Quantitative Techniques

02 Sep

1. a. “Statistics is the nerve center for Operations Research.” Discuss.

b. State any four areas for the application of OR techniques in Financial Management, how itimproves the performance of the organization.

2. At the beginning of a month, a lady has Rs. 30,000 available in cash. She expects to receive certain revenues at the beginning of the months 1, 2, 3 and 4 and pay the bills after that, as detailed here:

Month Revenue Bills
1 Rs. 28,000 Rs. 36,000
2 Rs. 52,000 Rs. 31,000
3 Rs. 24,000 Rs. 40,000
4 Rs. 22,000 Rs. 20,000

It is given that any money left over may be invested for one month at the interest rate of 0.5%; for twomonths at 1.0% per month; for three months at 1.5% per month and for four months at 1.8% per month.

Formulate her problem as linear programming problem to determine an investment strategy that maximizes cash in hand at the beginning of month 5.

3. What is degeneracy? How does the problem of degeneracy arise in a transportation problem? How can we deal with this problem?

4. Give the various sequencing models that are available for solving sequential problems. Give suitable examples.

5. A company has determined from its analysis of production and accounting data that, for a part numberKC-438, the annual demand is equal to 10,000 units, the cost to purchase the item is Rs 36 per order, and the holding cost is Rs 2/unit/pear


a. What should the Economic Order Quantity be?

b. What is the optimum number of days supply per optimum order?

6. A TV repairman finds that the time spent on his jobs has an exponential distribution with a mean 30 minutes. If he repairs sets on the first-come-first-served basis and if the arrival of sets is with an average rate of 10 per 8-hour day, what is repairman‘s expected idle time each day? Also obtain average number of units in the system.

7. What is critical path? State the necessary and sufficient conditions of critical path. Can a project havemultiple critical paths?

8. Explain and illustrate the following principles of decision making:

a. Laplace

b. Maximin

c. Maximax

d. Hurwicz

e. Savage

f. Expectation

9. A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city on a weekly basis and never visits the same city in successive weeks. If he visits city X in a given week, then he visits city Z in next week. However, if he visits city Y or Z, he is twice as likely to visit city X than the other city. Obtain the transition probability matrix. Also determine the proportionate visits by him to each of the cities in the long run.

10. When it becomes difficult to use an optimization technique for solving a problem, one has to resort to simulation‖. Discuss.


Quantitative Techniques

02 Jul

Answer the following question.

Q1. What factors should be considered in industrial analysis?

Q2. Which factors influence operating environment?

Case Studies

Case Study

Lexicographic Goal Programming is used to solve a series of Linear The biggest problem which the managers face is allotting little resources among different programs and projects. Linear programming Method is being used to allot resources in the best possible way. This method is mostly used as a tool for research operation and has helped in decision making in most of the manufacturing companies and the finance and service organizations. The most vital and thriving methods in the quantitative evaluation to solve the business problems has been found in the physical allocation of products, generally called transportation problems. Actually, the idea is to bring down the expenses of shipping goods from one place to another, so that the needs of each receiving place are fulfilled and the shipping areas can function within their own capacity. Nevertheless, quantitative evaluation is used for a lot of problems instead of the physical allocation of goods. For instance, it is used to employ the workers proficiently for some particular jobs within the industry. The CEO of an XYZ Sawmill company asked for the following month’s log hauling plan for the three sawmills. He wanted to ensure that there is appropriate flow of logs provided to his sawmills to benefit from the good timber market. Secondly, he wanted to bring down the transportation expenses. The harvesting group had planned to shift to three new locations. The average cost of hauling loaded and unloaded trucks is 2 dollars per mile. The logging manager calculated the number of loaded trucks arriving from each day’s harvesting site. The number of loaded trucks is different due to variation in tl1e area and cutting methods which are different for each site. At last, the manager of sawmill calculated the loaded trucks they would require for their mills per day. Ascertaining expenses to haul from each site to the mill is the next step. Linear programming problem is fixed for minimizing the expenses; i.e., the hauling expenses had to be brought down and the daily requirement of sawmills had to be met, while keeping the number of loaded trucks lower. The best solution for 5,760 dollars had to sort out through three axes. 5,760 dollars show the least every day hauling expense for the XYZ Sawmill Company from three logging places to the three sawmills. All the units should be used for this kind of problem. As seen in the above mentioned problem, it is seen that the sawmill used all the loaded trucks which were available. If the supply is appropriate to meet the demands, the surplus can be overlooked and .the whole supply can be considered equal to the total requirement. By using the simplex method, the problem of transportation can be solved; nevertheless, this method takes up time for calculation. Error can occur when done manually. Transportation method is beneficial since the process includes only the important variables; there is no need for artificial variables since they occur in the simplex process. Though the transportation method is being used for solving problems for moving goods from one place to another, it can also be used for other problems too, like, the above mentioned example, as far as the problem can be fixed in the form of transportation problem.

The railways play an important role in the economy and infrastructure of Britain. Not very many people traveled back in the 1920 as compared to present time, in spite of 50% reduction in rain routes as compared to the 1960s. Rail is also used for transporting goods around Britain. Rail proves to be more eco-friendly and safest means of transportation as compared to other vehicles so, not surprisingly, the number of people commuting have gone 40% more since the past ten years. By 2034, this figure can go up. The work of network rail has to look after the tracks, bridges and tunnels which comprises of the British rail network. The railway infrastructure is made up of signals and level crossings. It has to look after the 20,000 mile long track and 40,000 bridges and tunnels. Britain’s 18 main rail stations, from Edinburg Waverley to London King’s Cross, are looked after by the Britain rail system. Ten years ago, when the network rail took up these responsibilities, it had to face some challenges. The rail network was facing some problems. Trains were running late, the costs were too high and there was shortage of assets in both the people and machinery. Due to these issues, people had less confidence in the rail network. Ever since then, rail network has aimed at sustaining operations to reduce the expenses. There has been 28% reduction in expenses mainly because of economy of scale. New tracks and machinery have been bought, and there has been 90% rise in the rail punctuality. Huge projects have been given on time and towards the budget, as a result the confidence of the people has improved. Rail network has moved from ‘find and fix’ to ‘predict and prevent’ policy. This has proved to be more cost effective and competent and enabled in avoiding delay or obstruction for the people in their travel. The rail network invested approx. 12 billion pounds between 2009 and 2014, towards the rail network. Britain has the fastest developing network in whole of Europe. By investing in people, the rail network is investing in the future to. Britain has the largest working personnel of 35,000 workers. It has people working in various positions, like, engineers for maintenance and signaling to project managers. Each area offers an opportunity to work. They also consist of HR (human resources), IT (information technology), and finance and customer service. Network Rail needs to employ and keep capable engineers in order to get the work done. Presently, its engineers are doing some of the most stimulating projects in Europe. The projects include HS2, which is the new super speed rail link between the north and south Britain, and the project of London Crossrail. Some of the biggest and busiest rail stations are being upgraded, like, London King’s Cross and Birmingham New Street. The main focus of the HR of Network Rail is to recruit various personnel. This not only deepens the culture of business but it also makes sure that it can reach every talent. It offers training for every applicant, whether he is a school drop-out or a graduate, whether male or female, a continued flow of appropriate talent is ensured to keep its long term project going. The company above gives many opportunities to its workers to receive recognized qualifications, such as an exclusive programmer in post graduation, sponsoring the Master’s Degree in project management and trainee.

Answer the following question.

Q1. What is the new super speed rail link between the north and south Britain called? (Hint: HS2)

Q2. What were the initial problems that Network Rail of Britain face? (Hint: It has to look after the 20,000 mile long track and 40,000 bridges and tunnels. Trains were running late, the costs were too high and there was shortage of assets in both the people and machinery).


Multi Criteria decision making

MCDA (Multi Criteria Decision Analysis) is considered to be one of the fastest growing research operations in the last several years. The researcher focus towards MCDA led to development of many different approaches and ways in the field. There are two types of procedures: theoretical assumptions and decision addressed type. This difference throws challenges to the procedure of choosing the most ideal method for the decision making problem. Most of the time, the initial approach towards applying MCDA in the real world problems relates to the set up of simple understanding Of the context and recognizing the problem of decision. This step includes the ones who make decisions and other important participants who make important contributions for the MCDA procedure by sharing their knowledge. The common insight of the decision framework is received by knowing the goals of the decision making body and recognizing not only those people who make decisions but also those who face the decision. Dooley (2009) says that the first three steps take up more time in the process of MCDA, particularly because of their qualitative features. Assigning of comparative significant weights to the selected criteria is the next step: These weights can be ascertained directly, for example ranking, swing, trade off; or indirectly, for example- centrality, regression and interactive. Later, the DM has to give individual scores, considering his or her views, to each of the recognized options according to the criteria which seem vital. These scores show the decision of DM related to spreading of each substitute to every performance standard. The information which is attained is maintained distinctively into performance template, which is also as consequence matrix, options matrix, or just decision table. \ . ‘ I The next process includes abstract of the information consisting of the performance matrix in the form of multi criteria scores, for every possible plan. Mostly, this is attained by combining the individual scores of matrix so that total valuation of .each substitute which allows more comparison. The groups of substitut<:s ar<: ranked on the basis of all these scores. Finally, the procedure can include a warm evaluation of the outcome to amendments in the scores or criteria, to conclude the sturdiness of the result of MCDA. At the end, the analysis and trade offs included in the respective choices are given to and conferred with the DM. In many cases, the ultimate decision that DM takes, does not match with the highest level of alterative, as they are more focused towards the process of knowing the effect of each and every factor in ranking of choices than in the exactness of the ranking. Also, it should be observed that the generalizations are not used to of the outcome given by the process of MCDA, and they only appropriate for the group of choices which were assessed.

Answer the following question.

Q1. What role does MCDA play in decision making? (Hint: MCDA is considered to be one of the fastest growing research operations, these scores show the decision of DM related to spreading of each substitute to every performance standard).

Q2. What does MCDA stand for? (Hint: multi criteria decision analysis)