Unit 10 Assignment 1 Stateline Shipping And Transport Company
Week 10 – Assignment # 4 06/16/13
Stateline Shipping & Transport Company
Question #1 – Transportation Model Plant Waste Disposal | A. White Water | B. Los Canos | C. Duras | Supply | 1. Kingsport | 12 | 15 | 17 | 35 | 2. Danville | 14 | 9 | 10 | 26 | 3. Macon | 13 | 20 | 11 | 42 | 4. Selma | 17 | 16 | 19 | 53 | 5. Columbus | 7 | 14 | 12 | 29 | 6. Allentown | 22 | 16 | 18 | 38 | Demand | 65 | 80 | 105 | |
Xij = Shipping from plant to disposal site. i = PLANT = 1,2,3,4,5,6 j = disposal sites = A, B, C
The objective function of the manager is to minimize the total transportation cost for all shipments. Therefore, the objective function is the sum of the individual shipping costs …show more content…
from each plant to each waste disposal site:
Minimize Z = 121A + 151B + 171C+142A+92B+102C+133A+203B+113C
+174A+164B+194C+75A+145B+125C+226A+166B+186C
The constraints in the model are the number of barrels of wastes available per week at each plant and the number of barrels of wastes accommodated at each waste disposal site.
There are 9 constraints- one for each plant supply and one for each waste disposal site’s demand.
Subject …show more content…
to:
X1A + x1B + X1C = 35
X 2A + X 2B + X 3C= 26
X3A + X3B + X 3C = 42
X4A + X 4b + X4C = 53
X5A + X5b + x5C = 29
X6a + x 6B + x 76b = 38
X1A + X 2A + X 3A + X 4A+ X5A + X 6A = 65
X1B + X 2B + X 3B = X 4B + X5B + X 6B = 80
X1C + X 2C + X 3C = X 4C + X5C + X 6C = 105
XIJ ≥ 0
1 A
2
3 B
4
5 C
6
Question # 2
Numbers entered in the QM: A B C SUPPLY 1 12 15 17 35 2 14 9 10 26 3 13 20 11 42 4 17 16 19 53 5 7 14 12 29 6 22 16 18 38
65 80 105
Solution:
Optimal solution value = $2822 Plant | Waste Disposal Sites | Supply | Waste Shipped | | Whitewater | Los Canos | Duras | | | Kingsport | 35.0 | 0.0 | 0.0 | 35.0 | 35.0 | Danville | 0.0 | 0.0 | 26.0 | 26.0 | 26.0 | Macon | 0.0 | 0.0 | 42.0 | 42.0 | 42.0 | Selma | 1.0 | 52.0 | 0.0 | 53.0 | 53.0 | Columbus | 29.0 | 0.0 | 0.0 | 29.0 | 29.0 | Allentown | 0.0 | 28.0 | 10.0 | 38.0 | 38.0 | Waste Received | 65.0 | 80.0 | 105.0 | | 223.0 | Waste Disposed | 65.0 | 80.0 | 78.0 | 223.0 | | | | | | | | Cost= | $ 2,822 | | | | |
The optimum solution of the transportation problem is given in the following table. From | To | Shipment unit | Cost per unit | Shipment cost | Kingsport | Whitewater | 35 | $12 | $420 | Danville | Duras | 26 | $10 | $260 | Macon | Duras | 42 | $11 | $462 | Selma | Whitewater | 1 | $17 | $17 | Selma | Los Canos | 52 | $16 | $832 | Columbus | Whitewater | 29 | $7 | $203 | Allentown | Los Canos | 28 | $16 | $448 | Allentown | Duras | 10 | $18 | $180 | Total Cost | $2822 |
Question # 3
If each of the plant and waste disposal sites is considered as intermediate shipping points, the transportation model becomes a transshipment model. The additional decision variables included in the revised model are = Number of barrels of waste shipped from plant ‘i’ to plant ‘j’, where i = 1, 2, 3, 4, 5, 6 and j = 1, 2, 3, 4, 5, 6 = Number of barrels of waste shipped from waste disposal site ‘k’ to waste disposal site ‘l’, where k = A, B, C and l = A, B, C.
The new objective function of the transshipment model is
Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 + 17 +16 +19 +7 +14 +12 +22 +16 +18 + 6+ 4+ 9+ 7+ 8+ 6+ 11+ 10 +12+ 7 + 5+ 11+ 3+ 7+ 15+ 9+ 10+ 3 + 3+ 16 + 7+ 12+ 7+ 3+ 14+ 8+ 7+ 15 + 16+ 14 + 12+ 10+ 12+ 15+ 10+ 15
The number of barrels of wastes available at plant ‘i’ for shipment to one or more of the waste disposal sites is given by (Number of barrels already available at plant ‘i’) + (Number of barrels shipped to plant ‘i’ from other plants) – (Number of barrels shipped from plant ‘i’ to other plants)
Therefore, the six supply constraints is now: + + = 35 + (+ + + +) – (+ + + + ) + + = 26 + (+ + + +) – (++ ++ ) + + = 42 + (+ + + +) – (++++) + + = 53 + (+ + + +) – (++ + +) + + = 29 + (+ + + +) – (++++) + + = 38 + (+ + + +) – (++ + +)
The number of barrels that can accommodate in the i-th waste disposal site is given by (Number of barrels transported from the six plants to the i-th waste disposal site)
+ (Number of barrels shipped from other waste disposal sites to i-th waste disposal site)
– (Number of barrels shipped to other waste disposal sites from i-th waste disposal site)
Thus the three demand constraints is now: (+ + ++ +) + (+) – (+) ≤ 65 (+ + + + +) + (+) – (+) ≤ 80 (+ ++ + +) + (+) – (+) ≤ 105
Thus the linear programming model for the transshipment problem is summarized as follows:
Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 + 17 +16 +19 +7 +14 +12 +22 +16 +18 + 6+ 4+ 9+ 7+ 8+ 6+ 11+ 10 +12+ 7 + 5+ 11+ 3+ 7+ 15+ 9+ 10+ 3 + 3+ 16 + 7+ 12+ 7+ 3+ 14+ 8+ 7+ 15 + 16+ 14 + 12+ 10+ 12+ 15+ 10+ 15
Subject to: + + = 35 + (+ + + +) – (+ + + + ) + + = 26 + (+ + + +) – (++ ++ ) + + = 42 + (+ + + +) – (++++) + + = 53 + (+ + + +) – (++ + +) + + = 29 + (+ + + +) – (++++) + + = 38 + (+ + + +) – (++ + +) (+ + ++ +) + (+) – (+) ≤ 65 (+ + + + +) + (+) – (+) ≤ 80 (+ ++ + +) + (+) – (+) ≤ 105 Question # 4
The computer solution for the transshipment model is obtained using Excel Solver and the output is given below.
For doing the analysis using Excel solver we assume the shipping cost per barrel for the decision variables , , , ,,,,, are assumed to be 100 in order to make sure that the variable representing that routes do not have a value in the optimal solution. Plant | Plant | | Kingsport | Danville | Macon | Selma | Columbus | Allentown | Kingsport | 0.0 | 0.0 | 19.0 | 0.0 | 0.0 | 0.0 | Danville | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Macon | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Selma | 0.0 | 0.0 | 17.0 | 0.0 | 36.0 | 0.0 | Columbus | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Allentown | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Waste Received | 0.0 | 0.0 | 36.0 | 0.0 | 36.0 | 0.0 | | | | | | | | | | | | | | | | Plant | Waste Disposal Sites | Supply | Accum Supply | | | Whitewater | Los Canos | Duras | | | | Kingsport | 0.0 | 16.0 | 0.0 | 35.0 | 16.0
| | Danville | 0.0 | 26.0 | 0.0 | 26.0 | 26.0 | | Macon | 0.0 | 0.0 | 78.0 | 42.0 | 78.0 | | Selma | 0.0 | 0.0 | 0.0 | 53.0 | 0.0 | | Columbus | 65.0 | 0.0 | 0.0 | 29.0 | 65.0 | | Allentown | 0.0 | 38.0 | 0.0 | 38.0 | 38.0 | | Waste Received | 65.0 | 80.0 | 78.0 | 223.0 | 223.0 | | | | | | | | | | | | | | | | Waste Disposal Site | Waste Disposal Site | Waste Dispatched | | | | Whitewater | Los Canos | Duras | | | | Whitewater | 0.0 | 0.0 | 0.0 | 0.0 | | | Los Canos | 0.0 | 0.0 | 0.0 | 0.0 | | | Duras | 0.0 | 0.0 | 0.0 | 0.0 | | | Waste Received | 0.0 | 0.0 | 0.0 | | | | Waste Accommodation | 65.0 | 80.0 | 105.0 | | | | Waste Disposed | 65.0 | 80.0 | 78.0 | 223.0 | | | | | | | | | | | | | | | | Cost= | $ 2,630 | | | | | |
Thus the optimum solution of the transshipment problem is given in the following table. From | To | Shipment unit | Cost per unit | Shipment cost | Kingsport | Macon | 19 | $4 | $76 | Kingsport | Los Canos | 16 | $15 | $240 | Danville | Los Canos | 26 | $9 | $234 | Macon | Duras | 78 | $11 | $858 | Selma | Macon | 17 | $3 | $51 | Selma | Columbus | 36 | $3 | $108 | Columbus | Whitewater | 65 | $7 | $455 | Allentown | Los Canos | 38 | $16 | $608 | Total Cost | $2630 |
Thus, the total transportation cost for the optimal route is $2630.
Question # 5
5) The total transportation cost for the initial transportation model is obtained is $2822. The optimal routes and the corresponding units to be shipped if the units are shipping directly from each of the six plants to each of the three waste disposal sites is as follows: From (Plant) | To (Waste Disposal Site) | Shipment unit | Kingsport | Whitewater | 35 | Danville | Duras | 26 | Macon | Duras | 42 | Selma | Whitewater | 1 | Selma | Los Canos | 52 | Columbus | Whitewater | 29 | Allentown | Los Canos | 28 | Allentown | Duras | 10 |
If each of the plants and waste disposal sites is considered an intermediate shipping points, the total transportation cost is $2630. The optimal routes and the corresponding barrels to be shipped as follows:
From (Plant) | To | Shipment unit | Kingsport | Macon (Plant) | 19 | Kingsport | Los Canos (Waste Disposal Site) | 16 | Danville | Los Canos (Waste Disposal Site) | 26 | Macon | Duras (Waste Disposal Site) | 78 | Selma | Macon (Plant) | 17 | Selma | Columbus (Plant) | 36 | Columbus | Whitewater (Waste Disposal Site) | 65 | Allentown | Los Canos (Waste Disposal Site) | 38 |
If Rachel considers each of the plants and waste disposal sites as intermediate shipping points she will reduce the total transportation cost by $192 per week.
Stateline Shipping & Transport Company
Question #1 – Transportation Model Plant Waste Disposal | A. White Water | B. Los Canos | C. Duras | Supply | 1. Kingsport | 12 | 15 | 17 | 35 | 2. Danville | 14 | 9 | 10 | 26 | 3. Macon | 13 | 20 | 11 | 42 | 4. Selma | 17 | 16 | 19 | 53 | 5. Columbus | 7 | 14 | 12 | 29 | 6. Allentown | 22 | 16 | 18 | 38 | Demand | 65 | 80 | 105 | |
Xij = Shipping from plant to disposal site. i = PLANT = 1,2,3,4,5,6 j = disposal sites = A, B, C
The objective function of the manager is to minimize the total transportation cost for all shipments. Therefore, the objective function is the sum of the individual shipping costs …show more content…
from each plant to each waste disposal site:
Minimize Z = 121A + 151B + 171C+142A+92B+102C+133A+203B+113C
+174A+164B+194C+75A+145B+125C+226A+166B+186C
The constraints in the model are the number of barrels of wastes available per week at each plant and the number of barrels of wastes accommodated at each waste disposal site.
There are 9 constraints- one for each plant supply and one for each waste disposal site’s demand.
Subject …show more content…
to:
X1A + x1B + X1C = 35
X 2A + X 2B + X 3C= 26
X3A + X3B + X 3C = 42
X4A + X 4b + X4C = 53
X5A + X5b + x5C = 29
X6a + x 6B + x 76b = 38
X1A + X 2A + X 3A + X 4A+ X5A + X 6A = 65
X1B + X 2B + X 3B = X 4B + X5B + X 6B = 80
X1C + X 2C + X 3C = X 4C + X5C + X 6C = 105
XIJ ≥ 0
1 A
2
3 B
4
5 C
6
Question # 2
Numbers entered in the QM: A B C SUPPLY 1 12 15 17 35 2 14 9 10 26 3 13 20 11 42 4 17 16 19 53 5 7 14 12 29 6 22 16 18 38
65 80 105
Solution:
Optimal solution value = $2822 Plant | Waste Disposal Sites | Supply | Waste Shipped | | Whitewater | Los Canos | Duras | | | Kingsport | 35.0 | 0.0 | 0.0 | 35.0 | 35.0 | Danville | 0.0 | 0.0 | 26.0 | 26.0 | 26.0 | Macon | 0.0 | 0.0 | 42.0 | 42.0 | 42.0 | Selma | 1.0 | 52.0 | 0.0 | 53.0 | 53.0 | Columbus | 29.0 | 0.0 | 0.0 | 29.0 | 29.0 | Allentown | 0.0 | 28.0 | 10.0 | 38.0 | 38.0 | Waste Received | 65.0 | 80.0 | 105.0 | | 223.0 | Waste Disposed | 65.0 | 80.0 | 78.0 | 223.0 | | | | | | | | Cost= | $ 2,822 | | | | |
The optimum solution of the transportation problem is given in the following table. From | To | Shipment unit | Cost per unit | Shipment cost | Kingsport | Whitewater | 35 | $12 | $420 | Danville | Duras | 26 | $10 | $260 | Macon | Duras | 42 | $11 | $462 | Selma | Whitewater | 1 | $17 | $17 | Selma | Los Canos | 52 | $16 | $832 | Columbus | Whitewater | 29 | $7 | $203 | Allentown | Los Canos | 28 | $16 | $448 | Allentown | Duras | 10 | $18 | $180 | Total Cost | $2822 |
Question # 3
If each of the plant and waste disposal sites is considered as intermediate shipping points, the transportation model becomes a transshipment model. The additional decision variables included in the revised model are = Number of barrels of waste shipped from plant ‘i’ to plant ‘j’, where i = 1, 2, 3, 4, 5, 6 and j = 1, 2, 3, 4, 5, 6 = Number of barrels of waste shipped from waste disposal site ‘k’ to waste disposal site ‘l’, where k = A, B, C and l = A, B, C.
The new objective function of the transshipment model is
Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 + 17 +16 +19 +7 +14 +12 +22 +16 +18 + 6+ 4+ 9+ 7+ 8+ 6+ 11+ 10 +12+ 7 + 5+ 11+ 3+ 7+ 15+ 9+ 10+ 3 + 3+ 16 + 7+ 12+ 7+ 3+ 14+ 8+ 7+ 15 + 16+ 14 + 12+ 10+ 12+ 15+ 10+ 15
The number of barrels of wastes available at plant ‘i’ for shipment to one or more of the waste disposal sites is given by (Number of barrels already available at plant ‘i’) + (Number of barrels shipped to plant ‘i’ from other plants) – (Number of barrels shipped from plant ‘i’ to other plants)
Therefore, the six supply constraints is now: + + = 35 + (+ + + +) – (+ + + + ) + + = 26 + (+ + + +) – (++ ++ ) + + = 42 + (+ + + +) – (++++) + + = 53 + (+ + + +) – (++ + +) + + = 29 + (+ + + +) – (++++) + + = 38 + (+ + + +) – (++ + +)
The number of barrels that can accommodate in the i-th waste disposal site is given by (Number of barrels transported from the six plants to the i-th waste disposal site)
+ (Number of barrels shipped from other waste disposal sites to i-th waste disposal site)
– (Number of barrels shipped to other waste disposal sites from i-th waste disposal site)
Thus the three demand constraints is now: (+ + ++ +) + (+) – (+) ≤ 65 (+ + + + +) + (+) – (+) ≤ 80 (+ ++ + +) + (+) – (+) ≤ 105
Thus the linear programming model for the transshipment problem is summarized as follows:
Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 + 17 +16 +19 +7 +14 +12 +22 +16 +18 + 6+ 4+ 9+ 7+ 8+ 6+ 11+ 10 +12+ 7 + 5+ 11+ 3+ 7+ 15+ 9+ 10+ 3 + 3+ 16 + 7+ 12+ 7+ 3+ 14+ 8+ 7+ 15 + 16+ 14 + 12+ 10+ 12+ 15+ 10+ 15
Subject to: + + = 35 + (+ + + +) – (+ + + + ) + + = 26 + (+ + + +) – (++ ++ ) + + = 42 + (+ + + +) – (++++) + + = 53 + (+ + + +) – (++ + +) + + = 29 + (+ + + +) – (++++) + + = 38 + (+ + + +) – (++ + +) (+ + ++ +) + (+) – (+) ≤ 65 (+ + + + +) + (+) – (+) ≤ 80 (+ ++ + +) + (+) – (+) ≤ 105 Question # 4
The computer solution for the transshipment model is obtained using Excel Solver and the output is given below.
For doing the analysis using Excel solver we assume the shipping cost per barrel for the decision variables , , , ,,,,, are assumed to be 100 in order to make sure that the variable representing that routes do not have a value in the optimal solution. Plant | Plant | | Kingsport | Danville | Macon | Selma | Columbus | Allentown | Kingsport | 0.0 | 0.0 | 19.0 | 0.0 | 0.0 | 0.0 | Danville | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Macon | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Selma | 0.0 | 0.0 | 17.0 | 0.0 | 36.0 | 0.0 | Columbus | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Allentown | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | Waste Received | 0.0 | 0.0 | 36.0 | 0.0 | 36.0 | 0.0 | | | | | | | | | | | | | | | | Plant | Waste Disposal Sites | Supply | Accum Supply | | | Whitewater | Los Canos | Duras | | | | Kingsport | 0.0 | 16.0 | 0.0 | 35.0 | 16.0
| | Danville | 0.0 | 26.0 | 0.0 | 26.0 | 26.0 | | Macon | 0.0 | 0.0 | 78.0 | 42.0 | 78.0 | | Selma | 0.0 | 0.0 | 0.0 | 53.0 | 0.0 | | Columbus | 65.0 | 0.0 | 0.0 | 29.0 | 65.0 | | Allentown | 0.0 | 38.0 | 0.0 | 38.0 | 38.0 | | Waste Received | 65.0 | 80.0 | 78.0 | 223.0 | 223.0 | | | | | | | | | | | | | | | | Waste Disposal Site | Waste Disposal Site | Waste Dispatched | | | | Whitewater | Los Canos | Duras | | | | Whitewater | 0.0 | 0.0 | 0.0 | 0.0 | | | Los Canos | 0.0 | 0.0 | 0.0 | 0.0 | | | Duras | 0.0 | 0.0 | 0.0 | 0.0 | | | Waste Received | 0.0 | 0.0 | 0.0 | | | | Waste Accommodation | 65.0 | 80.0 | 105.0 | | | | Waste Disposed | 65.0 | 80.0 | 78.0 | 223.0 | | | | | | | | | | | | | | | | Cost= | $ 2,630 | | | | | |
Thus the optimum solution of the transshipment problem is given in the following table. From | To | Shipment unit | Cost per unit | Shipment cost | Kingsport | Macon | 19 | $4 | $76 | Kingsport | Los Canos | 16 | $15 | $240 | Danville | Los Canos | 26 | $9 | $234 | Macon | Duras | 78 | $11 | $858 | Selma | Macon | 17 | $3 | $51 | Selma | Columbus | 36 | $3 | $108 | Columbus | Whitewater | 65 | $7 | $455 | Allentown | Los Canos | 38 | $16 | $608 | Total Cost | $2630 |
Thus, the total transportation cost for the optimal route is $2630.
Question # 5
5) The total transportation cost for the initial transportation model is obtained is $2822. The optimal routes and the corresponding units to be shipped if the units are shipping directly from each of the six plants to each of the three waste disposal sites is as follows: From (Plant) | To (Waste Disposal Site) | Shipment unit | Kingsport | Whitewater | 35 | Danville | Duras | 26 | Macon | Duras | 42 | Selma | Whitewater | 1 | Selma | Los Canos | 52 | Columbus | Whitewater | 29 | Allentown | Los Canos | 28 | Allentown | Duras | 10 |
If each of the plants and waste disposal sites is considered an intermediate shipping points, the total transportation cost is $2630. The optimal routes and the corresponding barrels to be shipped as follows:
From (Plant) | To | Shipment unit | Kingsport | Macon (Plant) | 19 | Kingsport | Los Canos (Waste Disposal Site) | 16 | Danville | Los Canos (Waste Disposal Site) | 26 | Macon | Duras (Waste Disposal Site) | 78 | Selma | Macon (Plant) | 17 | Selma | Columbus (Plant) | 36 | Columbus | Whitewater (Waste Disposal Site) | 65 | Allentown | Los Canos (Waste Disposal Site) | 38 |
If Rachel considers each of the plants and waste disposal sites as intermediate shipping points she will reduce the total transportation cost by $192 per week.