abhishek transshipment
TRANSCRIPT
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Case Problem : Distribution System design
Abhishek SaxenaPGDMA 1101
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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
…
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Per unit Shipping Cost (in $) from Production plant to Distribution centers
Plant Fort Worth Santa Fe Las Vegas
El Paso 3.20 2.20 4.20
San Bernardino
------ 3.90 1.20
No shipments are allowed from the San Bernardino to Fort Worth
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Quarterly Demand Forecast
Customer Zone Demand(Meters)
Dallas 6300
San Antonio 4880
Wichita 2130
Kansas City 1210
Denver 6120
Salt Lake City 4830
Phoenix 2750
Los Angeles 8580
San Diego 4460
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Shipping Cost ($) 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)
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• 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.
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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.
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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
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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
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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
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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
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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)
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Thank you…!