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assignment 1 of operation management with a lot of maths
Typology: Thesis
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a) Multifactor Productivity = Total output/ Total input The following table shows total input and output of productivity at present and with new paint in order to calculate the multifactor productivity. Productivity at present Productivity with new paint Total Output
Total Input Cost/ unit Units consumed/day Total Cost/unit Units consumed/day Total Labor $10 7 $70 $10 7 $ Material $3.50 280 $980 $3.50 360 1260 Supplies per day
Energy cost per day
Multifactor productivity= Total output/ total Input
Answer: Multifactor Productivity at present = 0.256 dolls/dollar Multifactor Productivity with new paint= 0.262 dolls/dollar b) Using the new paint Joanna’s material cost per doll increase by 0 without reducing the present multifactor productivity. Present Multifactor Productivity is 0.256 dolls/dollar from part a. Given that,
Total output = 360 dolls Supplies per day = $ Energy cost= $ Labor cost= 7 hours for $10 an hour = $ Let, Material cost be X Therefore, Total input = 40 +4+70+360X= 360X+ We know, Multifactor productivity = Total output/ Total input Or, 0.256 = 360/ 360X + 114 Or, 360X + 114 = 350/0. Or, X = (360/0.256 + 114) / 360 Or X =$ 4. Therefore, Current material cost is $3.50 and the estimated material cost is 4.22. Hence, material cost is already at optimal level and can be increased by maximum. Increase in material cost= Maximum material cost – current material cost = 4.22- 3. = $0. Answer: Joanna’s increase in material cost without changing the present multifactor productivity is $0.
a) Simple 3-month moving average Forecast= Average of previous 3 month’s Actual Demand [Using formula: 4th^ month forecast = (1st^ month+ 2nd^ month + 3rd^ Month)/3] Months Actual Demand Forecast using 3-month moving average 1 63 2 65 3 68 4 70 65. 5 72 67. 6 75 70 b) Given weights,
Initial Trend T1= 2. Therefore, [ Using formula: Level Ft= a*A(t-1) + (1-a) {F(t-1) + T(t-1)} And, Trend Tt= b{Ft - F(t-1)} + (1-b) * T(t-1) Month Actual Demand (At) Level (Ft) Trend (Tt) Forecast [Ft + Tt] 1 63 60 2.0 62 2 65 62.3 2.09 64. 3 68 64.57 2.14 66. 4 70 67.09 2.25 69. 5 72 69.54 2.31 71. 6 75 71.89 2.32 74. e) To calculate the MAD, we need to first calculate the forecast error (FE) for each forecast period, which is the difference between the actual demand and the forecast. Then we calculate the absolute value of the forecast error (|FE|) and take the average of these absolute values. For the simple 3-month moving average forecast: FE4 = 70 - 65.33 = 4. FE5 = 72 - 67.67 = 4. FE6 = 75 - 70 = 5 MAD = (|4.67| + |4.33| + |5|)/3 = 4. For the weighted 3-month moving average forecast: FE4 = 70 - 66.10 = 3. FE5 = 72 - 68.40 = 3. FE6 = 75 - 70.60 = 4. MAD = (|3.90| + |3.60| + |4.40|)/3 = 3. For the exponential smoothing forecast: FE4 = 70 – 64.58 = 5.
For the double exponential smoothing forecast: FE4 = 70 – 67.09 = 2. FE5 = 72 – 69.54 = 2. FE6 = 75 – 71.89 = 3. MAD = (|2.91| + |2.46| + |3.11|)/3 = 2. Based on the MAD values, the double exponential smoothing forecast has the lowest MAD, indicating that it has the best accuracy among the four forecasting methods.Therefore, we will use this method to forecast the demands for the following 2 months (months 7-8): [ Using formula: Level Ft= a*A(t-1) + (1-a) {F(t-1) + T(t-1)} And, Trend Tt= b{Ft - F(t-1)} + (1-b) * T(t-1) Month Actual Demand (At) Level (Ft) Trend (Tt) Forecast [Ft + Tt] 5 72 69.54 2.31 71. 6 75 71.89 2.32 74. 7 77 74.45 2.39 76. 8 80 76.89 2.40 79. Answer: Therefore, the forecast for period 7 is 76.84 and the forecast for period 8 is 79.29.
a) In the following instances, a management may favor a linear trend strategy over a basic moving average technique:
Year Revenue A(t) Exponential Smoothing Alpha= 0. Ft |Error| |Error|^ 1 3889.9 4867. 2 4066.4 4476.70 410.30 168346. 3 4535.6 4312.58 223.02 49737. 4 4731.8 4401.79 330.01 108906. 5 4498.7 4533.79 35.09 1231. 6 4519. 7 2711. MAD 249. MSE 82055. Lastly, we use double exponential smoothing to forecast year 6 and 7 [Using formula: Level Ft= a*A(t-1) + (1-a) (F(t-1) + T(t-1)) Trend Tt= b(A(t-1) - F(t-1)) + (1-b) * T(t-1) Year Revenue A(t) Holt’s Model Alpha (a) 0.4 |Error| |Error|^ Beta (b) 0. Ft Tt Ft + Tt 1 3889.9 4867.90 201.50 5069. 2 4066.4 4397.60 107.14 4704.74 638.34 407477. 3 4535.6 4449.40 56.07 4505.48 30.12 907. 4 4731.8 4517.53 53.48 4575.01 155.79 24270. 5 4498.7 4638.33 70.95 4709.27 210.57 44340. 6 4625.04 54.10 4679. 7 2807.49 -320.23 2487. MAD 258. MSE 119249. Here, from the above 3 tables we can easily identify that MAD=249.61 and MSE=82055.86 from exponential smoothing is the lowest. Answer: Therefore, Exponential smoothing is recommended to forecast upcoming year 6 and 7 revenues.