Model Question Paper with Solution

Transcription

1 Annexure P Model Question Paper with Solution Section A (Very Short Answer Questions) Q.1. Write down three differences between PERT and CPM in brief? Ans.1. The Program Evaluation and Review Technique (PERT) is a project management technique or tool which is suitable for projects that have unpredictable activities while the Critical Path Method (CPM) is a project management tool which is suitable for projects that have predictable activities. 2. CPM uses a single estimate for the time that a project can be completed while PERT uses three estimates for the time that it can be completed. 3.CPM is a deterministic project management tool while PERT is a probabilistic project management tool. 4.CPM allows project management planners to determine which aspect of the project to sacrifice when a trade-off is needed in order to complete the project while PERT does not. 3. Give three advantages of linear programming. Ans. Some of the advantages of linear programming are: Utilized to analyze numerous economic, social, military and industrial problem.

2 Linear programming is most suitable for solving complex problems. Helps in simplicity and productive management of an organization which gives better outcomes. Improves quality of decision: A better quality can be obtained with the system by making use of linear programming. Provides a way to unify results from disparate areas of mechanism design. Q-3. Name the important techniques of Operation Research. Ans. Some of the important techniques used in Operation Research are : 1. Linear Programming 2. Transportation Problem 3. Assignment Problem 4. Queuing Theory 5. Game Theory 6. Inventory Control Models 7. Linear Programming 8. Integer Programming Q-4. Define time estimates in Network Analysis. Ans. There are three estimation times involved in PERT; Optimistic Time Estimate (TOPT), Most Likely Time Estimate (TLIKELY), and Pessimistic Time Estimate (TPESS).

3 In PERT, these three estimate times are derived for each activity. This way, a range of time is given for each activity with the most probable value, TLIKELY. Following are further details on each estimate: 1. TOPT: This is the fastest time an activity can be completed. For this, the assumption is made that all the necessary resources are available and all predecessor activities are completed as planned. 2. TLIKELY: Most of the times, project managers are asked only to submit one estimate. In that case, this is the estimate that goes to the upper management. 3. TPESS: This is the maximum time required to complete an activity. In this case, it is assumed that many things go wrong related to the activity. A lot of rework and resource unavailability are assumed when this estimation is derived. Q-5. What do you mean by assignment problem? Ans. Assignment problem is one of the special cases of transportation problems. The goal of the assignment problem is to minimize the cost or time of completing a number of jobs by a number of persons. An important characteristic of the assignment problem is the number of sources is equal to the number of destinations.it is explained in the following way. 1. Only one job is assigned to person. 2. Each person is assigned with exactly one job. SECTION B (SHORT ANSWER TYPE QUESTIONS) Q-6. Enumerate the role of operation research in decision making.

4 Ans. Effective Decisions: Operations Research (OR) helps the managers to take better and quicker decisions. It increases the number of alternatives. It helps the managers to evaluate the risk and results of all the alternative decisions. So, OR makes the decisions more effective. 2. Better Coordination: Operations Research (OR) helps to coordinate all the decisions of the organization. It coordinates all the decisions taken by the different levels of management and the various departments of the organization. For e.g. It coordinates the decisions taken by the production department with the decisions taken by the marketing department. 3. Facilitates Control: Operations Research (OR) helps the manager to control his subordinates. It helps the manager to decide which work is most important. The manager does the most important work himself, and he delegates the less important work to his subordinates. Operations Research (OR) helps a manager to fix standards for all the work. It helps him to measure the performance of the subordinates. It helps the manager to find out and correct the deviations (difference) in the performance. So, OR facilitates control. 4. Improves Productivity: Operations Research (OR) helps to improve the productivity of the organisation. It helps to decide about the selection, location and size of the factories, warehouses, etc. It helps in inventory control. It helps in production planning and control. It also helps in manpower planning. OR is used in expansion, modernisation, installation of technology, etc. OR uses many different mathematical and statistical techniques to improve productivity. Simulation is used by many organisations to improve their productivity. That is, they try out many production improvement techniques on a small scale. If these techniques are successful then they are used on a large scale. Q.7. What do you understand by Unbalanced transportation problem? How would you convert it into a balanced problem? Ans. When the total supply of all the sources is not equal to the total demand of all destinations, the problem is an unbalanced transportation problem. Total supply Total demand Demand Less than Supply In real-life, supply and demand requirements will rarely be equal. This is because of variation in production from the supplier end, and variations in forecast from the customer end. Supply variations may be because of shortage of raw materials, labour problems, Transportation Model improper planning and scheduling. Demand variations may be because of change in customer preference, change in prices and introduction of new products by competitors. These unbalanced problems can be easily solved by introducing dummy sources and dummy destinations. If the total supply is greater than the total demand, a dummy destination (dummy column) with demand equal to the supply surplus is added. If the total demand is greater than the total supply, a dummy source (dummy row) with supply equal to the demand surplus is added. The unit transportation cost for the dummy column and

5 dummy row are assigned zero values, because no shipment is actually made in case of a dummy source and dummy destination. Q.8. A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. In view of the need to ensure, certain nutrient constituents, it is necessary to buy two products (call them A and B) in addition. The contents of the various products, per unit, in nutrient constituents (e.g., vitamins, proteins, etc.) is given in the following table: NUTRIENTS Nutrient Content in Product Minimum amount of A B nutrient M M M The last column of the above table gives the minimum amounts of nutrient constituents M1, M2, M3 which must be given to the pigs. If products A and B cost` 20 and ` 40 per unit respectively, how much each of these two products should be bought, so that the total cost is minimized? Solution: Let x units of A and y units B be purchased. Our goal is to minimize the total cost C = 20x + 40y By using x units of A and y units of B, we shall get 36x + 6y units of M1 Since we need at least 108 units of M1, we must have 36x + 6y 108 Similarly for M2 we have 3x + 12y 36 and for M3 we have 20x + 10y 100. Also, we cannot use negative numbers of x and y. Thus, our problem is Minimize C = 20x + 40y Subject to 36x + 6y 108 3x + 12y 36 20x + 10y 100, x 0, y 0 SECTION C (DETAILED ANSWER QUESTIONS) Q.9. What do you mean by Operation Research? Discuss its scope in various areas. Ans. According to Philip McCord Morse and George E. Kimball, "Operations research is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control." According to Russell L. Ackoff and C. West Churchman, "Operations research is the application of scientific methods to arrive at the optimal solutions to the problems. Operations research means to apply scientific and mathematical methods for decision making and problem solving.

6 OR does not provide decisions else it provides quantitative data to the managers. The managers use this data for making decisions. OR tries to find better solutions to different problems. Hence, it is used to solve complex management problems. OR helps to take decisions about operations and production.or was first used during the Second World War by England to solve their complex war problems. England made OR teams. These teams included expert mathematicians, statisticians, scientists, engineers, etc. These OR teams were very successful in solving England's war problems. Therefore, United States of America (USA) also started using OR to solve their war problems.after the war, soon industries and businesses also started using OR to solve their complex management problems. SCOPE OF OPERATION RESEARCH: In recent years of organized development, OR has entered successfully in many different areas of research. It is useful in the following various important fields In agriculture With the sudden increase of population and resulting shortage of food, every country is facing the problem of Optimum allocation of land to a variety of crops as per the climatic conditions Optimum distribution of water from numerous resources like canal for irrigation purposes Hence there is a requirement of determining best policies under the given restrictions. Therefore a good quantity of work can be done in this direction. In finance In these recent times of economic crisis, it has become very essential for every government to do a careful planning for the economic progress of the country. OR techniques can be productively applied To determine the profit plan for the company To maximize the per capita income with least amount of resources To decide on the best replacement policies, etc In industry If the industry manager makes his policies simply on the basis of his past experience and a day approaches when he gets retirement, then a serious loss is encounter ahead of the industry. This heavy loss can be right away compensated through appointing a young specialist of OR techniques in business management. Thus OR is helpful for the industry director in deciding optimum

7 distribution of several limited resources like men, machines, material, etc to reach at the optimum decision. In marketing With the assistance of OR techniques a marketing administrator can decide upon Where to allocate the products for sale so that the total cost of transportation is set to be minimum The minimum per unit sale price The size of the stock to come across with the future demand How to choose the best advertising media with respect to cost, time etc? How, when and what to buy at the minimum likely cost? In personnel management A personnel manager can utilize OR techniques To appoint the highly suitable person on minimum salary To know the best age of retirement for the employees To find out the number of persons appointed in full time basis when the workload is seasonal In production management A production manager can utilize OR techniques To calculate the number and size of the items to be produced In scheduling and sequencing the production machines In computing the optimum product mix To choose, locate and design the sites for the production plans In L.I.C OR approach is also applicable to facilitate the L.I.C offices to decide What should be the premium rates for a range of policies? How well the profits could be allocated in the cases of with profit policies? Q.10. Maximize Z= 8x1+9x2 Su je t to: x + x x + x X + x X,x. Q-11. Give three variations in transportation problems. How are these resolved?

8 Ans. (I) North-West corner method (NWCM) The North West corner rule is a method for computing a basic feasible solution of transportation problem where the basic variables are selected from the North West corner (top left corner). Steps: 1. Select the north west (upper left-hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand requirements, i.e., min (s1, d1). 2. Adjust the supply and demand numbers in the respective rows and columns allocation. 3. If the supply for the first row is exhausted then move down to the first cell in the second row. 4. If the demand for the first cell is satisfied then move horizontally to the next cell in the second column. 5. If for any cell supply equals demand then the next allocation can be made in cell either in the next row or column. 6. Continue the procedure until the total available quantity is fully allocated to the cells as required. (II) Least Cost Method (LCM) Matrix minimum method is a method for computing a basic feasible solution of a transportation problem where the basic variables are chosen according to the unit cost of transportation. Steps: 1. Identify the box having minimum unit transportation cost (cij). 2. If there are two or more minimum costs, select the row and the column corresponding to the lower numbered row. 3. If they appear in the same row, select the lower numbered column. 4. Choose the value of the corresponding xij as much as possible subject to the capacity and requirement constraints. 5. If demand is satisfied, delete that column. 6. If supply is exhausted, delete that row. 7. Repeat steps 1-6 until all restrictions are satisfied. III Vogel s Approxi atio Method VAM The Vogel approximation method is an iterative procedure for computing a basic feasible solution of the transportation problem. Steps: 1. Identify the boxes having minimum and next to minimum transportation cost in each row and write the difference (penalty) along the side of the table against the corresponding row. 2. Identify the boxes having minimum and next to minimum transportation cost in each column and write the difference (penalty) against the corresponding column

9 3. Identify the maximum penalty. If it is along the side of the table, make maximum allotment to the box having minimum cost of transportation in that row. If it is below the table, make maximum allotment to the box having minimum cost of transportation in that column. 4. If the penalties corresponding to two or more rows or columns are equal, select the top most row and the extreme left column. Q.12. Draw network for the following project: Activity Duration(Hrs.)