CASE International Textile Company, Ltd. Lawrence L. Lapin, San Jose State University
1. a. The following following spreadsheet spreadsheet solution is obtained for for the cotton production. PROBLEM: International Textile (cotton)
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 1000 Hong 6 7 8 10 2 9 4 8 0 2000 Kor 5 6 8 11 4 9 1 7 0 1000 Nig 14 12 6 9 11 7 5 10 0 2000 Ven 4 3 5 1 9 6 11 4 0 1000 Demand 500 800 900 900 800 100 200 700 2100 Cost Solution $15,400.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 300 0 0 0 0 0 700 0 1000 Hong 0 100 0 0 800 0 0 0 1100 2000 Kor 500 300 0 0 0 0 200 0 0 1000 Nig 0 0 900 0 0 100 0 0 1000 2000 Ven 0 100 0 900 0 0 0 0 0 1000 Total 500 800 900 900 800 100 200 700 2100 Note: Two mills will operate below capacity: Hong Kong by 1,100 units and Nigeria by 1, 000 units. There are multiple optimal solutions tying the one shown. b.
The following spreadsheet solution is obtained for the polyester production.
PROBLEM: InternationalTextile Co.-Polyester
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Capacity Baha 2 2 3 3 7 4 7 1 3000 Hong 6 7 8 10 2 9 4 8 2500 Kor 5 6 8 11 4 9 1 7 3500 Nig 14 12 6 9 11 7 5 10 0 Ven 4 3 5 1 9 6 4 4 2000 Dum* 0 0 0 0 0 0 0 0 1000 Demand 1000 2000 3000 1500 400 700 900 2500 Cost Solution $40,300.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Total Baha 0 0 500 0 0 0 0 2500 3000 Hong 0 0 2100 0 400 0 0 0 2500 Kor 1000 1500 100 0 0 0 900 0 3500 Nig 0 0 0 0 0 0 0 0 0 Ven 0 500 0 1500 0 0 0 0 2000 Dum* 0 0 300 0 0 700 0 0 1000 Total 1000 2000 3000 1500 400 700 900 2500 Note: Two distribution centers will be shorted: London by 300 units and Rome by 700 units.
c.
The following spreadsheet solution is obtained for the silk production.
PROBLEM: International Textile Co.--Silk
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Capacity Baha 2 2 3 3 7 4 7 1 0 Hong 6 7 8 10 2 9 4 8 1000 Kor 5 6 8 11 4 9 1 7 500 Nig 14 12 6 9 11 7 5 10 0 Venz 4 3 5 1 9 6 11 4 0 Dum* 0 0 0 0 0 0 0 0 450 Demand 100 100 200 50 400 200 700 200 Cost Solution $5,000.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Total Baha 0 0 0 0 0 0 0 0 0 Hong 100 100 200 0 400 0 200 0 1000 Kor 0 0 0 0 0 0 500 0 500 Nig 0 0 0 0 0 0 0 0 0 Venz 0 0 0 0 0 0 0 0 0 Dum* 0 0 0 50 0 200 0 200 450 Total 100 100 200 50 400 200 700 200 Note: Three distribution centers will be shorted: Mexico City by 50 units, Rome by 200 units, and New York by 200 units. 2.
The following spreadsheet solution is obtained for silk production with the Nigeria plant activated.
PROBLEM: International Textile Co.--Silk
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 0 Hong 6 7 8 10 2 9 4 8 0 1000 Kor 5 6 8 11 4 9 1 7 0 500 Nig 14 12 6 9 11 7 5 10 0 1000 Venz 4 3 5 1 9 6 11 4 0 0 Demand 100 100 200 50 400 200 700 200 550 Cost Solution $8,050.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 0 0 0 0 0 0 0 0 0 Hong 100 100 0 0 400 0 200 200 0 1000 Kor 0 0 0 0 0 0 500 0 0 500 Nig 0 0 200 50 0 200 0 0 550 1000 Venz 0 0 0 0 0 0 0 0 0 0 Total 100 100 200 50 400 200 700 200 550 Note: The added cost of the new plant must be added to the shipping costs, so that the total cost becomes $8,050 + 2,000 = $10,050. Note also that Nigeria will operate 550 units below capacity.
3. a.
The following spreadsheet solution is obtained for the cotton production.
PROBLEM: International Textile Co.--Cotton
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 1000 Hong 6 7 8 10 2 9 4 8 0 2000 Kor 5 6 8 11 4 9 1 7 0 1000 Nig 14 12 6 9 11 7 5 10 0 2000 Venz 4 3 5 1 9 6 11 4 0 1000 Demand 500 800 900 990 880 100 200 700 1930 Cost Solution $16,010.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 300 0 0 0 0 0 700 0 1000 Hong 0 190 0 0 880 0 0 0 930 2000 Kor 500 300 0 0 0 0 200 0 0 1000 Nig 0 0 900 0 0 100 0 0 1000 2000 Venz 0 10 0 990 0 0 0 0 0 1000 Total 500 800 900 990 880 100 200 700 1930 Note: Two mills will operate below capacity: Hong Kong by 930 units and Nigeria by 1,000 units. b.
The following spreadsheet solution is obtained for the polyester production.
PROBLEM: International Textile Co.-Polyester
From To Destination Source L.A. Chic Lond MexC Man Baha 2 2 3 3 Hong 6 7 8 10 Kor 5 6 8 11 Nig 14 12 6 9 Venz 4 3 5 1 Dum* 0 0 0 0 Demand 1000 1800 3000 1500 Solution From To Destination Source L.A. Chic Lond MexC Man Baha 0 0 750 0 Hong 0 0 2100 0 Kor 1000 1300 150 0 Nig 0 0 0 0 Venz 0 500 0 1500 Dum* 0 0 0 0 Total 1000 1800 3000 1500
Rome 7 2 4 11 9 0 400
Tok
4 9 9 7 6 0 700
Rome 0 400 0 0 0 0 400
0 0 150 0 0 550 700
N.Y. 7 4 1 5 11 0 900
Tok
Capacity 1 3000 8 2500 7 3500 10 0 4 2000 0 550 2250 Cost $41,350.00
N.Y. Total 0 2250 0 0 900 0 0 0 0 0 0 0 900 2250
3000 2500 3500 0 2000 550
Note: The Rome distribution center will be shorted by 350 units. 4. To solve this problem as a transportation problem, a new source (row) must be incorporated for each mill to represent the respective overtime production; the applicable production cost must be added to the unit shipping cost. A new source (row) must be included for each distribution center, reflecting the amount to be shorted; all cost cells in these rows, except in the column of the respective destination, are given a high shipping cost to reflect the impossibility of shipments over those routes.
a.
The following spreadsheet solution is obtained for the cotton production.
PROBLEM: International Textile Co. (cotton)
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 1000 Hong 6 7 8 10 2 9 4 8 0 2000 Kor 5 6 8 11 4 9 1 7 0 1000 Nig 14 12 6 9 11 7 5 10 0 2000 Ven 4 3 5 1 9 6 11 4 0 1000 BOT 12 12 13 13 17 14 17 11 0 1000 HKOT 21 22 23 25 17 24 19 23 0 2000 KOT 10 11 13 16 9 14 6 12 0 1000 NOT 20 18 12 15 17 13 11 16 0 2000 VOT 11 10 12 8 16 13 12 17 0 1000 LASh 10 1000 1000 1000 1000 1000 1000 1000 0 500 ChSh 1000 10 1000 1000 1000 1000 1000 1000 0 800 LoSh 1000 1000 10 1000 1000 1000 1000 1000 0 900 MeSh 1000 1000 1000 10 1000 1000 1000 1000 0 900 MaSh 1000 1000 1000 1000 10 1000 1000 1000 0 800 RoSh 1000 1000 1000 1000 1000 10 1000 1000 0 100 ToSh 1000 1000 1000 1000 1000 1000 10 1000 0 200 NYSh 1000 1000 1000 1000 1000 1000 1000 10 0 700 Demand 500 800 900 900 800 100 200 700 14000 Cost Solution $15,400.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 300 0 0 0 0 0 700 0 1000 Hong 0 100 0 0 800 0 0 0 1100 2000 Kor 500 300 0 0 0 0 200 0 0 1000 Nig 0 0 900 0 0 100 0 0 1000 2000 Ven 0 100 0 900 0 0 0 0 0 1000 BOT 0 0 0 0 0 0 0 0 1000 1000 HKOT 0 0 0 0 0 0 0 0 2000 2000 KOT 0 0 0 0 0 0 0 0 1000 1000 NOT 0 0 0 0 0 0 0 0 2000 2000 VOT 0 0 0 0 0 0 0 0 1000 1000 LASh 0 0 0 0 0 0 0 0 500 500 ChSh 0 0 0 0 0 0 0 0 800 800 LoSh 0 0 0 0 0 0 0 0 900 900 MeSh 0 0 0 0 0 0 0 0 900 900 MaSh 0 0 0 0 0 0 0 0 800 800 RoSh 0 0 0 0 0 0 0 0 100 100 ToSh 0 0 0 0 0 0 0 0 200 200 NYSh 0 0 0 0 0 0 0 0 700 700 Total 500 800 900 900 800 100 200 700 14000 Note: Two mills will operate below capacity: Hong Kong by 1,100 units and Nigeria by 1,000 units. The solution is identical to that of Question 1. a., and it has multiple optimal solutions.
b.
The following spreadsheet solution is obtained for the polyester production.
PROBLEM: International Textile Co. (polyester)
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 3000 Hong 6 7 8 10 2 9 4 8 0 2500 Kor 5 6 8 11 4 9 1 7 0 3500 Nig 14 12 6 9 11 7 5 10 0 0 Ven 4 3 5 1 9 6 11 4 0 2000 BOT 12 12 13 13 17 14 17 11 0 3000 HKOT 18 19 20 22 14 21 16 20 0 2500 KOT 13 14 16 19 12 17 9 15 0 3500 NOT 1000 1000 1000 1000 1000 1000 1000 1000 0 0 VOT 10 9 11 7 15 12 11 16 0 2000 LASh 20 1000 1000 1000 1000 1000 1000 1000 0 500 ChSh 1000 20 1000 1000 1000 1000 1000 1000 0 800 LoSh 1000 1000 20 1000 1000 1000 1000 1000 0 900 MeSh 1000 1000 1000 20 1000 1000 1000 1000 0 900 MaSh 1000 1000 1000 1000 20 1000 1000 1000 0 800 RoSh 1000 1000 1000 1000 1000 20 1000 1000 0 100 ToSh 1000 1000 1000 1000 1000 1000 20 1000 0 200 NYSh 1000 1000 1000 1000 1000 1000 1000 20 0 700 Demand 1000 2000 3000 1500 400 700 900 2500 14900 Cost Solution $52,000.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 0 500 0 0 0 0 2500 0 3000 Hong 0 0 1400 0 400 700 0 0 0 2500 Kor 1000 1600 0 0 0 0 900 0 0 3500 Nig 0 0 0 0 0 0 0 0 0 0 Ven 0 400 1100 500 0 0 0 0 0 2000 BOT 0 0 0 0 0 0 0 0 3000 3000 HKOT 0 0 0 0 0 0 0 0 2500 2500 KOT 0 0 0 0 0 0 0 0 3500 3500 NOT 0 0 0 0 0 0 0 0 0 0 VOT 0 0 0 1000 0 0 0 0 1000 2000 LASh 0 0 0 0 0 0 0 0 500 500 ChSh 0 0 0 0 0 0 0 0 800 800 LoSh 0 0 0 0 0 0 0 0 900 900 MeSh 0 0 0 0 0 0 0 0 900 900 MaSh 0 0 0 0 0 0 0 0 800 800 RoSh 0 0 0 0 0 0 0 0 100 100 ToSh 0 0 0 0 0 0 0 0 200 200 NYSh 0 0 0 0 0 0 0 0 700 700 Total 1000 2000 3000 1500 400 700 900 2500 14900 Note: The Venezuela mill will operate on an overtime basis, and no customers will be shorted. This solution is different from that obtained in Question 1. b., and there are multiple optimal solutions.
c.
The following spreadsheet solution is obtained for the silk production.
PROBLEM: International Textile Co. (silk)
From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Capacity Baha 2 2 3 3 7 4 7 1 0 0 Hong 6 7 8 10 2 9 4 8 0 1000 Kor 5 6 8 11 4 9 1 7 0 500 Nig 14 12 6 9 11 7 5 10 0 0 Ven 4 3 5 1 9 6 11 4 0 0 BOT 1000 1000 1000 1000 1000 1000 1000 1000 0 0 HKOT 31 32 33 35 27 34 29 33 0 1000 KOT 27 28 30 33 26 31 23 29 0 500 NOT 1000 1000 1000 1000 1000 1000 1000 1000 0 0 VOT 1000 1000 1000 1000 1000 1000 1000 1000 0 0 LASh 50 1000 1000 1000 1000 1000 1000 1000 0 500 ChSh 1000 50 1000 1000 1000 1000 1000 1000 0 800 LoSh 1000 1000 50 1000 1000 1000 1000 1000 0 900 MeSh 1000 1000 1000 50 1000 1000 1000 1000 0 900 MaSh 1000 1000 1000 1000 50 1000 1000 1000 0 800 RoSh 1000 1000 1000 1000 1000 50 1000 1000 0 100 ToSh 1000 1000 1000 1000 1000 1000 50 1000 0 200 NYSh 1000 1000 1000 1000 1000 1000 1000 50 0 700 Demand 100 100 200 50 400 200 700 200 5950 Cost Solution $17,950.00 From To Destination Source L.A. Chic Lond MexC Man Rome Tok N.Y. Dum* Total Baha 0 0 0 0 0 0 0 0 0 0 Hong 0 0 200 50 400 200 0 150 0 1000 Kor 0 100 0 0 0 0 350 50 0 500 Nig 0 0 0 0 0 0 0 0 0 0 Ven 0 0 0 0 0 0 0 0 0 0 BOT 0 0 0 0 0 0 0 0 0 0 HKOT 0 0 0 0 0 0 0 0 1000 1000 KOT 100 0 0 0 0 0 350 0 50 500 NOT 0 0 0 0 0 0 0 0 0 0 VOT 0 0 0 0 0 0 0 0 0 0 LASh 0 0 0 0 0 0 0 0 500 500 ChSh 0 0 0 0 0 0 0 0 800 800 LoSh 0 0 0 0 0 0 0 0 900 900 MeSh 0 0 0 0 0 0 0 0 900 900 MaSh 0 0 0 0 0 0 0 0 800 800 RoSh 0 0 0 0 0 0 0 0 100 100 ToSh 0 0 0 0 0 0 0 0 200 200 NYSh 0 0 0 0 0 0 0 0 700 700 Total 100 100 200 50 400 200 700 200 5950
Note: The Korea mill will operate on an overtime basis and no distribution centers will run short. The solution differs from that of Question 1. c., and there are multiple optimal solutions. 5. It may be possible to open a transshipment center in Europe or Asia to take advantage of bulk shipping rates. Some mills might be expanded and others closed.
