Exponential Smoothing Method MCQ Quiz - Objective Question with Answer for Exponential Smoothing Method - Download Free PDF

Concept:

In Simple Exponential Smoothing, the forecast is updated based on the previous actual and forecasted values using the formula:

\( F_{t} = \alpha A_{t-1} + (1 - \alpha) F_{t-1} \)

Where, F_t is the forecast for the current period, \(A_{t-1}\) is the actual demand of the previous period, and \(F_{t-1}\) is the forecast for the previous period.

Calculation:

Given:

Actual demand in January = 600 units, Forecast for January = 500 units

Actual demand in February = 700 units

Smoothing coefficient, \(\alpha\) = 0.8

Forecast for February:

\( F_{Feb} = 0.8 \times 600 + 0.2 \times 500 = 480 + 100 = 580 \)

Forecast for March:

\( F_{Mar} = 0.8 \times 700 + 0.2 \times 580 = 560 + 116 = 676 \)

Concept:

The given sales data for the last four years are: 840, 860, 850, and 870 units.

The three-period moving average is given by:

\( F_5 = \frac{A_2 + A_3 + A_4}{3} \)

\( F_5 = \frac{860 + 850 + 870}{3} \)

\( F_5 = \frac{2580}{3} = 860 \)

The simple exponential smoothing equation is:

\( F_5 = \alpha A_4 + (1 - \alpha) F_4 \)

Where:

A₄ = 870 (Actual sales in Year 4)

F₄ = 855 (Forecast for Year 4)

F₅ = 860 (Forecast for Year 5 using both methods)

Calculation:

Substituting values in the equation:

\( 860 = \alpha (870) + (1 - \alpha)(855) \)

Expanding:

\( 860 = 870\alpha + 855 - 855\alpha \)

\( 860 - 855 = (870 - 855) \alpha \)

\( 5 = 15\alpha \)

\( \alpha = \frac{5}{15} = \frac{1}{3} \)

Calculation:

Forecast for the January is not given.

Assuming the forecast for January is equal to demand in January. so, the table can be generated using the forecasting formula for February, March, and April month to get the forecast for May month.

F2 = F1 + α (D1 - F1)

⇒ F2 = 1080 + 0.3 (1080 - 1080) = 1080

⇒ F3 = 1080 + 0.3 (950 - 1080) = 1041

⇒ F4 = 1041 + 0.3 (1050 - 1041) = 1044

Next month's forecast using exponential smoothening

F₅ = F₄ + α (D₄ - F₄)

F5  =1044 + 0.3 (1120-1044) = 1066.8

⇒ F5 ≃1067 water purifiers
Forecast using weighted moving average is given as,

⇒ F'5 =1120 × 0.4 + 1050 × 0.3 + 950 × 0.2 + 1080 ×  0.1

⇒ F'5 = 1061 water purifiers

Therefore difference in forecast = 1067-1061 = 6

Concept:

Exponential smoothing method:

\({F_t} = {F_{t - 1}} + α \left[ {{D_{t - 1}} - {F_{t - 1}}} \right]\)

where α = smoothing constant and the term (Dt-1 - Ft-1) represents the error present in the forecast.

Additional Information In the exponential smoothing method of the forecast, the forecast for the next period is equal to 

Ft = α Dt-1 + (1 - α) Ft-1 

If we further expand the expression

Ft = α Dt-1 + (1 - α) (α Dt-2 + (1-α) Ft-2

Ft = α Dt-1 + α (1-α ) Dt-2 + (1 - α )2 Ft-2

If we put the value of α = 0.8 (Close to 1) then,

Ft = 0.8 Dt-1 + 0.16 Dt-2 + 0.04 Ft-2 

It can be observed from the above expression that recent data is given more weightage compared to the previous data, therefore, the higher value of exponential smoothing constant (Close to 1) is used for changing pattern of demand or to follow recent demand.

Concept:

Exponential smoothing method:

This method gives weight to all the previous data and the pattern of weight assigned is exponentially decreasing in order with most recent data is given highest weight.

The forecast for next period is equal to:

F_t = α D_t-1 + (1- α) F_t-1

where, Ft-1 = old forecast, α = exponential smoothing constant,

Dt-1 = latest figure sale or latest demand, F_t = next forecast

Calculation:

Given:

α = 0.2 , Dt-1 = 120 units , error e = 20 units

e = Dt-1 - Ft-1 = 20 ⇒ Ft-1 = 100

Ft = α Dt-1 + (1- α) Ft-1

F_t = 0.2 × 120 + (1- 0.2) 100

Ft = 24 + 80 = 104 units

Explanation:

• Forecasting is the prediction of future sells or demand of the particular product.
• It is a projection based upon past data and art of human judgement.

Types of forecasting method

Concept:

The general form of forecasting is Ft = Ft-1 + α. (Dt-1 – Ft-1)

where α = smoothing constant and its range is 0 ≤ α ≤ 1 

For Immediate forecast → high value of "α" is high and less for other forecasts.

Hence the high value of forecast is only chosen when the nature of demand is not reliable rather unstable.

\(α = \frac{2}{{n + 1}}\)

where, n = no. of period of moving average, F_t = recent forecast, F_t-1 = previous forecast, D_t-1 = previous demand

• If α = 0, then F_t = F_t-1 ……….…..(limit of stability)
• If α = 1 then F_t = D_t-1…………….(limit of responsiveness)​

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Explanation:

Forecast value in Smoothing constant method is given by-

F_t = F_t-1 + α [ D_t-1 - F_t-1 ]

where F_t = Current period forecast, F_t-1 = last period forecast, D_t-1 = last period demand, α = smoothing constant

for α = 0 

Ft = Ft-1 

Hence for α = 0 only the current period forcast becomes equal to last period forecast.

Important Points

For α = 1 current period forecast will become equal to the last period demand.

Explanation:

Forecasting

• Forecasting is defined as estimating the future value that a parameter will take. Most scientific forecasting methods forecast the future value using past data.
• Some simple forecasting models using time series data are simple average, moving average and simple exponential smoothing.

Moving average Method or rolling average Method: 

• In this method, fresh average is calculated at the end of each period by adding the actual demand data for the most recent period and deleting the data for the order period. It gives equal weight to each of the most recent observations.

\({F_{n+1}} = \frac{{{D_1} + {D_2} + {D_3} + {D_4} + \ldots \ldots \ldots \ldots \ldots \ldots + {D_n}}}{n}\)

Weighted moving average Method: 

• This method gives unequal weight to each demand data with more weight to recent data.

\({F_{n+1}} = \left[ {{w_{1}} \times {D_{1}} +{w_{2}\times {D_{2}}} +..........+ {w_{n}} \times {D_{n}}} \right]\)

Exponential Smoothing Method: 

• This method gives weight to all the previous data and the pattern of weight assigned is exponentially decreasing in order with most recent data is given the highest weight.
• In exponential smoothing method of forecast, the forecast for the next period is equal to 

F_t = α D_t-1 + (1 - α) F_t-1 

where, D_t-1 = latest figure sale or latest demand,  F_t-1 = old forecast, α = exponential smoothing constant

Additional Information

Project

• A project may be defined as a combination of interrelated activities which must be executed in a certain order before the entire task can be completed.
• The aim of planning is to develop a sequence of activities of the project so that the project completion time and cost are properly balanced.
• To meet the objective of systematic planning, the management has evolved several techniques applying network strategy.
• PERT (Programme Evaluation and Review Technique) and CPM (Critical Path Method) are network techniques which have been widely used for planning, scheduling and controlling the large and complex projects.

Difference between PERT and CPM (Critical Path Method)

Gantt charts:

• Gantt charts are mainly used to allocate resources to activities.
• The resources allocated to activities include staff, hardware, and software.
• Gantt charts are useful for resource planning. A Gantt chart is a special type of bar chart where each bar represents an activity.
• The bars are drawn along a timeline.
• The length of each bar is proportional to the duration of time planned for the corresponding activity.

Control charts:

• Control chart is a graphical representation of the collected information.
• It indicates whether a process is in control or out of control.
• It determines process variability and detects unusual variations taking place in a process.
• It ensures product quality level.
• It provides information about the selection and setting of tolerance limits.

Explanation:

Forecast error (ei) for a period is defined as the difference between actual and actual and forecasted demand.

e_i = Actual demand - Forecast demand ⇒ D_i - F_i

Exponential forecasting:

\({F_T} = {F_{T - 1}} + α ({D_{T - 1}} - {F_{T - 1}})\)

where

F_T is the forecast for the next period 

\(({D_{T - 1}} - {F_{T - 1}})\) is the forecast error and 

α is the smoothing constant.

Thus exponential smoothing takes into account the forecast error of the previous period, for the forecast of the next period.

Additional Information

Simple Average Method:

In the simple moving average, we take the average of the past data points for future demand.

For 'n' period moving average forecast will be given by:

\({F_{n+1}} = \frac{{{D_1}\;+\;{D_2}\;+\;{D_3}\;+ \;{D_4}\;+\;\ldots \ldots \ldots \ldots \ldots \ldots \;+\;{D_n}}}{n}\)

Weighted Moving Average Method:

In weighted moving average, the highest weightage is given to recent data & it decreases for older data points.

For n period weighted moving average, weightage is as follows:

\(\frac{n}{{{\rm{\Sigma }}n}},\;\frac{{n - 1}}{{{\rm{\Sigma }}n}},\;\frac{{n - 2}}{{{\rm{\Sigma }}n}}, \;- - - - - - - ,\frac{1}{{{\rm{\Sigma }}n}}\)

\({F_{n+1}} = \left[ ({{w_{1}} \times {D_{1}})\;+\;({w_{2}\times {D_{2}}})\;+\;..........+\;({w_{n}} \times {D_{n}}})\right]\)

Concept:

𝐹𝑡+1 = 𝛼𝐷𝑡 + (1 − 𝛼) 𝐹𝑡 = 𝐹𝑡 + α (Dt - Ft)

This equation can be used when simple exponential smoothing is used as a forecasting model.

Here Ft represents the forecast for period t, Dt is the known demand for period t and α is the smoothing constant.

Calculation:

Forecaster for February:

F₂ = 400 + 0.75 (500 – 400) = 475

Forecaster for March:

Concept:

Exponential smoothing method:

This method gives weight to all the previous data and the pattern of weight assigned is exponentially decreasing in order with most recent data is given highest weight.

The forecast for next period is equal to:

F_t = α D_t-1 + (1- α) F_t-1

where, Ft-1 = old forecast, α = exponential smoothing constant,

Dt-1 = latest figure sale or latest demand, F_t = next forecast

Calculation:

Given:

α = 0.2 , Dt-1 = 120 units , error e = 20 units

e = Dt-1 - Ft-1 = 20 ⇒ Ft-1 = 100

Ft = α Dt-1 + (1- α) Ft-1

F_t = 0.2 × 120 + (1- 0.2) 100

Ft = 24 + 80 = 104 units

Concept:

When only demand/sales are given from previous data, then forecast for the next month:

\(F_t=F_{t-1}+\alpha(D_{t-1}-F_{t-1})\)

f_t = forecast of next month,

f_t-1 = forecast for the previous month and so on.

D_t-1 = Demand of the previous month

Calculation:

Given:

\(F_t=F_{t-1}+\alpha(D_{t-1}-F_{t-1})\)

\(F_2=F_{1}+\alpha(D_{1}-F_{1})\)

\(F_2=70+0.4 \times (70-70)\)

F₂ = 70

\(F_3=F_{2}+\alpha(D_{2}-F_{2})\)

\(F_3=70+0.4 \times (68-70)\)

F₃ = 69.2

\(F_4=F_{3}+\alpha(D_{3}-F_{3})\)

\(F_4=69.2+0.4 \times (82-69.2)\)

F₄ = 74.32

\(F_5=F_{4}+\alpha(D_{4}-F_{4})\)

\(F_5=74.32+0.4 \times (95-74.32)\)

F₅ = 82.59

Note: In the options, 82.59 is not available so always select the higher number from the given answer.

Explanation:

In exponential smoothing method of forecast the forecast for the next period is equal to 

Ft = α Dt-1 + (1 - α) Ft-1 

If we further expand the expression

Ft = α Dt-1 + (1 - α) (α Dt-2 + (1-α) Ft-2

Ft = α Dt-1 + α (1-α ) Dt-2 + (1 - α )2 Ft-2

If we put the value of α = 0.8 (Close to 1) then,

Ft = 0.8 Dt-1 + 0.16 Dt-2 + 0.04 Ft-2 

It can be observed from the above expression that recent data is given more weightage compared to the previous data, therefore, the higher value of exponential smoothing constant (Close to 1) is used for changing pattern of demand or to follow recent demand.

Concept:

For exponential smoothing method,

\(F_t = F_{t-1} + α (D_{t-1} – F_{t-1})\)

where F_t-1 = previous year's forecast, Ft  = current year's forecast, Dt-1 = previous year's demand, α = smoothing constant

Calculation:

Given:

F_t-1 =  57, Dt-1 = 62, α = 0.3

\(F_t = F_{t-1} + α (D_{t-1} – F_{t-1})\)

\(\Rightarrow F_{t}= 57+ 0.3\times (62 – 57)\)

F t  = 58.5.