8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
1/37
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
2/37
Controlling the system
Production controlInventory controlLabor controlCost control
I. FORECASTING AS A PREREQUISITESTEP FOR MOST PLANNING ACTIVITIES
Information on most recent demand and production
Demand forecast for operations
Planning the System(designing)Product designProcess designEquipment investmentand replacementCapacity Planning
Scheduling the system
Aggregate ProductionPlanningOperations scheduling
Output of goods and services
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
3/37
Forecasting Vs. Prediction
3 Most social and nature phenomena carry with them aninertia. Forecasting intends to cast the historical pattern intothe future.
Comparisons Forecasting Prediction
Goal Estimating a futureevent (Usually infigures)
Estimating a future event
M ethod A predetermined way(a defined model)
Subjective considerations
Information Bas
ePast data Knowledge, intuition, preference, emotion ...
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
4/37
II. THE UNDERLYINGPATTERN OF THE DATA
Season(Cyclical)
Linear trend
ConstantProduction Demand(units)
Time
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
5/37
II. THE UNDERLYINGPATTERN OF THE DATA
Production demand(units)
Time
Low NoiseHigh Noise
Demand Patternwith trend andseasonalcomponents
Noise in demand
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
6/37
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
7/37
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
8/37
II. THE UNDERLYINGPATTERN OF THE DATA
3 (4)Cyclical:5 similar to a seasonal pattern, but the length of a
cycle is generally longer than a year.5 For example:
x Number of housing startsx price of metals
x GNP
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
9/37
III. THE CRITERIA IN EVALUATINGFORECASTING PERFORMANCE
(FORECAST ERROR)For a single period, the forecast error is the
difference between actual data and forecasteddata.
E t = F t - D t3 where
5 E t: error 5 F t: forecast for period t (made prior to period t)
5 D t: actual demand of period t
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
10/37
IV. FORECAST ERROR MEASURES
3 When multiple periods are involved,usually we derive some single measures toreflect forecasting performance.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
11/37
(A) Mean Absolute Deviation(MAD)
3 If E t ~ N ( U , )3 i.e.,forecast errors follow a normal distribution
with zero mean and a variance,3 then3 TheoreticallyTheoretically
MAD
F D
n
t t t
n
=
=
1
e2
e MAD= 1 25.
E MADe( ) =
2
2
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
12/37
(B) Bias
( ) Bias
F D
n
t t t
n
=
=
1
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
13/37
(C) Mean Square Error (MSE)
( )M E S F Dn
t t t
n
=
=2
1
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
14/37
IV-1. Comparisons:
3 MADMAD measures the absolute magnitude of errors.
3
Bias Bias reflects the direction of errors (positiveor negative).3 MSE MSE intends to amplify large errors.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
15/37
IV-2. A thought question :
3 Question : Which one is the best measure?3 Answer:
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
16/37
IV-3. Computation of forecasterror measures
3 Example:
5 MAD = 5.755 Bias = 3.255 MSE = 39.75
Period Forecast Demand E t=F t-Dt
1 100 90 102 110 105 53 120 117 34 130 135 -5
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
17/37
V. FORECASTING TECHNIQUESCOMPARISONS
3 Qualitative vs. Quantitative
Comparisons Qualitative Quantitative
Structure Problem is notwell structured
Problem is wellstructured
Past Data Past data is notavailable
Past data isavailable
Implementation Throughindividual orgroup judgment
Through models
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
18/37
Time Series vs. Causal
Comparisons Time Series CausalPlanning
Horizon
Short-run
planning
Long-term planning
Purpose Operations processes
Strategic consideration
Assumption Inertia exists Cause-effect relationship
Implementation Empirical studies Theoretical
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
19/37
Regression Analysis vs.Econometric Modeling
Y = a 0 + a 1X1 (Simple Regression)
Y = b 0 + b 1x1 + b 2x2 (Multiple Regression)Y1 = C 1X1 + C 2X2Y2 = D 0 + D 1X1 + D 2X2 (An econometric model)Y3 = E 0 + E 1X2 + E 2X1 (A system of equations)
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
20/37
Forecasting Techniques3 Qualitative
5Delphi Method
5 Market Research5 Historical Analogy
3
Time Series5 Moving Average5 Exponential Smoothing5
Box-Jenkins3 Causal
5 Regression5
Econometric Models
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
21/37
Forecasting Techniques
3 Question: What is the naive model?3 Answer:
5
In Forecasting, "using the most recent demandas the forecast for next period" is referred to asthe naive model.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
22/37
VI. USEFUL FORECASTINGMODELS FOR OPERATIONS
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
23/37
VI-1. Simple Average (Mean)
3 Use the mean of historical demand to identifythe constant level of demand pattern.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
24/37
VI-2. Linear Regression
3 Use regression analysis to identify the increaserate or decrease rate of trend in the demand
pattern.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
25/37
VI-3. Simple Moving Average
3 for n period moving average3 t = 1 is the oldest period3 t = n is the most recent period
MA D
n
t t n m
n
=
=
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
26/37
VI -4. Simple ExponentialSmoothing
3 F t: Forecast for period t3 D t-1 :Demand of period t-1
3 F t-1 :Forecast for period t-13 The weight assigned to the most recent
demand,
( ) F D F t t t = + 1 11
0 1
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
27/37
Why is this model called exponential smoothing?
3 Substituting Ft-n-1
into Ft-n
, continuing the procedure, wehave an expanded form as follows:
3 The weights , (1- ), . . ., assigned to the past datadecrease exponentially. " Smoothing " means " averagingout " errors by using more than one period's data.
( ) F D F t t t = + 1 11
( ) F D F t t t = + 1 2 21
( ) F D F t t 2 13 3= +
( ) ( ) ( ) F D D D D F t t t t n
t n
n
t n= + + + + +
1 2
2
3
11 1 1 1.... ( )
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
28/37
VI-5. Weighted Moving Average(WMA)
3 C t is the weight assigned to D t3 where , and
WMA C Dt t
n
t ==
1
0 1 C t C t t
n
= =
11
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
29/37
VI -6. Adaptive Model
3 The parameter value of the model isallowed to change, and the procedure isdesigned in the forecasting model to changeautomatically when the model detects theneed to change.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
30/37
VII. EXAMPLE:
3 Time series data for monthly sales :
Jan 460
Feb 440Mar 460Apr 510May 520June 495July 470
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
31/37
VII-1.Use the three-month movingaverage model to forecast the demand
for May, June, and July.
MA April = (460 + 440 + 460)/3 = 453
MA May= (440 + 460 + 510)/3 = 470
MA June= (460 + 510 + 520)/3 = 497
MA July= (510 + 520 + 495)/3 = 508
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
32/37
VII-2.Use simple exponential
smoothing model to forecast thedemand for May, June and July.
Question:What do you need to know to make
the forecast?
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
33/37
Answer:
3 (1) the initial forecast for March (assume it is440)
3 (2) the parameter value (assume = 0.6)FApril = (0.6)(460)+(0.4)(440) = 452
FMay = (0.6)(510)+(0.4)(452) = 487
FJune = (0.6)(520)+(0.4)(487) = 507FJuly= (0.6)(495)+(0.4)(507) = 500
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
34/37
VII-3.Use a weighted moving averagemodel to forecast the demand for May,
June and July.
3 Question: What do you need to know toimplement the forecast?
3 Answer:
5 The relative weights of selected number of periods.
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
35/37
Assuming C 1 = .2, C 2 = .3, C 3 = .5
WMA April = (.2)(460)+(.3)(440)+(.5)(460) = 454
WMA May = (.2)(440)+(.3)(460)+(.5)(510) = 481
WMA June = (.2)(460)+(.3)(510)+(.5)(520) = 505WMA July = (.2)(510)+(.3)(520)+(.5)(495) = 506
VII 4 U Bi MAD & MSE
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
36/37
VII-4.Use Bias, MAD & MSE toevaluate the performance of these
models.
x *:the best performance for each measurex In this example, exponential smoothing is the best
model.
Demand 3-month MA Exp. Smoothing Weighted MAForecast Error Forecast Error Forecast Error
Aprial 510 453 -57 452 -58 454 -56
May 520 470 -50 487 -33 481 -39June 495 497 2 507 12 505 10July 475 508 33 500 25 506 31
BIAS = -18.0 -13.5* -13.5*MAD = 35.5 32.0* 34.0MSE = 1,710.5 1,305.5* 1,429.5
8/8/2019 3201~ W1 & 2 - MRP Forecasting From TS 20100722
37/37
VIII. SUGGESTED READING
3 Chapter 13 Forecasting pp.497-510 (Background & Time Series
Forecasting) pp.513-516 (Forecast Error) pp.529-530 (Choosing A Forecasting
Method)3 Study Solved Problem 1, pp.537-538