SOLVED MGMT717 Assignment 1 Solution and Discussion

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ADVANCED PRODUCTION PLANNING & INVENTORY CONTROL (MGMT717)
ASSIGNMENT # 1
Due Date: November 27, 2019 Marks: 10 SCENARIO:
The supply chain manager of a manufacturing company is interested in finding the best method of forecasting for a special set of gears that enhances the speed of the car. He is
confused between “Weighted Moving Average” method and “Exponential Smoothing” method. The demand of the product is given in the following table:

Month	1	2	3	4	5	6	7	8	9	10	11	12	13
Demand	60	55	43	65	52	42	47	59	63	44	55	49	?

QUESTIONS:

1. Your task is to help the manager to arrive at a decision by forecasting the demands for all possible months through the following methods:
   a. 3-Period Weighted Moving Average with weights 0.5, 0.3 and 0.2 (the most recent period carries maximum weight). (4)
   b. Exponential Smoothing with 𝛼 = 0.2 (4)
2. Calculate Mean Absolute Deviation (MAD) for both methods and conclude which forecasting model is more appropriate for the product. (2)
   Instructions:
   • Use the demand of the first month as the Forecast of the first month for the sake of calculations
   • You have to calculate forecasts and present these in tables
   • Write formulae and show necessary calculations
   • You may solve the problem in MS Excel and copy-paste tables in your solution file (MS
   Word format)
   • Watch video lectures and consult book to complete the assignment
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Solution: 1.
a) Weighted Moving Average:

Month	Demand	Forecast	Error	Error
1	60
2	55
3	43
4	65	50.0	15.0	15.0
5	52	56.4	-4.4	4.4
6	42	54.1	-12.1	12.1
7	47	49.6	-2.6	2.6
8	59	46.5	12.5	12.5
9	63	52.0	11.0	11.0
10	44	58.6	-14.6	-14.6
11	55	52.7	2.3	2.3
12	49	53.3	-4.3	4.3
13	?	49.8	Total	78.8

• Forecast for Period 4 = 430.5 + 550.3 + 60*0.2
• Forecast for Period 5 = 650.5 + 430.3 + 55*0.2
• Forecast for Period 13 = 490.5 + 550.3 + 44*0.2 = 49.8

b) Exponential Smoothing:
𝛼=0.2

Month Demand Forecast Error	Error
Month	Demand	Forecast	Error	Error
1	60	60.00
2	55	60.00	-5.00	5.00
3	43	59.00	-16.00	16.00
4	65	55.0	9.20	9.20
5	52	55.8	-5.64	5.64
6	42	57.64	-14.51	14.51
7	47	56.51	-6.61	6.61
8	59	53.61	6.71	6.71
9	63	53.63	9.37	9.37
10	44	55.50	-11.50	11.50
11	55	53.2	1.80	1.80
12	49	53.56	-4.56	4.56
13	?	52.65	Total	90.90

• Ft+1 =Ft +α(At –Ft) or Ft+1 =αAt +(1–α)Ft
• F1 = A1 (Supposed) = 60
• F2 =F1 +α(A1 –F1)=60+0.2(60–60)=60
• F3 =F2 +α(A2 –F2)=60+0.2(55–60)=59
• F13 =F12 +α(A12 –F12)=53.56+0.2(49–53.56)=52.65

2. MAD
   MAD = ∑ |Actual Demand – Forecast| / n
   a) Weighted Moving Average:

• MAD=78.8/9=8.76
  b) Exponential Smoothing:
• MAD=90.90/11=8.26
  As MAD of Exponential Smoothing is less than that of Weighted Moving Average, it is concluded that Exponential Smoothing is more appropriate.

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Solution: 1.
a) Weighted Moving Average:

Month	Demand	Forecast	Error	Error
1	60
2	55
3	43
4	65	50.0	15.0	15.0
5	52	56.4	-4.4	4.4
6	42	54.1	-12.1	12.1
7	47	49.6	-2.6	2.6
8	59	46.5	12.5	12.5
9	63	52.0	11.0	11.0
10	44	58.6	-14.6	-14.6
11	55	52.7	2.3	2.3
12	49	53.3	-4.3	4.3
13	?	49.8	Total	78.8

• Forecast for Period 4 = 430.5 + 550.3 + 60*0.2
• Forecast for Period 5 = 650.5 + 430.3 + 55*0.2
• Forecast for Period 13 = 490.5 + 550.3 + 44*0.2 = 49.8

b) Exponential Smoothing:
𝛼=0.2

Month Demand Forecast Error	Error
Month	Demand	Forecast	Error	Error
1	60	60.00
2	55	60.00	-5.00	5.00
3	43	59.00	-16.00	16.00
4	65	55.0	9.20	9.20
5	52	55.8	-5.64	5.64
6	42	57.64	-14.51	14.51
7	47	56.51	-6.61	6.61
8	59	53.61	6.71	6.71
9	63	53.63	9.37	9.37
10	44	55.50	-11.50	11.50
11	55	53.2	1.80	1.80
12	49	53.56	-4.56	4.56
13	?	52.65	Total	90.90

• Ft+1 =Ft +α(At –Ft) or Ft+1 =αAt +(1–α)Ft
• F1 = A1 (Supposed) = 60
• F2 =F1 +α(A1 –F1)=60+0.2(60–60)=60
• F3 =F2 +α(A2 –F2)=60+0.2(55–60)=59
• F13 =F12 +α(A12 –F12)=53.56+0.2(49–53.56)=52.65

2. MAD
   MAD = ∑ |Actual Demand – Forecast| / n
   a) Weighted Moving Average:

• MAD=78.8/9=8.76
  b) Exponential Smoothing:
• MAD=90.90/11=8.26
  As MAD of Exponential Smoothing is less than that of Weighted Moving Average, it is concluded that Exponential Smoothing is more appropriate.