IMT-24: QUANTITATIVE TECHNIQUE

PART-A

Q1. 'Quantitative techniques are frequently used in organizations for decision making. Discuss

Q2. What precautions will you keep in mind while designing a questionnaire?

 Q3. Calculate arithmetic mean for the following data:

Class Interval 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45

Frequency 6 5 15 10 5 4 3 2 

Q4. (a) What are the properties that a good measure of variation should possess?

(b) 1000 light bulbs with a mean life of 120 days are installed in a new factory and their length of life is normally distributed with a standard deviation of 30 days.

a. How many bulbs will expire in less than 85 days?

b. If it is decided to replace all the bulbs together, what interval should be allowed between replacement if not more than 15 per cent should expire before replacement?

Q5. (a) Karl Pearson coefficient of skewness of distribution is + 0.32. Its standard deviation is 6.5 and mean is 29.6. Find the mode and median of the distribution.

(b) If the mode of the above distribution is 24.8, what will be the standard deviation?

(c) For a distribution, Bowley's coefficient of skewness is -0.36, Q₁ is 8.6 and median is 12.3. "What is quartile coefficient of dispersion?

(d) Compute quartile deviation and coefficient of skewness for the following given values: Me = 18.8, Q₁ = 14.6, Q₃ = 25.2

PART-B

 Q1. (a) What are the properties of the regression coefficient?

(b) The following is the data of 10 cities. Calculate correlation coefficient between the density of population and the death rate:

Comment on the result.

Q2. (a) You are given the following information on advertising expenditure and sales in a company. Average Advertising expenditure Rs. 10 lakhs and standard deviation Rs. 3.0 lakhs. Average sales Rs. 120 lakhs and the standard deviation Rs. 12 lakhs. The value of correlation coefficient is 0.5.

Find two regression lines and values of sales when advertising is Rs. 15 lakhs.

(b) Fit a straight line trend to the following time series data and forecast the sales for 2009

Year 2001 2002 2003 2004 2005 2006 2007

Sales ( in tones) 80 90 92 93 94 102 109

Q3. (a) Two insurance schemes A and B are to be sold. An agent has the chance of finding customers as 60 percent for A and 40 per cent for B. Assuming the sale of A and B is independent find the probability that the scheme A has been sold given that at least one insurance scheme has been sold.

(b) A mail order company has three boys: Amar, Akbar and Anthony, for packing and dispatching the goods. They all make mistakes now and then. The probability of their making mistaks in packaging, dispatching etc. are one in a hundred, five times in hundred and three times in hundred. They deal with respectively 30 per cent, 40 per cent and 30 per cent orders. Find the probability that if a mistake is detectd, the order was handled by Amar?

Q4. (a) What are the components of a time series?

(b) Assume that a factory has two machines. Past records show that Machine 1 produces 30 per cent of the output. 5 per cent of items produced by Machine 1 were defective and only 1 per cent produced by Machine 2 were defective. If an item selected at random is found to be defective, what is the probability that it was produced by Machine 2.5. Explain the circumstances when the following probability distributions are used:

(a) Binomial distribution

(b) Poisson distribution

PART-C 

Q1. How does hypothesis help a researcher to test the logical or empirical consequences? 

Q2. The average score of two groups A and B were found to be 25 and 22 with standard deviation 4 and 5.5 respectively. Test for the equality of the two group scores. Given n₁ = n₂ = 400.

Q3. (a) In a test given to two groups of students, the marks obtained were as follows:

First Group: 18, 20, 36, 50, 49, 36, 34, 49, 41

Second Group: 29, 28, 26, 35, 30, 44, 46

Examine the significance of difference between the mean marks obtained by the students of the above two groups. (At 5% level of significance the value of t for 14 degrees of freedom is 2.14).

(b) The following table gives the number of units produced per day by two workers A and B for a number of days:

A: 40, 30, 38, 41, 38, 35

B: 39, 38, 41, 33, 32, 49, 49, 34

Should these results be accepted as evidence that B is the more stable worker? Use F-test.

Q4. Two random samples are drawn from two normal populations and the size of various items of the two samples are:

First Sample: 20, 16, 26, 27, 23, 22, 18, 24, 25, 19

Second Sample: 27, 33, 42, 35, 32, 34, 38, 28, 41, 43, 30, 37 

Obtain the estimates of the variances of the population. Test whether the two populations have the same variance.

Q5. On of the basis of information given below about the treatment of 200 patients suffering from a disease, state whether the new treatment is comparatively superior to the conventional treatment.

For drawing your inference use the value of %2 for one degree of freedom at the 5 per cent level of significance, viz., 3.841.

CASE STUDY - I

 Forecasting has today become key success factor for companies with long lead times. Resources and capabilities within a company have to be anaged in an optimal way, which requires buffering fluctuations in future demand. The demand forecasting model was formulated for resources required in Retail Vertical of Wipro Technologies. It was examined to know how Retail Vertical of Wipro Technologies makes its forecast of resources and which processes are considered to make forecast. Both quantitative and qualitative approaches were identified which were used to model the forecasting process in the short-to-medium-term range. The time series approach was adopted for the quantitative model in order to capture various elements of the data series like trend, seasonality and level to forecast the resources. The qualitative approach was adopted when the task involved predicting a new technology for which no historical data was available or in a situation where a drastic change in historical trend was foreseen. The error measure which needs to be studied for evaluation of a specific parameter of interest like accuracy or sensitivity were identified as the model parameters and described how these parameters could be used to make the model more accurate and to adjust the model as per the changes occurring in the external environment. The accuracy of the model was maximized by adopting a method which combined the qualitative and quantitative parts of the model.

Problem Formulation: Resource forecasting at Retail Vertical was being done on an intuitive basis with persons at the top levels of hierarchy blending their knowledge and experience to find out the quantum of resources required in the future. Though this approach worked well for short-range forecasts, it showed a higher percentage of error for medium-to-long-range forecasts. Also, even for short-range forecasts, the intuitive method of forecasting works well till the person preparing the forecast has sufficient expertise. However, if a new person has to step into the role of deciding on the number of resources required in the future, then it may result in a higher percentage of error. Thus, the need arises for developing a scientific approach towards forecasting the resource requirements with a desired level of accuracy.

Research Problem: The project dealt with outlining the process of breaking up the revenues of the Retail Vertical, visa-vis the different technologies that were used to implement the various projects in the accounts.

The project finally attempted to forecast the break-up of IT resources in various technologies using a quantitative and qualitative model. The project was to help the Retail Vertical of Wipro Technologies to forecast the following:

• Technology-level revenue

• Number of resources required in each skill area

• Fresher/lateral ratio

• Onsite/offshore ratio

Expected Outcome: The expected outcome from the project was as follows:

• Gain key insights into the drivers for resource requirement, i.e., the factors that directly or indirectly affect the resource requirement

• Identify the trends prevalent in the respective technologies

• Get an insight into an approach towards the breakdown of revenue from the highest level to the level of the technology

• Understand how the qualitative method needed to be mixed with the quantitative model

The maximum value of alpha was set to be 0.7 and its minimum value was set to be 0.1.

This project is about formulating a standard procedure, whereby the whole process of demand forecasting could be made more accurate, more scientific and almost error-free. The model also attempted to break up the whole problem into smaller parts and used a mix of mathematical and judgmental procedures to analyze and solve the problem. This, it was felt, would provide real value addition as the researchers attempted to look at an optimal solution to how to integrate the various domains like project implementation, resource allocation and revenue forecasting.

Questions:

1. Resource forecasting on an intuitive basis works well for short-range forecasts. However, it shows a higher percentage of error for medium-to-long-range forecasts. Comment on this statement.

2. Can you suggest an alternative to reduce the error percentage?

3. How would the use of relational database help to improve the forecasting model?

CASE STUDY-II

 Manufacturing excellence is one of the competitive advantages that Exide enjoys vis-a-vis its competitors. To sustain this advantage, organization-wide Enterprise Resource Planning (ERP) implementation was initiated. This was done with the objective of streamlining organizational processes. With the growing demand for Exide products, the need for shorter production cycles had become essential. Material Requirement Planning (MRP) based on requirement forecasts from regions and segments was undertaken to ensure minimum wastage of raw materials and low inventory levels. This activity was of critical importance as Exide endeavoured to maintain little or no inventory levels in its factories. Three-month Rolling Plans carrying requirement projections for the subsequent three months from the regions and segments acted as inputs for the creation of a document called Plant Independent Requirement (PIR). This document was a consolidated list of all the possible types of batteries and acted as a precursor to MRP. However, the Rolling Plan process was a disorganized one with no uniformity in templates or material codes. This resulted in a lot of confusion and time being wasted unnecessarily to compile the data. This project involved the creation of a Data Collation System (DCS) that would make available to the user, consolidated and periodic data. This required exact material codes to overcome the possibility of using erroneous codes. Finally, a Troubleshooting Guide was also created to enable the controller sort out common problems. The application was designed on Microsoft Excel in order to maintain simplicity and ensure ease of use. The system met the criteria of making the required data available to the controller at the click of a mouse. DCS would significantly reduce the time required to compile the data requirements and its output would be fed into the SAP system in place, prior to MRP. The system was flexible enough to accommodate changes, thereby ensuring a long work life.

Project Objectives: The project involved the development of an accurate DCS that would compile data in the beginning of the Rolling Plan process and transfer it to the SAP system as an input to MRP. The primary objective was to streamline and automate the process so that data could be available easily to the user at a single click. The secondary objective was to develop a simple system, easy to use and maintain. Additionally, it was decided to give users restricted access to the templates they were using in order to prevent them from tampering with the formatting. Three specific objectives were enumerated which are listed below:

• Identification of Correct Product Codes: This was done in consultation with the controller at the Head Office. Segments and regions were requested to send the repository of material codes that was being used.

• Calculation of Variations: A policy was prevalent in Exide Technologies whereby projection of requirements in the current month matched the actual material dispatched. This was followed in order to maintain a zero-inventory level of finished goods at all factories. Hence, variations would be automatically displayed on entry of actual off-take data, updated on a daily basis by the controller.

Additionally, requirement projection of a particular month in the preceding month's plan could have a maximum variation of+10 per cent or -10 per cent with the projection of the current month.

Details and Requirements: Indents were to be received from regions and segments on the 25th of the previous month, plan containing requirement for the next three months, i.e., plan containing weekly breakup for the current month and monthly data for the next two months. The first month's requirements should conform 100 per cent to actual off-take. This was done at the end of that particular month. The second month's requirements could have a maximum deviation of +10 per cent to -10 per cent from previous requirement projections.

In order to achieve this, it was imperative that all activities prior to actual production were carried out in minimum time with the greatest possible accuracy. The policy of maintaining little or no inventory necessitated the need to have highly accurate demand projections. The DCS was instrumental in streamlining certain aspects of the planning process that preceded Material Requirement Planning and actual manufacturing. An Excel-based

application compiled the requirements data, making it readily available to the user for his reference and perusal.

It also displayed variations between projected and actual data, enabling the user to focus on segments where the difference violated permissible limits. Output from DCS would act as inputs to the subsequent MRP. This represented advancement in the endeavour to automate business processes in order to accomplish tasks quickly with minimum errors.

Questions: 

1. Analyse the need and importance of Data Collation System. Justify the inclusion of the SAP system and Excel-based application system.

2. Analyse the project objectives. Do you feel the information collected would act as a precursor to effective Material Requirement Planning and supply system?

3. Discuss the requirement planning methodology for the current month followed by the next two months. Why is it important?