1. Forecasting is an important process in order to understand the future possibilities for a business. Quantitative forecasting requires historical data to generate the forecast. Therefore, the first condition required for quantitative forecasting is the availability of time series or historical data that can be used to generate a prediction for the future.
Further, for quantitative forecasting to be effective, there must be existing evidence that the historical data available for forecasting is relevant and can be used for forecasting.
Therefore, for appropriateness of quantitative forecasting historical data, that are measurable, must be available and there must be proof that these data is relevant for forecasting. When these conditions are not met, then quantitative forecasting cannot be done.
2. Error in moving average is determined by the difference between the actual value at time period say t and the forecast value at next time period i.e. t+1. As moving average is the arithmetic mean of the data, the most recent values will give a smaller error as the recent forecast would be closer to recent values than values in distant past.
The number of terms is decided on the nature of fluctuations in the series. When more number of data is chosen, lesser weight is given to the recent data and vice versa. However, how many numbers of observations are taken is decided by the nature of the data.
If there are great fluctuations in the time series data then a larger number of data is desirable while if the data shows relatively smooth trend, then a smaller data will also be appropriate for forecasting.
In the former case, the difference in data is large and therefore the error is higher and in the latter case the error is smaller. Therefore with higher error the number of observations taken is higher while when error is smaller, the number of observations taken is smaller while computing moving average.
While making this choice one assumption is made regarding the future i.e. the future too will follow similar trend in fluctuations in the values of the observations as according to their past trend. In other words, when error is large indicating a large seasonal fluctuation in data, it is assumed that similar fluctuation will be seen in future.
3. Seasonal index values can be used for forecast by the following method. First, the seasonal indices of the observations have to be computed for all the years taken for the forecasting. Then the index values have to be ranked from lowest to highest such that there are five values observable under each month.
Then the sum of the three central values of each month are taken which is done by eliminating the first and the last value each month and they added together. The aim of the this step is to eliminate any extreme value from the data .
4. Irregular index is used in forecasting. The irregular index is actually the error component that accounts for the fluctuations in a time series data, which cannot be explained by seasonal variations or trend analysis.
Therefore, the irregular index used in forecasting actually indicates the unaccounted fluctuations in the time series, which are unlike the seasonal fluctuations in the time series. This forms the error variable in the time series data and is used as irregular index for forecasting.
5. While quantitative techniques employ time series data for analysis, qualitative techniques use opinions of expert analysts. Qualitative modeling for forecasting follows the following methods – Delphi technique, jury of executive opinion, sales force composite, and consumer market survey.
In the Delphi model experts located in different locations are asked to make forecasts. The experts used the Delphi model are expert analysts, decision makers, staff, or respondents.
When it is the decision makers, usually 5 to 10 analysts are used while in other cases a detailed survey is done. In case of jury of executive opinion model, forecasting is done after views of high-level management experts are taken, which is usually combined with statistical models.
6. The difference between profit and contribution in an objective function provides the range of optimality of the function. The difference between the profit and the contribution shows the optimal coefficient.
It is important for decision makers to know the coefficients as they present either the upper or the lower limit of the slope of the function indicating the rate of change in the function.
7. Graphical solutions are easier to understand. They present the same quantitative findings in a more understandable format that even a nonprofessional can interpret.
Further, graphical solutions help in identifying the area, which requires attention with ease. Graphical solutions provide easy, professional and relatively accurate findings for a problem. They are best adopted when there are two variable decision problems.
8. When a linear programming problem is infeasible it is essential to look for the reason that makes the problem infeasible. In such a situation, the best possible option is to drop one or more constraints and solve the problem. If after omitting the constraints an optimal solution can be reached, it can be concluded that the constraints that were omitted were the root cause of the infeasibility of the problem.
Unbounded linear programming occurs when the solution to the problem is infinitely large even though none of the constraints are violated in case of a maximization problem, in case of a minimization problem, the solution would be infinitely small in case of unbounded problem.
9. In case of optimality problem, the corners of a feasible plans are called extremes. This is because the corners of a feasible region will always provide the optimal or extreme values. The intersection of the boundary of two or more constraints in the feasibility region actually forms the corner indicating optimality in a linear programming.
This occurs due to the geometrical shape of the problem. Graphically, the feasible regions intersect in a half plane which results in the boundary of the feasible region to either become flat or have a corner that is always pointed outwards.
Therefore, the corners are usually called the extreme points as they possess the characteristics of singularity as in, they do not have a pair of points in the feasible region. Therefore, the lines connecting these points form a corner point.
Thus, the optimal solution in a linear programming is always at the corner of a feasible region as this is formed by the intersection of the geometric representation of two or more constraint functions. This is the reason why corners are considered to be extremes in a linear programming problem.
References
Bozarth, C. C., & Handfield, R. B. (2006). Introduction to Operations and Supply Chain Management. SA: Pearson Education.
Jain, C. L., & Malehorn, J. (2005). Practical guide to business forecasting. New York: Institute of Business Forec.
Render, B., Stair, R. M., Hanna, M. E., & Badri, T. (2009). Quantitative Analysis For Management. New York: Pearson Education.