Answer

1. INTRODUCTION

   Pricing and production decision-making relies much on information about demand. Information on future demand condition is very useful to managers for price-setting and price taking for firms during scheduling and advertising campaigns. Therefore, these aspects have brought an element of forecasting or prediction in production. Though these terms are used interchangeably in the business world, they are not equivalent as they are perceived. Nonetheless, forecasting related to prediction since prediction is a technical world for prediction while forecasting is the substance-matter setting. Consequently, many firms depend on forecasting to provide a prediction for firm-level demand. There are four reasons why forecasting is carried out:

   1. Curiosity the need to know the future.
   2. Decision-making for prediction purposes.
   3. Policy evaluation for modification of policies to change expectations hence modeling behaviour.
   4. Model evaluation to attain the quality of modeling as descriptive tools and for model-based predictions.

   Forecasting can be grouped into three major classes:

   1. Magical forecasting where there is no familiar cause-effect relationship and a good example of such forecast is oracles.
   2. Subjective that involves judgmental forecasts and makes use of Delphi method, which makes use of averages in questionnaires.
   3. The objective that involves the use of univariate or one-time series only and multivariate or many variables briefed in a vector.

   Among the three, the most commonly used forecast method in practice by an institution is most institutional forecasts known as a mix of subjective and objective elements.

   Forecasting of the model can also be classified in terms of model adopting system used:

   1. Model-free procedures, which make use of extrapolation by free hand, trend fitting and exponential smoothing.
   2. Model-based procedures such as data-driven in time series or theory-driven. This typed is mostly used in econometric models and is thus what will be adopted widely in this task.

   Of most useful is the model-based procedure, which makes use of exponential smoothing. In this procedure, variables are the sophisticated procedure of free-hand method.  Also, technically: a causal filter obtains the filtered value of a data point  from observations  where and a smoother define the smoothed value of a data point  from observation  and

   The most common model-based procedure is ‘Single Exponential Smoothing (SES)’.

   Single Exponential Smoothing (SES)

   SES defines the filtered value  from a weighted average over past observation and past filtered value:

   where  and is a damping or smoothing factor.

   SES can be represented simply as .

   Quality Control in Forecasting

   The success of a business is defined by the correct and accurate quality control of foresting method used. There are three measures of accuracy of forecast:

   Measures of Accuracy

   1. Mean Absolute Deviation (MAD)
   2. Mean Squared Error (MSE)
   3. Mean Absolute Percentage Error (MAPE)

   In this task, focus is on MAPE

   MAPE

    

   where  is the total number of observations.

   TASK

   Given

    

   1. Computation for computation of MAPE for 12 months using excel. The results are indicated below:

    

    

    

   2. MAPE for the First 3 Months

    

   From theory, the main objective of forecasting in sale departments in a company is to project consumer sales over varied times: short, intermediate, and long-range time horizons. Whenever sales forecasting is made, major functional areas of a company: distribution, procurement, transportation, and manufacturing, make suitable operational pronouncements about transportation schedules, materials to obtain, workforce scheduling, and products to create and package.

   However, forecasting is an inconsistent science; as time horizons increase; forecast accuracy decreases, making capacity and resource planning difficult. This is what has been witnessed when MAPE for the first three months were calculated. For α=0.25, MAPE for 12 months ≈ 0.1 while for 3 months ≈ 0.2. Similarly, for α =0.85, MAPE for 12 months ≈ 0.39 while for 3 months ≈ 0.47. In both cases, MAPE for three months were more accurate than for twelve months.

   It thus a crucial task for procurement and manufacturing to have product-specific forecasts, that will make forecasting more accurate. Therefore, forecasting should be aimed at shorter durations.