Production Control & Planning
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Transcript of Production Control & Planning
PPC 201
Who is he/ she Mohamad Maaroff Bahurdin
Where does he/ she come fromHow to contact
Write & send to▪ [email protected]
Ring me up▪ 019 470 8987
2
Who Are YouWhat is Your Background
3
Basic of Manufacturing
“If an organization can produce the best quality product / service with the lowest cost and on time delivery, without forgetting the environment and safety regulations, surely can survive in the present day business climate.” Ridzuan 2004
5
Topic 1
After studying this lesson, you should be able to: Describe the production function and
its component Define production management
7
• Production system function is to convert a set of inputs into a set of desired outputs
InputsConversion process
Outputs
Control
•Land•Building•Machines•Labour capital•Management•Material•other
8
Is a strategic decision Consists of form and function Should be dictated by the market
demand
9
a) Standardizationb) Reliabilityc) Maintainabilityd) Servicinge) Sustainabilityf) Product simplification
g) Quality commensuration with cost
h) Product valuei) Consumer qualityj) Reproducibilityk) Needs and tastes of
consumers
•Factors to consider: -
• Above of all, the product design should be dictate by the market demand
10
Is the framework within which the production activities of an enterprise take place
To ensures the coordination of various production operations
No single pattern of production system which is universally applicable to all types of production system
11
1. Continuous production
o standardized products with a standard set of process - mass flow or assembly line production
2. Job or unit production
o production as per customer's specification - varied products
3. Intermittent production
o the goods are produced partly for inventory and partly for customer's orders - Automobile plants, printing presses, electrical goods plant
12
Different types of production system are distinct and require different conditions of manufacturing process
Selection of manufacturing process is also a strategic decision as changes are costly.
13
Jobbing production one or few units of the products are produced as per
the requirement and specification of the customer
Batch production limited quantities of each of the different types of
products are manufactured on same set of machines
Mass or flow production production run is conducted on a set of machines
arranged according to the sequence of operations
Process Production the production run is conducted for an indefinite
period. 14
Effect of volume/variety volume is low and variety is high, intermittent process increase in volume and reduction in variety continuous
process Capacity of the plant
Projected sales volume is the key factor to make a choice between batch and line process.
Lead time continuous process normally yields faster deliveries as
compared to batch process
Flexibility and Efficiency to adapt contemplated changes and volume of
production 15
JobbingJobbing
BatchingBatching
LineLine
ProcessProcessDegree of
repetitiveness
One Many
16
Is essentially required for efficient and economical production
Involve generally the organization and planning of manufacturing process
Ultimate objective is to organize the supply, movement of materials, labor, machines utilization and related activities
17
Production planning without production control is like a bank without a bank manager
Planning initiates action while control is an adjusting process, providing corrective measures for planned development
18
19
Production Planning
& Control
Production Planning Production Control
Planning
Routing
Scheduling
Loading
Dispatching
Follow up
Inspection
Corrective
the technique of foreseeing every step in a long series of separate operations
to determine the best and cheapest sequence of operations
time that should be required to perform each operation. Production, Master, Manufacturing schedule
execution of the schedule plan as per the route chalked out it includes the assignment of the work to the operators at their machines or work places
important step as it translates production plans into production.
helps to reveal detects in routing and scheduling, misunderstanding of orders and instruction, under loading or overloading of work etc.
to ensure the quality of goods
adjusting the route, rescheduling of work changing the workloads, repairs and maintenance of machinery or equipment, control over inventories
an important method of minimizing work-in-process inventory
a pull system means you only do what your customer wants just in time
the system pace is determined by the slowest workstation in the system
Pull !Don’t Push !
22
1. Explain the meaning of following key words in your own words
(a) Production planning(b) Production control(c) Routing(d) Scheduling
2. What do you understand by production planning and control? Discuss its elements in brief.
23
Topic 2
By the end of this topic, you should be able to: Define forecast; Identify types of forecasts; Explain forecasting approaches; Solve typical problems using above
approaches; Describe the measures of forecast accuracy;
and Discuss ways of evaluating and controlling
forecasts. 25
A forecast is a prediction of what will occur in the future.
A forecast of product demand is the basis for most important planning decisions.
26
Good forecasts are important Affect the decisions relating to future
operating plans The impact of product forecast:
Human resources Capacity Supply-Chain Management
27
28
Time Series Model
Time Series Model
Causal Model
Causal Model
J udgmental Model
J udgmental Model
Forecasting model
Forecasting model
Time Series Model
Time Series Model
Causal Model
Causal Model
J udgmental Model
J udgmental Model
Forecasting model
Forecasting model
29
Analysis of subjective inputs obtained from various sources, such as: consumer surveys the sales staff managers and executives panels of experts
30
The future values of series can be estimated from the past values.
The data may be measurements of
demand, earnings, profits, shipments, accidents, output, productivity and so on.
31
This model uses equations that consist of one or more explanatory variables that can be used to predict future events
Incorporate the variables or factors that might influence the quantity being forecasted into the forecasting model
32
Application
Time Horizon
Short Term (0–3 months)
Medium Term (3 months–2 years)
Long Term (more than 2 years)
Forecast quantity •Individual products or services
•Total sales•Groups or families of products or services
•Total sales
Decision area •Inventory management •Final assembly Scheduling•Workforce scheduling•Master production scheduling
•Staff planning•Production planning•Master production scheduling•Purchasing•Distribution
•Facility location•Capacity planning•Process management
Forecasting technique
•Time series•Causal •Judgment
•Causal•Judgment
•Causal•Judgment
33
34
uses a single previous value of a time series as the basis of a forecast: For a stable series; the demand in the next period = the demand in
the most recent period. ▪ For example:
Sales in a store for last week were 60 units. Therefore, the sale for this week is forecasted to be 60 units also.
For data with trend, the forecast = to the last value of the series plus or minus the difference between the last two values of the series.
▪ For example: Productions in a company for last two months are as follows:
Month Actual change from Previous Month Forecast
April 40
May 43 +3
June 43+3=4635
A moving average forecast uses a number of the most recent actual data values in generating a forecast.
Can be computed using the following equation:
n
AMAF
n
it
nt
11
Where i = An index that corresponds to time periods n = Number of periods (data points) in the moving average At = Actual value in period t-iMA = Moving average F = Forecast for time period t
36
1. Simple Moving Average Model2. Weighted Moving Averages Model
37
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
FF44 = 397.0 = 397.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
FF44 = 397.0 = 397.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
22 38038033 41141144 415415
FF55 = = 415 + 411 + 380415 + 411 + 38033
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
22 38038033 41141144 415415
FF55 = 402.0 = 402.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
3-week MA3-week MAforecastforecast
6-week MA6-week MAforecastforecast
Compute three-month moving average forecast, given the production for the last 5 periods as follows:
47
Period Demand
1 42
2 40
3 43
4 40
5 41F6 = ??
If actual demand in period 6 turns out to be 38, the moving average forecast for period 7 would be:
Period Demand
1 42
2 40
3 43
4 40
5 41
6 38F7 = ??
48
A weighted moving average is calculated by assigning more weight to the most recent values in a time series.
49
Given the following data; Compute a weighted average forecast using a weight of 0.40 for the most recent period, 0.30 for the next most recent, 0.20 for the next and 0.10 for the next.
Period Demand
1 42
2 40
3 43
4 40
5 41F6 = ??
50
Solution: P6 = (0.10) (40) + (0.20) (43) + (0.30) (40) + 0.40 (41) = 41.0
51
Period Demand
1 42
2 40
3 43
4 40
5 41
If the actual demand for period 6 is 39, forecast demand for period weights as in previous part.
Period Demand
1 42
2 40
3 43
4 40
5 41
6 39 F7 = ??
52
Solution:F7= 0.10 (43) + (0.20) (40) + 0.30 (41) + (0.40) (39) = 40.2
Note that the weighted moving average is more reflective of the most recent occurrences.
53
Period Demand
1 42
2 40
3 43
4 40
5 41
6 39
The following gives the number of pints of type A blood used in a hospital in the past 6 weeks:
Week of Pints used
July31 360
August 7 389
August14 410
August21 381
August28 368
September 5 374
Use a 3-week weighted moving average, with weights of 0.1, 0.3 and0.6, using 0.6 for the most recent week. Forecast demand for the weekof September 12.
54
is a sophisticated weighted moving-average forecasting method that is fairly easy to use.
The basic exponential smoothing formula is:
55
The formula is: Ft =Ft-1 + α (Dt-1 – Ft-1)
Where, Ft = Forecast for period tFt-1 = Forecast for the previous period α = Smoothing constant Dt-1 = Actual demand or sales for the previous period
Each new forecast is equal to the previous forecast plus a percentage of the previous error.
56
For example, previous forecast was 24 units, actual demand was 20 and α = 0.1. The new forecast is,Ft =24 + 0.1 (20-24) = 23.6
Then, if the actual demand turns out to be 25, the next forecast would be Ft = 23.6 + 0.1(25-23.6) = 23.74
57
Period (t) Actual demand
α = .10 α = .40
Forecast Error Forecast Error
1 42
2 40 42 -2 42 -2
3 43 41.8 1.2 41.2 1.8
4 40 41.92 -1.92 41.92 -1.92
5 41 41.73 -0.73 41.15 -0.15
6 39 41.66 -2.66 41.09 -2.09
7 46 41.39 4.61 40.25 5.75
8 44 41.85 2.15 42.55 1.45
9 45 42.07 2.93 43.13 1.87
10 38 42.35 -4.35 43.88 -5.88
11 40 41.92 -1.92 41.53 -1.53
12 41.73 40.92 58
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11 12
DE
MA
ND
ACTUAL
α = 0.1
α = 0.4
59
The following gives the number of pints of type A blood used in a hospital in the past 6 weeks:
Week of Pints used
July31 360
August 7 389
August14 410
August21 381
August28 368
September 5 374
Calculate the forecast for the week of September 12 using exponential smoothing with a forecast for July31 of 360 and α = 0.2.
60
Previously, we have discussed simple exponential smoothing. Here we will discuss how the exponential smoothing must be modified when a trend is present.
The basic formula is as follows:
61
With trend-adjusted exponential smoothing, estimates for both the average and the trend are smoothed. This procedure requires two smoothing constants, α for the average and β for the trend. We then calculate the average and trend each period:
Ft = α (Actual demand last period) + (1- α) (Forecast last period + Trend estimate last period)
))(1()( 111 tttt TFAF
11 )1()( tttt TFFT
Tt = β (Forecast this period – Forecast last period) + (1- β) (Trend estimate last period)
62
))(1()( 111 tttt TFAF
11 )1()( tttt TFFT where
Ft = exponentially smoothed forecast of the data series in period t. Tt = exponentially smoothed trend in period t.At = actual demand in period t.α = smoothing constant for the average (0 ≤ α ≤ 1)β = smoothing constant for the trend (0 ≤ β ≤ 1)
63
So the three steps to compute a trend-adjusted forecast are:
Step 1: Compute Ft the exponentially smoothed forecast for period t.
Step 2: Compute the smoothed trend, Tt.
Step 3: Calculate the forecast including trend, FITt.
64
Example An Import Agency in Pasir Gudang uses exponential smoothing
to forecast demand for the industrial cleaning machine. It appears that an increasing trend is present.
Month (t)Actual Demand
(At)Month (t)
Actual Demand (At)
1 12 6 21
2 17 7 31
3 20 8 28
4 19 9 36
5 24 10 ?
Smoothing constants are assigned the values of α = 0.2 and β =0.4. Assume the initial forecast for month 1 (F1) was 11 units and the trend over that period (T1) was 2 units.
65
Step 1: Forecast for month 2: F2 = α At + (1 - α) (F1 + T1) F2 = (0.2) (12) + (1 - 0.2)(11 + 2) = 12.8 units
Step 2: Compute the trend in period 2: T2 = β (F2 – F1) + (1- β)(T1) T2 = (0.4)(12.8 - 11) +(1 - 0.4)(2) = 1.92
Step 3: Calculate the forecast including trend (FITt) FIT2 =F2 +T2 =12.8 + 1.92 = 14.72 units
66
We will also do the same calculations for the third month.
Step 1: F3 = α A2 + (1 - α) (F2 + T2 = (0.2) (17) + (1 - 0.2)
(12.8 + 1.92) = 15.18
Step 2: T3 = β (F3 – F2) + (1 – β) (T2) = (0.4)(15.18 – 12.8)
+ (1-0.4)(1.92)=2.10
Step3: FIT3 =F3 +T3 =15.18 + 2.10=17.28
67
The next table completes the forecasts for the 10-month period
MonthActual
DemandSmoothed
Forecast (Ft)Smoothed trend (Tt)
Forecast Including
Trend (FITt)
1 12 11 2 13.00
2 17 12.80 1.92 14.72
3 20 15.18 2.10 17.28
4 19 17.82 2.32 20.14
5 24 19.91 2.23 22.14
6 21 22.51 2.38 24.89
7 31 24.11 2.07 26.18
8 28 27.14 2.45 29.59
9 36 29.28 2.32 31.60
10 - 32.48 2.68 35.16
Forecast with α = 0.2 and β = 0.4 68
0
5
10
15
20
25
30
35
40
1 2 3 4 5 876 9
69
How do we identify the seasonal variations in a data?
We should understand that seasonal variations in a time series are related to recurring events such as weather or holidays. Seasonality may be applied to hourly, daily, monthly or other recurring patterns.
70
The monthly sales at a computer centre in Bandar Tun Dr Ismail for 2003 to 2005 is shown in the table below. Compute the seasonal indices of every month in a year.
Month
DemandAverage
2003-2005 demand
Average monthly demanda
Seasonal Indexb
2003 2004 2005
Jan. 80 85 105 90 94 0.957 (= 90/94)
Feb. 70 85 85 80 94 0.851 (= 80/94)
Mar. 80 93 82 85 94 0.904 (= 85/94)
Apr. 90 95 115 100 94 1.064 (= 100/94)
May 113 125 131 123 94 1.309 (= 123/94)
June 110 115 120 115 94 1.223 (= 115/94)
July 100 102 113 105 94 1.117 (= 105/94)
Aug. 88 102 110 100 94 1.064 (= 100/94)
Sept. 85 90 95 90 94 0.957 (= 90/94)
Oct. 77 78 85 80 94 0.851 (= 80/94)
Nov. 75 82 83 80 94 0.851 (= 80/94)
Dec. 82 78 80 80 94 0.851 (= 80/94)
Total average demand = 1 128
71
A) Average monthly demand = 1 128 = 94 12 months
B) Seasonal index = Average 2003 – 2005 monthly demand Average monthly demand
If we expected the 2006 annual demand for computers to be 1200 units, we would use these seasonal indices to forecast the monthly demand as follows:
72
Month Demand Month Demand
Jan.1 200 x 0.957 = 96
12July
1 200 x 1.117 = 11212
Feb.1 200 x 0.851 = 85
12Aug.
1 200 x 1.064 = 10612
Mar.1 200 x 0.904 = 90
12Sept.
1 200 x 0.957 = 9612
Apr.1 200 x 1.064 = 106
12Oct.
1 200 x 0.851 = 8512
May1 200 x 1.309 = 131
12Nov.
1 200 x 0.851 = 8512
June1 200 x 1.223 = 122
12Dec.
1 200 x 0.851 = 8512
73
QuarterQuarter Year 1Year 1 Year 2Year 2 Year 3Year 3 Year 4Year 4
11 4545 7070 100100 10010022 335335 370370 585585 72572533 520520 590590 830830 1160116044 100100 170170 285285 215215
TotalTotal 10001000 12001200 18001800 22002200
Year 5 quarterly demand?
Expected Year 5 annual demand to be 2600 units
Forecast error is the difference between the value that occurs and the value that was predicted for a given time period.
Forecast error = Actual demand - Forecast value
EtEt = = DtDt – – FtFt
75
Three commonly used measures to calculate the overall forecast errors are: Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Mean Absolute Percent Error (MAPE)
76
Measures of Forecast ErrorMeasures of Forecast Error
EEtt = = DDtt – – FFtt
||EEt t ||
nn
EEtt22
nn
CFE = CFE = EEtt
==MSE = MSE =
MAD = MAD = MAPE = MAPE = [[ ||EEt t | (100)| (100) ]] // DDtt
nn
((EEtt – E – E ))22
nn – 1– 1
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
Measures of Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
CFE = – 15
Measures of Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
= 27.4
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
E = = – 1.875– 15
8
= 27.4
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
MAPE = = 10.2%81.3%
8
E = = – 1.875– 15
8
= 27.4
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
MAPE = = 10.2%81.3%
8
E = = – 1.875– 15
8
= 27.4