Location A. A. Elimam This presentation covers the quantitative material in Chapter 8. This slide can be used to introduce the material and basic concepts. 1

Location Methods Preference Matrix Center of Gravity Load Distance Break-even Analysis Transportation Models

Location Health-Watch Erie A(50, 185) North 50 100 150 200 y (miles) 50 100 150 200 y (miles) Scranton State College B (175, 100) Pittsburgh Harrisburg The next 12 slides develop the single facility problem on pages 351-353. This uses two different methods of calculating distance, Euclidean and rectilinear. This map establishes the basics of the problem with coordinates assigned for the two points of interest, Erie and State College. Philadelphia Uniontown x (miles) 50 100 150 200 250 300 East

Location Health-Watch Erie A(50, 185) North 200 150 Scranton State College B (175, 100) y (miles) 100 Pittsburgh Harrisburg The first problem will be to calculate the distance between the two cities using the Euclidean measure. 50 Philadelphia Uniontown 50 100 150 200 250 300 x (miles) East

Location Health-Watch Euclidean distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) Euclidean distance dAB = ( xA - xB )2 + ( yA - yB )2 The worksheet shows the basic equation we will use.

Location Health-Watch Euclidean distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) Euclidean distance dAB = (50 - 175 )2 + (185 - 100 )2 The actual coordinates are substituted in the equation. This slide will automatically advance.

Location Health-Watch Euclidean distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) Euclidean distance dAB = (50 - 175 )2 + (185 - 100 )2 The arrows disappear leaving just the equation.

Location Health-Watch Euclidean distance dAB = 151.2 miles Erie Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) Euclidean distance dAB = 151.2 miles The equation is solved for the distance.

Location Health-Watch 151.2 miles Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) 151.2 miles The distance is shown on the map next to the related line and the rectilinear line is added to the map.

Location Health-Watch Rectilinear distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) 151.2 miles Rectilinear distance dAB = | xA - xB | + | yA - yB | The rectilinear equation is added to the worksheet.

Location Health-Watch Rectilinear distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) 151.2 miles Rectilinear distance dAB = | 50 - 175 | + | 185 - 100 | The data is substituted into the equation. The arrows will disappear automatically.

Location Health-Watch Rectilinear distance Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) 151.2 miles Rectilinear distance dAB = | 50 - 175 | + | 185 - 100 |

Location Health-Watch Rectilinear distance dAB = 210 miles 151.2 miles Erie A(50, 185) Pittsburgh Harrisburg Philadelphia Scranton Uniontown North 50 100 150 200 y (miles) x (miles) 250 300 East State College B (175, 100) 151.2 miles Rectilinear distance dAB = 210 miles The equation is solved for the relevant distance.

Location Health-Watch 151.2 miles 210 miles Erie A(50, 185) North 50 50 100 150 200 y (miles) 151.2 miles Scranton 210 miles State College B (175, 100) Pittsburgh Harrisburg The worksheet is removed and the rectilinear distance is added to the map. The authors make the point that while neither of these is likely to be the true distance one would travel, as long as one measure is used consistently, the relative distances should allow a comparison between alternatives. The following example shows how this is applied, though using a different measure. It is important to select a technique that best approximates reality. For example, modern highways might allow cross-country distances to be best approximated using Euclidean measures while distance within a city might require a rectilinear model since straight (or essentially straight) paths are generally not likely. Philadelphia Uniontown x (miles) 50 100 150 200 250 300 East

Location Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F (2.5, 2.5) (9, 2.5) Within Erie the firm needs to select between several different alternatives. They are shown here with their coordinates and population. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld (2.5, 2.5) (9, 2.5) A worksheet is added to evaluate the distance between location A and C. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 (2.5, 2.5) (9, 2.5) The coordinates and population (load) are added to the worksheet. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 (2.5, 2.5) (9, 2.5) A ‘post-it’ note is added for the simple calculations. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 5.5 - 2.5 = 3 Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 5.5 - 2.5 = 3 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 (2.5, 2.5) (9, 2.5) The arrows show the source of the data. These will change with an advance but remain in place to allow for discussion. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 5.5 - 2.5 = 3 4.5 - 4.5 = 0 (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 5.5 - 2.5 = 3 4.5 - 4.5 = 0 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 (2.5, 2.5) (9, 2.5) The arrows shift to show the next set of data. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 5.5 - 2.5 = 3 4.5 - 4.5 = 0 (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 5.5 - 2.5 = 3 4.5 - 4.5 = 0 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 (2.5, 2.5) (9, 2.5) The resulting values are placed on the master worksheet and the distance is calculated. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 2 * 3 = 6 Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 2 * 3 = 6 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 (2.5, 2.5) (9, 2.5) Finally the ld score is calculated for location A. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 (2.5, 2.5) (9, 2.5) The ‘post-it’ note is cleared to allow the next set of calculations. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 E (8, 5) 10 (2.5, 2.5) (9, 2.5) Location E will be the next location evaluated. The book, of course, progresses in alpha order. However, the order has been modified here to avoid a messy set of movements with the worksheets. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 8 - 5.5 = 2.5 5 - 4.5 = 0.5 (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 8 - 5.5 = 2.5 5 - 4.5 = 0.5 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 E (8, 5) 10 2.5 + 0.5 = 3 (2.5, 2.5) (9, 2.5) The arrows show, in an aggregated fashion, the source of the data, the calculations, and the destination of the results. This is the same process used for location A. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch 10 * 3 = 30 Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] 10 * 3 = 30 [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 E (8, 5) 10 2.5 + 0.5 = 3 30 (2.5, 2.5) (9, 2.5) Again the ld score is calculated and added to the worksheet. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Census Population Distance (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F Census Population Distance Tract (x,y) (l) (d) ld A (2.5, 4.5) 2 3 + 0 = 3 6 E (8, 5) 10 2.5 + 0.5 = 3 30 (2.5, 2.5) (9, 2.5) The ‘post-it’ note is removed. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Tract ld A 6 B 25 C 0 D 21 E 30 F 80 G 77 (a) Locate at C (5.5, 4.5) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) Tract ld A 6 B 25 C 0 D 21 E 30 F 80 G 77 Total 239 [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F (2.5, 2.5) (9, 2.5) A new ‘post-it’ note is added which contains the ld scores for all seven locations. Of course, C will have a zero score. The student should understand we are evaluating location C as highlighted at the top left of the screen, not the other locations. The total of 239 is neither good or bad by itself, it only is relevant in comparison to the ld score of other location alternatives. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch (b) Locate at F (7, 2) North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F (2.5, 2.5) (9, 2.5) This series of slides will evaluate location F in the same manner as we did for location C, but without going through all the calculations. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch (b) Locate at F (7, 2) North 1 2 3 4 5 6 y (miles) (5.5, 4.5) [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F (2.5, 2.5) (9, 2.5) The distances we are concerned with are shown in this slide. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Tract ld A 14 B 25 C 40 D 14 E 40 F 0 G 35 (b) Locate at F (7, 2) Health-Watch North 1 2 3 4 5 6 y (miles) (5.5, 4.5) Tract ld A 14 B 25 C 40 D 14 E 40 F 0 G 35 Total 168 [10] E A C (8, 5) (2.5, 4.5) [10] [2] B G D F (2.5, 2.5) (9, 2.5) The individual and total ld scores are shown on the ‘post-it’ note. Notice the total ld score for F is considerably lower than for C, suggesting this is a preferred location, all other things being equal. [5] (5, 2) (7, 2) [14] [7] [20] x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Alternative Locations North 1 2 3 4 5 6 y (miles) The preceding examples concerned just seven sites in the metropolitan area. But the same process would apply with more areas. This slide cleans off the map. x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Alternative Locations North 1 2 3 4 5 6 y (miles) 391 283 233 253 355 247 197 331 233 223 173 This slide adds in 15 new locations and the ld scores calculated for each of these alternatives. 326 228 218 168 x (miles) East 1 2 3 4 5 6 7 8 9 10

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Instead of evaluating all possible locations, you can also find the theoretically ‘best’ location and simply select the alternative closest to it. That is what this example shows. The examples so far have assumed we had locations that we needed to evaluate. But we may be in the position of having to determine where to look for locations with none in hand. The center of gravity approach can be used in such situation. Though the map would look the same, the locations would be the population centers of the regions, not specific locations.

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 B (2.5, 2.5) 5 C (5.5, 4.5) 10 D (5, 2) 7 E (8, 5) 10 F (7, 2) 20 G (9, 2.5) 14 Adding in a worksheet, the basic data is displayed.

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 B (2.5, 2.5) C (5.5, 4.5) D (5, 2) E (8, 5) F (7, 2) G (9, 2.5) The arrows show the source of the data for each calculation. This slide will advance automatically.

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) C (5.5, 4.5) D (5, 2) E (8, 5) F (7, 2) G (9, 2.5) This slide will advance automatically.

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) C (5.5, 4.5) D (5, 2) E (8, 5) F (7, 2) G (9, 2.5)

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 The remainder of the calculations are performed and the results added to the worksheet. This slide advances automatically.

Location Health-Watch Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 Finally, the totals are calculated.

Location Health-Watch x* = y* = Center of Gravity Approach North B A C D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) x* = y* = Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 A small worksheet is added for the calculation of the actual coordinates. This slide advances automatically.

Location Health-Watch 453.5 x* = 68 205.5 y* = Center of Gravity Approach Health-Watch North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) 453.5 68 205.5 x* = y* = Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 The arrows show the source of the data. This slide advances automatically.

Location Health-Watch 453.5 x* = 68 205.5 y* = Center of Gravity Approach Health-Watch North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) 453.5 68 205.5 x* = y* = Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 This slide advances automatically.

Location Health-Watch x* = 6.67 y* = 2.96 Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) x* = 6.67 y* = 2.96 Census Population Tract (x,y) (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40 G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 The actual coordinates of the center of gravity are calculated.

Location Health-Watch x* = 6.67 y* = 2.96 Center of Gravity Approach North B A C E G F D (2.5, 4.5) [2] (2.5, 2.5) [5] (5, 2) [7] (7, 2) [20] (9, 2.5) [14] (8, 5) [10] (5.5, 4.5) x (miles) East 1 2 3 4 5 6 7 8 9 10 y (miles) x* = 6.67 y* = 2.96 The large worksheet is removed to show that location F is the closest to the desirable location.

Location Break-Even Analysis Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 B $300,000 $38 C $500,000 $24 D $600,000 $30 To present the break-even analysis, the basic data is displayed.

Location Break-Even Analysis For 20,000 units Total Variable Costs Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 B $300,000 $38 C $500,000 $24 D $600,000 $30 A small worksheet is added to calculate the costs. Total Variable Costs

Location Break-Even Analysis For 20,000 units Total Variable Costs Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 B $300,000 $38 C $500,000 $24 D $600,000 $30 Arrows show the source of the data. This slide advances automatically. Total Variable Costs $62 (20,000)

Location Break-Even Analysis For 20,000 units Total Variable Costs Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 B $300,000 $38 C $500,000 $24 D $600,000 $30 The total variable cost is calculated. Total Variable Costs $62 (20,000) = $1,240,000

Location Break-Even Analysis For 20,000 units Total Variable Costs Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 $1,390,000 B $300,000 $38 C $500,000 $24 D $600,000 $30 Arrows show the source and results of the total cost calculation. This slide advances automatically. Total Variable Costs $62 (20,000) = $1,240,000

Location Break-Even Analysis For 20,000 units Total Variable Costs Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 $1,390,000 B $300,000 $38 C $500,000 $24 D $600,000 $30 Total Variable Costs $62 (20,000) = $1,240,000

Location Break-Even Analysis For 20,000 units Fixed Costs Variable Costs Total Costs Community per Year per Unit (Fixed + Variable) A $150,000 $62 $1,390,000 B $300,000 $38 $1,060,000 C $500,000 $24 $ 980,000 D $600,000 $30 $1,200,000 The worksheet is removed and the remaining totals are added to the data set.

Location Break-Even Analysis 200 400 600 800 1000 1200 1400 1600 2 4 6 Fixed Costs Total Costs Community per Year (Fixed + Variable) A $150,000 $1,390,000 B $300,000 $1,060,000 C $500,000 $ 980,000 D $600,000 $1,200,000 Break-Even Analysis Q (thousands of units) 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 14 16 18 20 22 Annual cost (thousands of dollars) Taking only the necessary information and placing it in the corner, the coordinates are drawn for the graph.

Location Break-Even Analysis 200 400 600 800 1000 1200 1400 1600 2 4 6 Fixed Costs Total Costs Community per Year (Fixed + Variable) A $150,000 $1,390,000 B $300,000 $1,060,000 C $500,000 $ 980,000 D $600,000 $1,200,000 Break-Even Analysis Q (thousands of units) 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 14 16 18 20 22 Annual cost (thousands of dollars) A (20, 1390) (20, 1200) D (20, 1060) B C (20, 980) The four total cost lines are added to the graph.

Location Break-Even Analysis 200 400 600 800 1000 1200 1400 1600 2 4 6 Fixed Costs Total Costs Community per Year (Fixed + Variable) A $150,000 $1,390,000 B $300,000 $1,060,000 C $500,000 $ 980,000 D $600,000 $1,200,000 Break-Even Analysis Q (thousands of units) 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 14 16 18 20 22 Annual cost (thousands of dollars) A (20, 1390) (20, 1200) D (20, 1060) B C (20, 980) The first break-even point occurs where A and B intersect and is shown here. Break-even point A best

Location Break-Even Analysis A D B C (20, 1390) (20, 1200) (20, 1060) (20, 980) A best 6.25 Break-even point Q (thousands of units) 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 14 16 18 20 22 Annual cost (thousands of dollars) Fixed Costs Total Costs Community per Year (Fixed + Variable) A $150,000 $1,390,000 B $300,000 $1,060,000 C $500,000 $ 980,000 D $600,000 $1,200,000 Break-Even Analysis Break-even point The second break-even point occurs where B and C intersect and is shown here. B best 14.3

Location Break-Even Analysis A D B C (20, 1390) (20, 1200) (20, 1060) A best 6.25 Break-even point Q (thousands of units) 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 14 16 18 20 22 Annual cost (thousands of dollars) Fixed Costs Total Costs Community per Year (Fixed + Variable) A $150,000 $1,390,000 B $300,000 $1,060,000 C $500,000 $ 980,000 D $600,000 $1,200,000 Break-Even Analysis (20, 980) Break-even point Beyond the second break-even point, C will remain the best alternative. B best C best 14.3

Location Break-Even Analysis 200 400 600 800 1000 1200 1400 1600 A (20, 1390) (20, 1200) D (20, 1060) B C Annual cost (thousands of dollars) (20, 980) Break-even point The data is removed for a clean view of the graph. Break-even point A best B best C best 2 4 6 8 10 12 14 16 18 20 22 6.25 14.3 Q (thousands of units)

Transportation Models: least cost location Several customer location Existing serving facilities - short of capacity Need to add one more facility Identify candidate locations for new facility Estimate the (Production + Shipping Cost) from candidate location to customers

Transportation Models: least cost location Formulate a Transportation Model sources: Existing Facilities + one of the new locations Destinations: customers Solution: Total production & shipping cost Repeat the above for each candidate location Select the location with the least cost