43.32.7

5.4 3.32.4

2.1

2.5

2.1

Constraints…

X(3,6) + X(4,6) = 6300

X(3,7) + X(4,7) = 4880

X(3,8) + X(4,8) = 2130

X(3,9) + X(4,9) = 1210

X(3,10) + X(4,10)+X(5,10) = 6120

X(4,11) + X(4,11) = 4830

X(4,12) + X(4,12) = 2750

X(4,13) + X(5,13) = 8580

X(4,14) + X(5,14) = 4460

Supply

Distribution Design System.xlsx

With the current system of assigning customers to distribution centres, the minimum total cost is $620,770.

Allowing customers to be serviced by any distribution centre reduces total cost to $600,942.This is a 3.19% decrease in total cost.

The company wants to explore the possibility of satisfying some of the customer demand directly from the production plants. In particular, the shipping cost is .30 per unit from San Bernardino to Los Angeles and $.70 from San Bernardino to San Diego. The cost for direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be further reduced by considering these direct plant-to-customer shipments?

Question .03

1. El Paso

2. San Bernar

dino

5. Las Vegas

3. Ft. Worth

4. Santa

Fe

6. Dallas

12. Phoenix

14. San Diego

7. San Antonio

13. Los Angeles

9. Kansas City

8. Wichita

11.Salt Lake City

10.Denver

4880

2130

1210

8580

2750

4460

6120

4830

6300

20,000

30,000

3.5

0.3

0.7

Constraints…

Demand

X(1,3) + X(1,4) + X(1,5) + X(1,7) <= 30000

X(2,4) + X(2,5) +X(2,13)+X(2,14) <= 20000

X(3,7) + X(4,7) + X(1,7) = 4880

X(4,13) + X(5,13) +X(2,13) = 8580

X(4,14) + X(5,14) +X(2,14) = 4460

Supply

Distribution Design System.xlsx

Over the next five years, Darby is anticipating moderate growth (5000 meters) to the north and west. Would you recommend that they consider plant expansion at this time?

Question .04

Name Final

ValueShadow price

ConstraintR.H. side

AllowableIncrease

AllowableDecrease

El paso shipment

21260 0 30000 1 E + 30 8740

San Berner dino net shipment

20000 -2.5 20000 620 2130

The dual price from problem 3 output indicates that each unit of added capacity will reduce distribution costs by $2.50. However, the range of feasibility shows this dual price is only applicable for the net 620 units of capacity. So Plant expansion for San Bernardino are recommended.

By producing 620 units the total cost will be reduced by $1550 (620 * $2.5)

Thank you…!