Speciality Packaging Case study

8/12/2019 Speciality Packaging Case study

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DEMAND FORECASTING

GROUP 9 MPE year II (2013-14 batch)

Jayant Iyer (Roll No: 16)

Mugdha Khandekar (Roll No: 22

Mrinal Singh (Roll No: 51)

Ruth Sequeira (Roll No: 45)Vinayak Srivastava (Roll No: 52)


2/20

SPC is into the business of supply of recyclable/disposable containers for the food

industry.

Food containers manufacturing is a two-step process. First polystyrene sheet get wound

into rolls and secondly rolls are loaded into transformation process to convert into

container.

Plastic for containers are either clear or black.

Demand for containers made from clear black plastic & are seasonal in nature.

Capacity on extruders is not sufficient to cover demand for sheets during peak seasons

and therefore company need to build inventory of sheet in anticipation of future

demand.

Julie Williams is about to be assigned to a team who will be responsible for developing

the demand forecasting model.


3/20

As demand for containers is seasonal and not linear, using the nave or

moving average methods will not be suitable for SPC. Seasonality of demand also can be noticed from following graph where it can

be seen that demand is highest in Q4 and then it goes to least in Q2. Howeverannual sales is growing year over year.

0

2000

4000

6000

8000

10000

12000

14000

0 5 10 15 20 25

Black Plastic

Black Plastic

Linear (Black Plastic)


4/20

As demand for containers is seasonal and not linear, using the nave ormoving average methods will not be suitable for SPC.

Seasonality of demand also can be noticed from following graph where it canbe seen that demand is highest in Q2 and then it goes to least in Q4. Howeverannual sales is growing year over year so there is trend also.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25

Clear Plastic

Clear Plastic

Linear (Clear Plastic)


5/20

Looking at the demand for containers Julie Williams & team can evaluate fromthe following four methods:

Static Regression Method

Trend & Seasonality Corrected Exponential Smoothing Method Trend Corrected Exponential Smoothing Method Simple Exponential Smoothing Method


6/20

In this first de-seasonalized demand has been computed for T3 to T18 usingfollowing formulae:

Herep is number of periods in a year which is 4 in this case.

Intercept and slope has been computed using excel formulae for deseasonalizeddemand of T3 to T18 with respect to T.

Using intercept and slope deasonalized demand has been computed for eachperiod using following formulae:

Intercept + Slope*t Seasonal factors has been computed for each period i.e. actual

demand/deseasonalized demand. Average of seasonal factors has been computed for each quarters. Forecast for each period has been computed using following formulae

Ft = (Intercept + Slope*t)*Season Factor of Quarter

MSE, MAD, MAPE & TS has been computed for forecast demand.


7/20

Level for Period 0 has been computed by taking average of actual demand.

Level for succeeding period has been computed using following formulae:Lt= D* + (1-)*Lt-1

Forecast of each period is equal to Level of immediately preceding period.



8/20

Level for Period 0 has been computed by computing interceptof deseaonalized demandcomputed under static method. Similarly Trend for Period 0 has been computed by

computing slopeof deseasonalized demand.

For all four periods of first year seasonal factor has been taken same which was computedunder static method.

Level for succeeding period has been computed using following formulae:

Lt= D/Seasonal Factor* + (1-)*(Lt-1+TRt-1)

Trend for succeeding period has been computed using following formulae:

TRt= (Lt - Lt -1)* + (1-)*TRt-1 Seasonal factors for 2ndyear onward has been computed using following formulae:

S5= D1/Seasonal Factor of Period 1* + (1-)*Seasonal Factor of Period1 In similar way S6, S7. Can be computed by dragging the formulae up to Perio 20.

Forecast of each period will be computed by following formulae:Ft=(Lt-1+TRt-1)*St



9/20

Level for Period 0 has been computed by computing interceptof actual demand. SimilarlyTrend for Period 0 has been computed by computing slopeof actual demand.

Level for succeeding period has been computed using following formulae:Lt= D* + (1-)*Lt-1

Trend for succeeding period has been computed using following formulae:

TRt= (Lt - Lt -1)* + (1-)*TRt-1 Forecast of each period is equal to sum of Leveland Trendof immediately

preceding period.



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Intercept Slope

2,592.75 226.86

Time

Period

Black

Plastic

Deseason

lized

Demand

Deseason

lized

Demand

Seasonal

FactorForecast Error Abs. Errror MSE MAD % Error MAPE TS

01 2250 2,819.60 0.80 2,535.61 285.61 285.61 81,573.45 285.61 12.69 12.69 1.00

2 1737 3,046.46 0.57 1,824.45 87.45 87.45 44,610.42 186.53 5.03 8.86 2.00

3 2412 3,575 3,273.32 0.74 2,283.37 (128.63) 128.63 35,255.80 167.23 5.33 7.69 1.46

4 7269 3,784 3,500.17 2.08 6,301.32 (967.68) 967.68 260,542.20 367.34 13.31 9.09 (1.97)

5 3514 3,965 3,727.03 0.94 3,351.64 (162.36) 162.36 213,706.06 326.35 4.62 8.20 (2.71)

6 2143 4,070 3,953.88 0.54 2,367.88 224.88 224.88 186,517.11 309.44 10.49 8.58 (2.14)

7 3459 4,119 4,180.74 0.83 2,916.36 (542.64) 542.64 201,937.57 342.75 15.69 9.60 (3.51)

8 7056 4,272 4,407.59 1.60 7,934.95 878.95 878.95 273,263.80 409.78 12.46 9.95 (0.79)

9 4120 4,237 4,634.45 0.89 4,167.66 47.66 47.66 243,153.59 369.54 1.16 8.98 (0.75)

10 2766 4,274 4,861.31 0.57 2,911.32 145.32 145.32 220,949.92 347.12 5.25 8.60 (0.38)

11 2556 4,595 5,088.16 0.50 3,549.35 993.35 993.35 290,567.48 405.87 38.86 11.36 2.12

12 8253 4,969 5,315.02 1.55 9,568.57 1,315.57 1,315.57 410,580.97 481.68 15.94 11.74 4.52

13 5491 5,390 5,541.87 0.99 4,983.69 (507.31) 507.31 398,794.86 483.65 9.24 11.55 3.45

14 4382 6,083 5,768.73 0.76 3,454.75 (927.25) 927.25 431,723.27 515.33 21.16 12.23 1.44

15 4315 6,575 5,995.59 0.72 4,182.34 (132.66) 132.66 404,114.95 489.82 3.07 11.62 1.25

16 12035 6,509 6,222.44 1.93 11,202.20 (832.80) 832.80 422,205.32 511.26 6.92 11.33 (0.44)

17 5648 6,490 6,449.30 0.88 5,799.72 151.72 151.72 398,723.75 490.11 2.69 10.82 (0.14)

18 3696 6,688 6,676.15 0.55 3,998.18 302.18 302.18 381,645.48 479.67 8.18 10.67 0.48

19 4843 6,903.01 0.70 4,815.33 (27.67) 27.67 361,599.16 455.88 0.57 10.14 0.45

20 13097 7,129.87 1.84 12,835.82 (261.18) 261.18 346,929.90 446.14 1.99 9.73 (0.13)

Seasonal Factor

QtrsSeasonal Factor(Static

Method)

Q1 0.90

Q2 0.60

Q3 0.70

Q4 1.80


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Time

Period

Black

PlasticLevel(L) Forecast Error Abs. Errror MSE MAD % Error MAPE TS

0 5,052.10

1 2250 5,049.30 5,052.10 2,802.10 2,802.10 7,851,764.41 2,802.10 124.54 124.54 1.00

2 1737 5,045.99 5,049.30 3,312.30 3,312.30 9,411,540.89 3,057.20 190.69 157.61 2.00

3 2412 5,043.35 5,045.99 2,633.99 2,633.99 8,586,987.31 2,916.13 109.20 141.48 3.00

4 7269 5,045.58 5,043.35 (2,225.65) 2,225.65 7,678,618.17 2,743.51 30.62 113.76 2.38

5 3514 5,044.05 5,045.58 1,531.58 1,531.58 6,612,040.32 2,501.12 43.59 99.73 3.22

6 2143 5,041.14 5,044.05 2,901.05 2,901.05 6,912,711.28 2,567.78 135.37 105.67 4.27

7 3459 5,039.56 5,041.14 1,582.14 1,582.14 6,282,778.48 2,426.97 45.74 97.11 5.17

8 7056 5,041.58 5,039.56 (2,016.44) 2,016.44 6,005,683.69 2,375.65 28.58 88.54 4.43

9 4120 5,040.66 5,041.58 921.58 921.58 5,432,753.03 2,214.09 22.37 81.19 5.17

10 2766 5,038.38 5,040.66 2,274.66 2,274.66 5,406,884.34 2,220.15 82.24 81.29 6.18

11 2556 5,035.90 5,038.38 2,482.38 2,482.38 5,475,551.57 2,243.99 97.12 82.73 7.22

12 8253 5,039.12 5,035.90 (3,217.10) 3,217.10 5,881,733.13 2,325.08 38.98 79.09 5.58

13 5491 5,039.57 5,039.12 (451.88) 451.88 5,444,999.65 2,180.99 8.23 73.64 5.75

14 4382 5,038.91 5,039.57 657.57 657.57 5,086,956.63 2,072.17 15.01 69.45 6.36

15 4315 5,038.19 5,038.91 723.91 723.91 4,782,762.74 1,982.29 16.78 65.94 7.02

16 12035 5,045.18 5,038.19 (6,996.81) 6,996.81 7,543,551.36 2,295.70 58.14 65.45 3.01

17 5648 5,045.79 5,045.18 (602.82) 602.82 7,121,188.71 2,196.11 10.67 62.23 2.8718 3696 5,044.44 5,045.79 1,349.79 1,349.79 6,826,785.24 2,149.10 36.52 60.80 3.57

19 4843 5,044.24 5,044.44 201.44 201.44 6,469,616.39 2,046.59 4.16 57.82 3.84

20 13097 5,052.29 5,044.24 (8,052.76) 8,052.76 9,388,485.80 2,346.90 61.49 58.00 (0.08)


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0.001 0.100

Time

Period

Black

Plastic Level(L) Trend(T) Forecast Error Abs. Errror MSE MAD % Error MAPE TS

0 2,042.74 286.61

1 2250 2,042.94 257.97 2,329.34 79.34 79.34 6,295.29 79.34 3.53 3.53 1.00

2 1737 2,042.64 232.14 2,300.91 563.91 563.91 162,145.03 321.63 32.46 18.00 2.00

3 2412 2,043.01 208.96 2,274.78 (137.22) 137.22 114,373.39 260.16 5.69 13.89 1.95

4 7269 2,048.23 188.59 2,251.97 (5,017.03) 5,017.03 6,378,428.81 1,449.38 69.02 27.67 (3.11)

5 3514 2,049.70 169.88 2,236.82 (1,277.18) 1,277.18 5,428,979.83 1,414.94 36.35 29.41 (4.09)

6 2143 2,049.79 152.90 2,219.58 76.58 76.58 4,525,127.16 1,191.88 3.57 25.10 (4.79)7 3459 2,051.20 137.75 2,202.69 (1,256.31) 1,256.31 4,104,153.82 1,201.08 36.32 26.71 (5.80)

8 7056 2,056.21 124.47 2,188.95 (4,867.05) 4,867.05 6,552,155.63 1,659.33 68.98 31.99 (7.13)

9 4120 2,058.27 112.23 2,180.68 (1,939.32) 1,939.32 6,242,022.52 1,690.44 47.07 33.67 (8.15)

10 2766 2,058.98 101.08 2,170.50 (595.50) 595.50 5,653,281.83 1,580.94 21.53 32.45 (9.09)

11 2556 2,059.48 91.02 2,160.06 (395.94) 395.94 5,153,598.87 1,473.22 15.49 30.91 (10.02)

12 8253 2,065.67 82.54 2,150.50 (6,102.50) 6,102.50 7,827,510.21 1,858.99 73.94 34.50 (11.23)

13 5491 2,069.09 74.63 2,148.21 (3,342.79) 3,342.79 8,084,952.23 1,973.13 60.88 36.53 (12.27)

14 4382 2,071.41 67.40 2,143.72 (2,238.28) 2,238.28 7,865,304.76 1,992.07 51.08 37.56 (13.28)15 4315 2,073.65 60.88 2,138.80 (2,176.20) 2,176.20 7,656,673.18 2,004.34 50.43 38.42 (14.28)

16 12035 2,083.61 55.79 2,134.53 (9,900.47) 9,900.47 13,304,335.46 2,497.85 82.26 41.16 (15.42)

17 5648 2,087.18 50.57 2,139.40 (3,508.60) 3,508.60 13,245,860.76 2,557.31 62.12 42.40 (16.44)

18 3696 2,088.79 45.67 2,137.74 (1,558.26) 1,558.26 12,644,877.65 2,501.80 42.16 42.38 (17.42)

19 4843 2,091.54 41.38 2,134.46 (2,708.54) 2,708.54 12,365,474.09 2,512.68 55.93 43.10 (18.43)

20 13097 2,102.54 38.34 2,132.92 (10,964.08) 10,964.08 17,757,754.39 2,935.25 83.71 45.13 (19.51)


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0.001 0.100 0.200

TimePeriod

BlackPlastic

Level(L) Trend(T) SeasonalFactor

Forecast Error Abs.Errror

MSE MAD % Error MAPE TS

0 2,592.75 226.86

1 2250 2,819.29 226.82 0.90 2,535.61 285.61 285.61 81,573.45 285.61 12.69 12.69 1.00

2 1737 3,045.96 226.81 0.60 1,824.24 87.24 87.24 44,592.14 186.43 5.02 8.86 2.00

3 2412 3,272.96 226.83 0.70 2,282.99 (129.01) 129.01 35,276.05 167.29 5.35 7.69 1.46

4 7269 3,500.32 226.88 1.80 6,300.63 (968.37) 968.37 260,892.21 367.56 13.32 9.10 (1.97)

5 3514 3,727.48 226.91 0.88 3,276.36 (237.64) 237.64 220,008.60 341.57 6.76 8.63 (2.82)

6 2143 3,954.04 226.87 0.59 2,345.56 202.56 202.56 190,178.59 318.40 9.45 8.77 (2.39)

7 3459 4,181.64 226.95 0.71 2,949.41 (509.59) 509.59 200,107.52 345.72 14.73 9.62 (3.67)

8 7056 4,407.98 226.89 1.86 8,180.42 1,124.42 1,124.42 333,134.23 443.05 15.94 10.41 (0.33)

9 4120 4,634.85 226.88 0.89 4,133.27 13.27 13.27 296,138.87 395.30 0.32 9.29 (0.33)

10 2766 4,861.62 226.87 0.58 2,833.99 67.99 67.99 266,987.29 362.57 2.46 8.60 (0.18)

11 2556 5,086.91 226.71 0.73 3,713.55 1,157.55 1,157.55 364,527.40 434.84 45.29 11.94 2.52

12 8253 5,312.88 226.64 1.80 9,588.96 1,335.96 1,335.96 482,881.54 509.93 16.19 12.29 4.77

13 5491 5,540.15 226.70 0.89 4,936.85 (554.15) 554.15 469,358.64 513.34 10.09 12.12 3.65

14 4382 5,768.64 226.88 0.58 3,345.48 (1,036.52) 1,036.52 512,573.56 550.71 23.65 12.95 1.52

15 4315 5,995.83 226.91 0.68 4,102.90 (212.10) 212.10 481,401.03 528.13 4.92 12.41 1.19

16 12035 6,223.38 226.98 1.75 10,916.91 (1,118.09) 1,118.09 529,446.65 565.00 9.29 12.22 (0.87)

17 5648 6,450.10 226.95 0.91 5,877.49 229.49 229.49 501,400.79 545.27 4.06 11.74 (0.48)

18 3696 6,676.37 226.88 0.62 4,113.22 417.22 417.22 483,215.96 538.15 11.29 11.71 0.29

19 4843 6,903.36 226.89 0.69 4,772.89 (70.11) 70.11 458,042.28 513.52 1.45 11.17 0.17

20 13097 7,130.44 226.91 1.79 12,764.96 (332.04) 332.04 440,652.75 504.45 2.54 10.74 (0.49)


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Seasonal Factor

Intercept Slope

3,611.98 263.94

Time

Period

Clear

Plastic

Deseason

lizedDemand

Deseason

lizedDemand

Seasonal

Factor Forecast Error Abs. Errror MSE MAD % Error MAPE TS

0

1 3200 3,875.92 0.83 2,951.64 (248.36) 248.36 61,681.69 248.36 7.76 7.76 (1.00)

2 7658 4,139.86 1.85 7,862.48 204.48 204.48 51,746.96 226.42 2.67 5.22 (0.19)

3 4420 4,472 4,403.80 1.00 4,174.99 (245.01) 245.01 54,507.91 232.62 5.54 5.32 (1.24)

4 2384 4,657 4,667.74 0.51 1,935.68 (448.32) 448.32 91,129.09 286.54 18.81 8.70 (2.57)

5 3654 4,944 4,931.68 0.74 3,755.64 101.64 101.64 74,969.38 249.56 2.78 7.51 (2.55)

6 8680 5,049 5,195.62 1.67 9,867.60 1,187.60 1,187.60 297,538.89 405.90 13.68 8.54 1.36

7 5695 5,132 5,459.56 1.04 5,175.90 (519.10) 519.10 293,528.78 422.07 9.12 8.62 0.08

8 1953 5,892 5,723.50 0.34 2,373.49 420.49 420.49 278,939.63 421.88 21.53 10.24 1.079 4742 6,634 5,987.44 0.79 4,559.64 (182.36) 182.36 251,641.49 395.26 3.85 9.53 0.69

10 13673 6,850 6,251.38 2.19 11,872.71 (1,800.29) 1,800.29 550,580.52 535.77 13.17 9.89 (2.85)

11 6640 6,791 6,515.32 1.02 6,176.80 (463.20) 463.20 520,032.40 529.17 6.98 9.63 (3.77)

12 2737 6,573 6,779.26 0.40 2,811.31 74.31 74.31 477,156.54 491.26 2.72 9.05 (3.90)

13 3486 6,363 7,043.20 0.49 5,363.63 1,877.63 1,877.63 711,645.22 597.91 53.86 12.50 (0.07)

14 13186 6,308 7,307.14 1.80 13,877.83 691.83 691.83 695,001.18 604.62 5.25 11.98 1.08

15 5448 6,932 7,571.08 0.72 7,177.71 1,729.71 1,729.71 848,127.53 679.62 31.75 13.30 3.50

16 3485 7,887 7,835.02 0.44 3,249.13 (235.87) 235.87 798,596.80 651.89 6.77 12.89 3.29

17 7728 8,662 8,098.96 0.95 6,167.63 (1,560.37) 1,560.37 894,841.13 705.33 20.19 13.32 0.83

18 16591 8,989 8,362.90 1.98 15,882.95 (708.05) 708.05 872,979.95 705.48 4.27 12.82 (0.17)

19 8236 8,626.84 0.95 8,178.62 (57.38) 57.38 827,206.94 671.37 0.70 12.18 (0.27)

20 3316 8,890.78 0.37 3,686.94 370.94 370.94 792,726.56 656.35 11.19 12.13 0.29

QtrsSeasonal Factor(Static

Method)

Q1 0.76

Q2 1.90

Q3 0.95

Q4 0.41


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0.001 0.100

Time

Period

Clear

Plastic Level(L) Trend(T) Forecast Error Abs. Errror MSE MAD % Error MAPE TS

0 4,133.70 210.66

1 3200 4,132.77 189.50 4,344.36 1,144.36 1,144.36 1,309,553.27 1,144.36 35.76 35.76 1.00

2 7658 4,136.29 170.90 4,322.26 (3,335.74) 3,335.74 6,218,342.77 2,240.05 43.56 39.66 (0.98)

3 4420 4,136.58 153.84 4,307.19 (112.81) 112.81 4,149,803.70 1,530.97 2.55 27.29 (1.51)

4 2384 4,134.82 138.28 4,290.41 1,906.41 1,906.41 4,020,956.66 1,624.83 79.97 40.46 (0.24)

5 3654 4,134.34 124.40 4,273.10 619.10 619.10 3,293,422.93 1,423.68 16.94 35.76 0.16

6 8680 4,138.89 112.42 4,258.75 (4,421.25) 4,421.25 6,002,434.07 1,923.28 50.94 38.29 (2.18)

7 5695 4,140.44 101.33 4,251.31 (1,443.69) 1,443.69 5,442,694.03 1,854.77 25.35 36.44 (3.04)

8 1953 4,138.26 90.98 4,241.78 2,288.78 2,288.78 5,417,168.90 1,909.02 117.19 46.53 (1.76)

9 4742 4,138.86 81.94 4,229.24 (512.76) 512.76 4,844,475.34 1,753.88 10.81 42.56 (2.21)

10 13673 4,148.39 74.70 4,220.80 (9,452.20) 9,452.20 13,294,432.14 2,523.71 69.13 45.22 (5.28)

11 6640 4,150.89 67.48 4,223.10 (2,416.90) 2,416.90 12,616,886.24 2,514.00 36.40 44.42 (6.26)

12 2737 4,149.47 60.59 4,218.37 1,481.37 1,481.37 11,748,349.52 2,427.95 54.12 45.23 (5.87)

13 3486 4,148.81 54.47 4,210.06 724.06 724.06 10,884,958.56 2,296.88 20.77 43.35 (5.89)

14 13186 4,157.85 49.92 4,203.27 (8,982.73) 8,982.73 15,870,987.82 2,774.44 68.12 45.12 (8.11)

15 5448 4,159.14 45.06 4,207.77 (1,240.23) 1,240.23 14,915,466.95 2,672.16 22.76 43.63 (8.89)16 3485 4,158.46 40.49 4,204.20 719.20 719.20 14,015,577.87 2,550.10 20.64 42.19 (9.03)

17 7728 4,162.03 36.79 4,198.95 (3,529.05) 3,529.05 13,923,732.73 2,607.68 45.67 42.39 (10.19)

18 16591 4,174.46 34.36 4,198.83 (12,392.17) 12,392.17 21,681,635.82 3,151.27 74.69 44.19 (12.36)

19 8236 4,178.52 31.33 4,208.82 (4,027.18) 4,027.18 21,394,086.32 3,197.37 48.90 44.44 (13.44)

20 3316 4,177.66 28.11 4,209.85 893.85 893.85 20,364,330.38 3,082.19 26.96 43.56 (13.66)


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Method MSE MAD MAPE

Min Max

Static Regression Method 346,929.90 446.14 9.73 (3.51) 4.52

Simple Exponential Smoothing 9,388,485.80 2,346.90 58.00 (0.08) 7.22

Trend Corrected Exponential Smoothing 17,757,754.39 2,935.25 45.13 (19.51) 2.00

Seanson and Trend Correct Exponential Smoothing 440,652.75 504.45 10.74 (3.67) 4.77

TS Range

Summary of Errors(Clear Plastic)

Method MSE MAD MAPE

Min Max

Static Regression Method 792,726.56 656.35 12.13 (3.90) 3.50

Simple Exponential Smoothing 15,835,322.56 3,162.49 65.54 (1.00) 6.00

Trend Corrected Exponential Smoothing 20,364,330.38 3,082.19 43.56 (13.66) 1.00

Seanson and Trend Correct Exponential Smoothing 994,545.40 719.72 13.20 (3.63) 4.04

TS Range


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Speciality Packaging Case study