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2123 - 5 This is a transportation problem 3 2-8 1 5 4 4-7 2...

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Unformatted text preview: 5. This is a transportation problem. 3 2 -8 1 5 4 4 -7 2 3 7 5 6. +5 6 +5 +5 -5 1 7 4 +4 2 3 8 5 -7 5 3 +8 5 9 4 +0 6 Chapter 5 - Network Modeling : S-5 ------------------------------------------------------------------------------------------ 12. The LP model is: MIN ST 12 X12 + 8 X13 + 15 X14 + 9 X23 + 16 X25 + 6 X34 + 7 X35 + 12 X54 -X12 - X13 - X14 = -15 -X23 - X25 = -15 +X13 + X23 -X34 -X35 = 0 +X14 + X34 + X54 = 20 +X25 +X35 -X54 = 10 0 d Xij d 10 The solution is: X13 = 5, X14 = 10, X23 = 5, X25 = 10, X34 = 10 Minimum total cost = $455 See file: Prb5_20.xls 13. The optimal solution is: X14=X49=X9,12= 1, Minimum cost = $8 million See file: Prb5_32.xls 14. a. This is a transportation problem. Note that demand exceeds supply by 20 units. Warehouses Stores 1 5 +20 -30 1 4 6 5 2 3 6 +25 -30 2 4 4 4 3 2 3 +30 -30 3 4 b. MIN 5 X11 + 4 X12 + 6 X13 + 5 X14 +3 X21 + 6 X22 + 4 X23 + 4 X24 +4 X31 + 3 X32 + 3 X33 + 2 X34 -X11 - X12 - X13 - X14 = -30 -X21 - X22 - X23 - X24 = -30 -X31 - X32 - X33 - X34 = -30 +X11 + X21 + X31 + XD1 d +20 +X12 + X22 + X32 + XD2 d +25 +X13 + X23+ X33 + XD3 d +30 +X14 + X24+ X34 + XD4 d +35 Xij t 0 +35 ST Chapter 5 - Network Modeling : S-11 ------------------------------------------------------------------------------------------ 24. a. Chic. 6 17 NY 7 +1 18 18 25 24 95 LA 2 32 Denver 3 50 27 19 30 14 14 24 35 St Lou 4 Memp 5 5 13 35 105 45 San Diego 1 -1 b. MIN 5 X12 + 13 X13 + 45 X15 + 105 X17 + 27 X23 + 19 X24 + 50 X25 + 95 X27 + 14 X34 + 30 X35 + 32 X36 + 14 X43 + 35 X45 + 24 X46 + 35 X54 + 18 X56 + 25 X57 + 24 X64 + 18 X65 + 17 X67 -X12 - X13 - X15 - X17 = -1 +X12 - X23 - X24 - X25 - X27 = 0 +X13 + X23 + X43- X34 - X35 - X36 = 0 +X24 + X34 + X54 + X64 - X43 - X45 - X46 = 0 + X15 + X25 + X35 + X45 + X65 - X54 - X56 - X57 = 0 + X36 + X46 + X56 - X64 - X65 - X67 = 0 + X17 + X27 + X57 + X67 = +1 Xij t 0 ST c. See file: Prb5_14.xls The solution is: X13=X36=X67=1 with a minimum total cost of $62. Chapter 5 - Network Modeling : S-18 ------------------------------------------------------------------------------------------ 33. a. -30 Doha 0 L.B. = 7.5 ($0, 999) Tanke r ($1.20, 999) ($1.40, 999) Rotter dam +6 5 1 ($1.35, 999) ($0.35, 22.5) Toulon ($0.25, 999) 6 Damietta +15 +0 4 ($0.20, 999) ($0.15, 999) ($0.16, 15) Suez +0 2 ($0.20, 999) +0 b. c. See file: Prb5_22.xls Total Cost = $25.43 million U.B . 22.5 999 999 999 999 999 15 999 999 999 999 999 999 Unit Cost ($1,000,000s ) $0.35 $0.00 $1.20 $1.40 $1.35 $0.20 $0.16 $0.27 $0.28 $0.19 $0.25 $0.20 $0.15 ($0.27, 999) ($0.28, 999) P. Said 3 ($0.19, 999) Palermo +9 7 Legend: (cost, upper bound) Flow 22.5 7.5 6 1.5 0 7.5 15 0 0 7.5 0 13.5 1.5 L.B. 0 7.5 0 0 0 0 0 0 0 0 0 0 0 From 0 Doha 0 Doha 1 Tanker 1 Tanker 1 Tanker 2 Suez 2 Suez 3 Port Said 3 Port Said 3 Port Said 4 Damietta 4 Damietta 4 Damietta To 2 1 5 6 7 3 4 5 6 7 5 6 7 Suez Tanker Rotterdam Toulon Palermo Port Said Damietta Rotterdam Toulon Palermo Rotterdam Toulon Palermo Chapter 5 - Network Modeling : S-19 ------------------------------------------------------------------------------------------ 34. a. -30 Reg 1 Reg 2 Reg 3 Reg 4 Reg 5 $6.50 $7.50 $7.00 $8.00 $8.25 $7.25 $6.75 $7.75 $7.00 $7.50 Eustis 7 Pine Hills 6 -40 60 -25 -35 70 -33 40 $6.75 Sanfor d 8 b. c. See file Prb5_9.xls 20,000 from Region 1 to Pine Hills, 10,000 from Region 1 to Eustis, 40,000 from Region 2 to Pine Hills, 25,000 from Region 3 to Eustis, 35,000 from Region 4 to Sanford, 25,000 from Region 5 to Eustis, 5,000 from Region 5 to Sanford. Total cost $1,132,500. ...
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  • Summer '04
  • asdasd
  • DVD region code, Network Modeling, Suez Tanker Rotterdam Toulon Palermo Port Said Damietta Rotterdam Toulon Palermo Rotterdam Toulon Palermo, Rotterdam Toulon Palermo

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