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ESTUDIO DE CASO SPECIALTY PACKAGING CORPORATION

DATOS

Año

2002

2003

2004

2005

2006

Trimestre

Demanda de plástico oscuro (000 lb)

Demanda de plástico claro (000 lb)

I II III IV I II III IV I II III IV I II III IV I II III IV

2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097

3,200 4,658 4,420 2,384 3,654 8,680 5,695 1,953 4,742 13,673 6,640 2,737 3,486 13,186 5,448 3,485 7,728 16,591 8,236 3,316

METODO 1: Mínimos Cuadrados

PRODUCTO: PLASTICO OSCURO

Año

Trimestre x (Periodo)

I II 2002 III IV I II 2003 III IV I II 2004 III IV I II 2005 III IV I II 2006 III IV SUMATORIAS

a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210

Y (Demanda de plástico oscuro (000 lb)) 2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097 101,042

Y  b  X b= 286.61

Estimación de la ecuación.

Y  2042.74  286.61X

X^2

Y^2

2,250 3,474 7,236 29,076 17,570 12,858 24,213 56,448 37,080 27,660 28,116 99,036 71,383 61,348 64,725 192,560 96,016 66,528 92,017 261,940 1,251,534

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 2,870

5,062,500 3,017,169 5,817,744 52,838,361 12,348,196 4,592,449 11,964,681 49,787,136 16,974,400 7,650,756 6,533,136 68,112,009 30,151,081 19,201,924 18,619,225 144,841,225 31,899,904 13,660,416 23,454,649 171,531,409 698,058,370

b

N

a= 2042.74

XY

N  XY   X Y N X 2   X 

2

PRODUCTO: PLASTICO CLARO

Año

Trimestre X (Periodo) Demanda de plástico XY claro (000 lb) I 1 3,200 3,200 II 2 4,658 9,316 2002 III 3 4,420 13,260 IV 4 2,384 9,536 I 5 3,654 18,270 II 6 8,680 52,080 2003 III 7 5,695 39,865 IV 8 1,953 15,624 I 9 4,742 42,678 II 10 13,673 136,730 2004 III 11 6,640 73,040 IV 12 2,737 32,844 I 13 3,486 45,318 II 14 13,186 184,604 2005 III 15 5,448 81,720 IV 16 3,485 55,760 I 17 7,728 131,376 II 18 16,591 298,638 2006 III 19 8,236 156,484 IV 20 3,316 66,320 SUMATORIAS 210 123,912 1,466,663

a

Y  b  X

b

N

a= 3581.07

b= 249.00

Estimación de la ecuación.

Y  3581.07  249 X

X^2

Y^2

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 2,870

10,240,000 21,696,964 19,536,400 5,683,456 13,351,716 75,342,400 32,433,025 3,814,209 22,486,564 186,950,929 44,089,600 7,491,169 12,152,196 173,870,596 29,680,704 12,145,225 59,721,984 275,261,281 67,831,696 10,995,856 1,084,775,970

N  XY   X Y N X 2   X 

2

Calculo de MSE para los pronósticos: Año

2002

2003

2004

2005

2006

Trimestre Periodo Demanda de plástico oscuro Pronostico Error2 (000 lb) (Yt) 2002 - I 1 2,250 2,329.34 6,295.29 2002 - II 2 1,737 2,615.95 772,551.12 2002 - III 3 2,412 2,902.55 240,644.10 2002 - IV 4 7,269 3,189.16 16,645,087.06 2003 - I 5 3,514 3,475.77 1,461.77 2003 - II 6 2,143 3,762.37 2,622,368.69 2003 - III 7 3,459 4,048.98 348,075.16 2003 - IV 8 7,056 4,335.58 7,400,657.98 2004 - I 9 4,120 4,622.19 252,195.78 2004 - II 10 2,766 4,908.80 4,591,578.95 2004 - III 11 2,556 5,195.40 6,966,448.24 2004 - IV 12 8,253 5,482.01 7,678,391.00 2005 - I 13 5,491 5,768.62 77,070.11 2005 - II 14 4,382 6,055.22 2,799,668.69 2005 - III 15 4,315 6,341.83 4,108,027.96 2005 - IV 16 12,035 6,628.43 29,230,965.83 2006 - I 17 5,648 6,915.04 1,605,388.08 2006 - II 18 3,696 7,201.65 12,289,547.66 2006 - III 19 4,843 7,488.25 6,997,353.53 2006 - IV 20 13,097 7,774.86 28,325,204.59 TOTAL 132,958,981.58 MSE 6,647,949.08

Año

2002

2003

2004

2005

2006

Trimestre Periodo Demanda de plástico claro Pronostico (000 lb) (Yt) 2002 - I 1 3,200 3,830.07 2002 - II 2 4,658 4,079.07 2002 - III 3 4,420 4,328.08 2002 - IV 4 2,384 4,577.08 2003 - I 5 3,654 4,826.08 2003 - II 6 8,680 5,075.09 2003 - III 7 5,695 5,324.09 2003 - IV 8 1,953 5,573.09 2004 - I 9 4,742 5,822.10 2004 - II 10 13,673 6,071.10 2004 - III 11 6,640 6,320.10 2004 - IV 12 2,737 6,569.10 2005 - I 13 3,486 6,818.11 2005 - II 14 13,186 7,067.11 2005 - III 15 5,448 7,316.11 2005 - IV 16 3,485 7,565.12 2006 - I 17 7,728 7,814.12 2006 - II 18 16,591 8,063.12 2006 - III 19 8,236 8,312.13 2006 - IV 20 3,316 8,561.13 TOTAL MSE

Error2 396,990.01 335,154.81 8,449.76 4,809,601.87 1,373,779.63 12,995,401.59 137,574.62 13,105,069.57 1,166,606.26 57,788,906.47 102,335.05 14,685,024.99 11,102,940.52 37,440,808.39 3,489,848.18 16,647,350.99 7,416.58 72,724,693.69 5,795.10 27,511,373.73 275,835,121.79 13,791,756.09

METODO 2: Promedio Móvil Se escogerá un intervalo de 2 periodos para el cálculo del promedio.

Año

2002

2003

2004

2005

2006

Trimestre

Periodo

Demanda de plástico oscuro (000 lb)

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097

Media Móvil

Error2

1,994 175,142.25 2,075 26,982,830.25 4,841 1,759,602.25 5,392 10,552,752.25 2,829 397,530.25 2,801 18,105,025.00 5,258 1,293,906.25 5,588 7,963,684.00 3,443 786,769.00 2,661 31,270,464.00 5,405 7,482.25 6,872 6,200,100.00 4,937 386,262.25 4,349 59,082,282.25 8,175 6,385,729.00 8,842 26,476,170.25 4,672 29,241.00 4,270 77,924,756.25 TOTAL 275,779,728.75 MSE 15,321,096.04

Año

2002

2003

2004

2005

2006

Trimestre

Periodo

Demanda de plástico claro (000 lb)

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3,200 4,658 4,420 2,384 3,654 8,680 5,695 1,953 4,742 13,673 6,640 2,737 3,486 13,186 5,448 3,485 7,728 16,591 8,236 3,316

Media Móvil

Error2

3,929 241,081.00 4,539 4,644,025.00 3,402 63,504.00 3,019 32,046,921.00 6,167 222,784.00 7,188 27,399,990.25 3,824 842,724.00 3,348 106,615,950.25 9,208 6,592,056.25 10,157 55,048,980.25 4,689 1,446,006.25 3,112 101,495,550.25 8,336 8,340,544.00 9,317 34,012,224.00 4,467 10,637,382.25 5,607 120,659,240.25 12,160 15,393,852.25 12,414 82,764,506.25 TOTAL 608,467,321.50 MSE 33,803,740.08

METODO 3: Promedio Móvil Ponderado Se escogerá un intervalo de 2 periodos para el cálculo del promedio.

Año

2002

2003

2004

2005

2006

Trimestre

Periodo

Demanda de plástico oscuro (000 lb)

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097

Media Móvil Ponderado

Error2

1,908 254,016.00 2,142 26,286,129.00 5,187 2,800,363.18 5,183 9,240,924.46 2,766 479,997.03 2,852 17,676,849.99 5,377 1,581,054.76 5,502 7,483,764.83 3,407 724,828.19 2,656 31,326,409.00 5,528 1,394.86 6,817 5,928,056.26 4,916 361,156.48 4,347 59,100,042.05 8,300 7,030,537.78 8,745 25,489,647.07 4,644 39,555.53 4,285 77,651,344.00 TOTAL 273,456,070.48 MSE 15,192,003.92

Año

2002

2003

2004

2005

2006

Trimestre

Periodo

Demanda de plástico claro (000 lb)

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3,200 4,658 4,420 2,384 3,654 8,680 5,695 1,953 4,742 13,673 6,640 2,737 3,486 13,186 5,448 3,485 7,728 16,591 8,236 3,316

Media Móvil Ponderado

Error2

4,172 61,504.00 4,515 4,542,013.44 3,257 157,949.47 3,090 31,253,069.09 6,395 490,636.57 7,073 26,211,249.33 3,699 1,087,292.80 3,430 104,928,689.69 9,443 7,854,153.75 9,989 52,592,194.67 4,604 1,249,146.38 3,126 101,193,942.63 8,516 9,410,351.54 9,184 32,473,884.76 4,435 10,844,911.28 5,671 119,251,032.77 12,286 16,403,425.73 12,301 80,722,940.03 TOTAL 600,728,387.93 MSE 33,373,799.33

METODO 4: Suavización Exponencial Se utiliza un α=0.20

Año

2002

2003

2004

2005

2006

Trimestre 2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

Ft 1  Yt  (1  )Ft Periodo

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Yt (Demanda de plástico Ft(Pronostico) oscuro (000 lb)) 2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097

Error2

2,250 2,147 168,428.16 2,200 44,808.42 3,214 16,442,570.84 3,274 57,578.50 3,048 818,727.90 3,130 108,195.82 3,915 9,864,279.55 3,956 26,829.15 3,718 906,614.68 3,486 864,398.85 4,439 14,545,189.26 4,650 708,042.25 4,596 45,812.28 4,540 50,548.72 6,039 35,953,642.86 5,961 97,775.96 5,508 3,282,449.58 5,375 282,813.94 6,919 38,164,693.49 TOTAL 122,433,400.20 MSE 6,121,670.01

Año

2002

2003

2004

2005

2006

Trimestre

Periodo

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Yt (Demanda de plástico Ft(Pronostico) claro (000 lb)) 3,200 4,658 4,420 2,384 3,654 8,680 5,695 1,953 4,742 13,673 6,640 2,737 3,486 13,186 5,448 3,485 7,728 16,591 8,236 3,316

Error2

3,200 3,492 1,360,488.96 3,677 551,633.00 3,419 1,070,446.82 3,466 35,457.19 4,509 17,400,917.01 4,746 900,890.49 4,187 4,991,998.14 4,298 196,938.57 6,173 56,247,331.32 6,267 139,470.63 5,561 7,972,908.20 5,146 2,754,627.63 6,754 41,373,638.43 6,493 1,091,215.36 5,891 5,789,269.24 6,258 2,159,512.47 8,325 68,327,125.99 8,307 5,066.89 7,309 15,943,615.18 TOTAL 228,312,551.52 MSE 11,415,627.58

ELECCION DE METODOS DE PRONOSTICOS Se elegirá el método de pronóstico que tenga el menor grado de error (MSE menor), para pronosticar los valores de la demanda para el periodo de tiempo de 2007 – 2009.

MSE MODELO Mínimos Cuadrados

Plástico Oscuro Plástico Claro 6,647,949.08 13,791,756.09

Promedio Móvil

15,321,096.04 33,803,740.08

Promedio Móvil Ponderado

15,192,003.92 33,373,799.33

Suavización Exponencial

6,121,670.01 11,415,627.58

Se tiene que el método de pronóstico elegido para pronosticar la demanda del Plástico Oscuro y el Plástico Claro es la Suavización Exponencial, por tener los menores valores del error.

PRONOSTICO DE LA DEMANDA PARA LOS AÑOS 2007 – 2009:

PLASTICO OSCURO Año Trimestre Periodo Yt (Demanda de plastico oscuro (000 lb))

2002

2003

2004

2005

2006

2007

2008

2009

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV 2007 - I 2007 - II 2007 - III 2007 - IV 2008 - I 2008 - II 2008 - III 2008 - IV 2009 - I 2009 - II 2009 - III 2009 - IV

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

2,250 1,737 2,412 7,269 3,514 2,143 3,459 7,056 4,120 2,766 2,556 8,253 5,491 4,382 4,315 12,035 5,648 3,696 4,843 13,097

Ft(Pronostico) 2,250.00 2,147.40 2,200.32 3,214.06 3,274.04 3,047.84 3,130.07 3,915.25 3,956.20 3,718.16 3,485.73 4,439.18 4,649.55 4,596.04 4,539.83 6,038.86 5,960.69 5,507.75 5,374.80 6,919.24 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39 5,535.39

PLASTICO CLARO Año Trimestre Periodo Yt (Demanda de plástico Ft(Pronostico) claro (000 lb))

2002

2003

2004

2005

2006

2007

2008

2009

2002 - I 2002 - II 2002 - III 2002 - IV 2003 - I 2003 - II 2003 - III 2003 - IV 2004 - I 2004 - II 2004 - III 2004 - IV 2005 - I 2005 - II 2005 - III 2005 - IV 2006 - I 2006 - II 2006 - III 2006 - IV 2007 - I 2007 - II 2007 - III 2007 - IV 2008 - I 2008 - II 2008 - III 2008 - IV 2009 - I 2009 - II 2009 - III 2009 - IV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

3,200 4,658 4,420 2,384 3,654 8,680 5,695 1,953 4,742 13,673 6,640 2,737 3,486 13,186 5,448 3,485 7,728 16,591 8,236 3,316

3,200.00 3,491.60 3,677.28 3,418.62 3,465.70 4,508.56 4,745.85 4,187.28 4,298.22 6,173.18 6,266.54 5,560.63 5,145.71 6,753.77 6,492.61 5,891.09 6,258.47 8,324.98 8,307.18 7,308.95 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16 5,847.16