Forecasting MCQ Quiz - Objective Question with Answer for Forecasting - Download Free PDF

Explanation:

Pre-Planning in Manufacturing Operations:

• Pre-planning in manufacturing operations involves identifying, analyzing, and preparing for all the necessary activities and requirements before the actual production process begins. It is a critical phase that ensures the smooth flow of operations, optimal resource utilization, and effective management of uncertainties.

Forecasting:

• Forecasting is the process of predicting future production requirements based on past data, market trends, and expected demand. It is a vital operational function that comes under pre-planning because it provides the foundation for all subsequent planning and decision-making activities. Accurate forecasting helps in determining the resources needed, scheduling production, and minimizing wastage.
• Forecasting involves analyzing historical data, considering external factors such as market demand, economic conditions, and seasonal variations, and using mathematical models or software tools to predict future requirements. This process enables manufacturers to anticipate challenges and prepare accordingly, ensuring that production meets demand efficiently.

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:

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

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

\( 5 = 15\alpha \)

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

Explanation:

Winter's Exponential Smoothing

• Winter's Exponential Smoothing, also known as the Holt-Winters method, is an advanced forecasting technique that adjusts forecasts for both linear trends and seasonality effects using three smoothing parameters. It is an extension of simple exponential smoothing and Holt's linear trend model, specifically designed to handle data with seasonal variations.
• Winter's Exponential Smoothing uses three components to make forecasts: the level, the trend, and the seasonality. The method applies three smoothing equations to update these components over time:
  • Level (L): This component represents the baseline value of the time series at any given point, adjusting for both trend and seasonality.
  • Trend (T): This component captures the underlying trend in the data, indicating whether the series is increasing or decreasing over time.
  • Seasonality (S): This component accounts for repetitive patterns or cycles that repeat at fixed intervals, such as monthly or quarterly seasonality.

The equations for Winter's Exponential Smoothing are as follows:

• Level: L_t = α(Y_t / S_t-m) + (1 - α)(L_t-1 + T_t-1)
• Trend: T_t = β(L_t - L_t-1) + (1 - β)T_t-1
• Seasonality: S_t = γ(Y_t / L_t) + (1 - γ)S_t-m
• Forecast: F_t+k = (L_t + kT_t)S_t-m+k

Where:

• Y_t = Actual value at time t
• L_t = Level component at time t
• T_t = Trend component at time t
• S_t = Seasonal component at time t
• α, β, γ = Smoothing parameters for level, trend, and seasonality, respectively
• m = Number of periods in a seasonal cycle
• k = Number of periods ahead to forecast

Advantages:

• Effectively handles data with both trend and seasonal patterns.
• Produces accurate short-term forecasts by adjusting for seasonality.
• Flexible model that can be applied to various time series data.

Disadvantages:

• Requires careful selection of smoothing parameters, which can be complex.
• May not perform well with non-seasonal data or data with irregular patterns.

Applications: Winter's Exponential Smoothing is widely used in various fields, including retail sales forecasting, inventory management, and financial planning, where accurate predictions of seasonal trends are crucial.

Explanation:

Box-Jenkins (ARIMA) Forecasting Model

• The Box-Jenkins methodology, also known as ARIMA (AutoRegressive Integrated Moving Average), is a popular statistical method used for time series forecasting.
• This model combines three components: Autoregressive (AR), Integrated (I), and Moving Average (MA)—to better understand and predict future values in a time series.

Components:

• Autoregressive (AR): This component uses the dependency between an observation and a number of lagged observations (previous time points). It reflects the relationship between the current value and its past values.
• Integrated (I): This component represents the differencing of raw observations to make the time series stationary, meaning its statistical properties do not change over time. This process involves subtracting the previous observation from the current observation, which helps in removing trends and seasonality in the data.
• Moving Average (MA): This component uses the dependency between an observation and a residual error from a moving average model applied to lagged observations. It captures the relationship between the current value and the past forecast errors.

Importance of Integration in ARIMA:

1. Trend Removal: Many time series data exhibit trends over time. For example, stock prices may generally increase over time, or sales figures may show a rising trend. The integrated component helps remove these trends by differencing the data, making it easier to model and forecast.

2. Seasonality Adjustment: Time series data often have seasonal patterns, such as higher sales during holiday seasons. Differencing can also help in removing seasonal effects, although sometimes seasonal differencing (subtracting the value from the same period in the previous year) is used to address seasonality more effectively.

3. Ensuring Stationarity: As mentioned earlier, many time series models assume stationarity. By incorporating the integrated component, ARIMA models ensure that the data meets this assumption, which is critical for accurate forecasting.

4. Simplicity in Modeling: Once the time series is made stationary through differencing, the autoregressive and moving average components can be more effectively applied, leading to simpler and more accurate models.

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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Concept:

The absolute deviation is |D – F|

The forecast for each period can be calculated using the regression line equation.

Calculation:

Sum of absolute deviations is = 0.2 + 0.3 + 0.6 + 0.5 + 0.6 = 2.2

Concept:

Simple Average method:

• It is a method for inventory valuation or delivery cost calculation, where even if accepting inventory goods with different unit costs, the average unit cost is calculated by multiplying the total of these unit costs simply by the number of receiving.

Calculation:

Given:

F _July= 200, F _August= 225, F _Sep= 245, F _Oct=?

\( \therefore {F_{Oct}} = \frac{{{F_{July}}~+~ {F_{Aug}} ~+~ {F_{Sep}}}}{3}\)

\(F_{Oct} = \frac{{200 + 225 + 245}}{3}\)

\(\therefore {F_{Oct}} = 224\;units\)

Explanation:

Exponential smoothing method:

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

where α = smoothing constant.

Moving Average Method:

The moving average method uses the average of the most recent 'n' data values in the time series as the forecast for the next period.

\({F_{t + 1}} = \frac{{{D_t} + {D_{t - 1}} + \ldots + {D_{t - n + 1}}}}{n}\)

Note that the 'n' past observations are equally weighted.

The simple moving average model described above has the undesirable property that it treats the last 'k' observations equally and completely ignores all preceding observations.

Intuitively, past data should be discounted in a more gradual fashion -- for example, the most recent observation should get a little more weight than 2^nd most recent, and the 2^nd most recent should get a little more weight than the 3rd most recent, and so on. The simple exponential smoothing model accomplishes this.

Thus, the simple exponential smoothing forecast is somewhat superior to the simple moving average forecast because it places relatively more weight on the most recent observation i.e., it is slightly more "responsive to changes" occurring in the recent past.

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 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 the prediction of future sales or demand for a particular product in the market. Forecasts can be made by using the past data of a product.

It can be done in two ways

i) Qualitative Technique: 

This approach is used for new product and used for long term forecasting. In this approach, there is no need for any data.

Opinion survey:

• In this method, opinions are collected from the customer, retailer and distributor regarding the demand pattern of the product.

Market trial:

• It is applied for new product and in this case, a product is introduced between a limited population in the form of a free sample.
• It is applied for low-cost products like toothpaste, chocolate, coldrinks etc.

Market research:

• In this method, the work of survey is assigned to an external marketing agency and the purpose of the research is to collect information regarding the demand of a product and the various factors which influence the demand like customer income, location, quality, quantity etc are required to get the forecast.

Delphi technique:

• This technique is used to make more realistic judgemental methods by minimizing bias.
• In this method, a panel of experts (including decision-makers, staff personnel, and respondents) is asked sequential questions. 
• It is the step by step procedure and the final forecast is obtained by the common opinion of all the experts.

ii) Quantitative Technique: 

This is used to forecast the demand for the existing product for short term

Here some previous data are given and based on that forecasting is done.

• Simple Moving Average Method
• Weighted Moving Average Method
• Simple Exponential Smoothing Method
• Trend Line Estimate or Linear Regression Method 

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:

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

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

Calculation:

Given:

• When the forecast value shows an increasing trend then the regression will forecast a higher value compared to the moving average.