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assignment 1 of operation management, Thesis of Business Finance

assignment 1 of operation management with a lot of maths

Typology: Thesis

2022/2023

Uploaded on 03/07/2023

mashroorverified
mashroorverified 🇨🇦

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Answer to the ques no. 1
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
$280 $360
Total
Input
Cost/
unit
Units
consumed/day
Total Cost/unit Units
consumed/day
Total
Labor $10 7 $70 $10 7 $70
Material $3.50 280 $980 $3.50 360 1260
Supplies
per day
$40 1 $40 $40 1 $40
Energy
cost per
day
$4 1 $4 $4 1 $4
$1094 $1374
Multifactor productivity= Total
output/ total Input
0.256 0.262
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,
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Answer to the ques no. 1

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.

Answer to the ques no. 2

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.

FE5 = 72 – 66.20 = 5.

FE6 = 75 – 67.94 = 7.

MAD = (|5.42| + |5.80| + |7.06|)/3 = 6.

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.

Answer to the ques no. 3

a) In the following instances, a management may favor a linear trend strategy over a basic moving average technique:

  1. When the data demonstrates a steady and apparent trend across time: If the data exhibits a clear and continuous trend over time, a linear trend approach may give a more accurate depiction of the trend and aid in the development of more precise predictions than a simple moving average technique. A simple moving average strategy may not be as efficient in capturing the trend.
  2. If the data exhibit a long-term trend, a linear trend approach may be preferable to a simple moving average technique. Simple moving averages tend to be more sensitive to short-term data volatility and may not reflect the long-term trend adequately.

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.