Logistics Management LSM 730 Lecture 14 Dr Khurrum

Logistics Management LSM 730 Lecture 14 Dr. Khurrum S. Mughal 1 -1

COG Method appraisal · A continuous location method · Locates on the basis of transportation costs alone The COG method involves · Determining the volumes by source and destination point · Determining the transportation costs based on $/unit/mi. · Overlaying a grid to determine the coordinates of source and/or destination points · Finding the weighted center of gravity for the graph CR (2004) Prentice Hall, Inc. 13 -2

COG Method (Cont’d) where Vi = volume flowing from (to) point I Ri = transportation rate to ship Vi from (to) point i Xi, Yi = coordinate points for point i = coordinate points for facility to be located CR (2004) Prentice Hall, Inc. 13 -3

COG Method (Cont’d) Example Suppose a regional medical warehouse is to be established to serve several Veterans Administration hospitals throughout the country. The supplies originate at S 1 and S 2 and are destined for hospitals at H 1 through H 4. The relative locations are shown on the map grid. Other data are: Note rate is a per mile cost Annual Rate, Point i 1 S 1 2 S 2 3 H 1 Products A B A&B Location Seattle Atlanta Los Angeles 4 H 2 A & B Dallas 5 H 3 A & B Chicago 6 H 4 A & B New York CR (2004) Prentice Hall, Inc. volume, $/cwt/ cwt. mi. 8, 000 0. 02 10, 000 0. 02 5, 000 0. 05 3, 000 4, 000 6, 000 0. 05 Xi 0. 6 8. 6 2. 0 Yi 7. 3 3. 0 5. 5 7. 9 10. 6 2. 4 5. 5 5. 2 13 -4

COG Method (Cont’d) Map scaling factor, K CR (2004) Prentice Hall, Inc. 13 -5

COG Method (Cont’d) Solve the COG equations in table form i 1 2 3 4 5 6 Xi 0. 6 8. 6 2. 0 5. 5 7. 9 10. 6 Yi Vi Ri 7. 3 8, 000 0. 02 3. 0 10, 000 0. 02 3. 0 5, 000 0. 05 2. 4 3, 000 0. 05 5. 5 4, 000 0. 05 5. 2 6, 000 0. 05 CR (2004) Prentice Hall, Inc. V i. R i 160 200 250 150 200 300 1, 260 V i. R i. X i 96 1, 720 500 825 1, 580 3, 180 7, 901 V i. R i. Y i 1, 168 600 750 360 1, 100 1, 560 5, 538 13 -6

COG Method (Cont’d) Now, X = 7, 901/1, 260 = 6. 27 Y = 5, 538/1, 260 = 4. 40 This is approximately Columbia, MO. The total cost for this location is found by: where K is the map scaling factor to convert coordinates into miles. CR (2004) Prentice Hall, Inc. 13 -7

COG Method (Cont’d) CR (2004) Prentice Hall, Inc. COG 13 -8

COG Method (Cont’d) Calculate total cost at COG i Xi Yi Vi Ri TC 1 0. 6 7. 3 8, 000 0. 02 509, 482 2 8. 6 3. 0 10, 000 0. 02 271, 825 3 2. 0 3. 0 5, 000 0. 05 561, 706 4 5. 5 2. 4 3, 000 0. 05 160, 733 5 7. 9 5. 5 4, 000 0. 05 196, 644 6 10. 6 5. 2 6, 000 0. 05 660, 492 Total 2, 360, 882 CR (2004) Prentice Hall, Inc. 13 -9

Example • The firm is considering 2 alternative sites for its new facility, France and Denmark • After evaluating the firm’s Needs, the Managers have Narrowed the list of Important Selection Criteria down into 5 major Factors. – Labor availability and attitude – People to car ratio – Per capita income – Tax structure – Education and Health

Factor Rating Example • Since factor weights, selected factors, and assigned scores are all determined subjectively, the managers should be very careful in selecting these items and numbers.