FALL-2015 Get solved assignments at nominal price of Rs.125 each. Visit www.instamojo.com/subjects4u search for your code pay and download fully solved assignments. Any issues mail us at: [email protected] or contact at 09882243490 Master of Business Administration - MBA Semester 2 MB0048-Operations Research-4 Credits (Book ID: B1631) Assignment (60 Marks) Note: Answer all questions within 300 to 400 words each. Each Question carries 10 marks 6 X 10=60 Q1. Describe the framework of Operations Research. Answer. a) The basic dominant characteristic feature of operations research is that it employs mathematical representations or models to analyze problems. This distinct approach represents an adaptation of the scientific methodology used by the physical sciences. The scientific method translates a real given problem into a mathematical representation which is solved and retransformed into the original context. The OR approach to problem solving consists of the following steps: Defining the problem, Constructing the Q2. a. Explain the graphical method of solving Linear Programming Problem. b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in a week. There are 160 production hours in a week. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper respectively. Formulate this as a Linear Programming Problem. Answer. a) Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. The procedure for mathematical formulation of a linear programming problem consists of the following major steps: Step 1: Study the given situation to find the key decision variables to be made. Q3. a. Explain some of the important terms of the transportation problem. b. Explain the procedure of MODI method of finding solution through optimality test. Answer. a) Degeneracy in transportation problem If the basic feasible solution of a transportation problem with m origins and n destinations has fewer than m + n – 1 positive (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages: 1. at the initial solution 2. during the testing of the optimal solution To resolve degeneracy, we make use of an artificial quantity (d). The quantity d is assigned to that unoccupied cell, which has the Q4. a. Explain the steps involved in Hungarian method of solving Assignment problems. b. Find an optimal solution to an assignment problem with the following cost matrix: J1 J2 J3 J4 M1 10 9 7 8 M2 5 8 7 7 M3 5 4 6 5 M4 2 3 4 5 Answer. a). Hungarian method algorithm is based on the concept of opportunity cost and is more efficient in solving assignment problems. Adopt the following steps mentioned below to solve an AP using the Hungarian method algorithm: Step 1: Prepare row ruled matrix by selecting the minimum values for each row and subtract it from other elements of the row. Step 2: Prepare column reduced matrix by subtracting minimum value of the column from the other values of that column. Q5. a. Explain Monte Carlo Simulation. b. A Company produces 150 cars. But the production rate varies with the distribution. Production Rate 147 148 149 150 151 152 153 Probability 0.05 0.10 0.15 0.20 0.30 0.15 0.05 At present the track will hold 150 cars. Using the following random numbers determine the average number of cars waiting for shipment in the company and average number of empty space in the truck. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02, 64, 47. Answer. a). Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. The technique is used by professionals in such widely disparate fields as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment. Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action.. It shows the extreme possibilities—the outcomes of going for Q6. a. State the assumptions of game theory. b. What are the characteristics of Markov chain? c. What are the rules for prioritizing jobs? Answer. a. In game theory one usually makes the following assumptions: (1) Each decision maker ["PLAYER"] has available to him two or more well-specified choices or sequences of choices (called "PLAYS"). (2) Every possible combination of plays available to the players leads to a well-defined end-state (win, loss, or draw) that terminates the game. (3) A specified payoff for each player is associated with each end-state (a [ZERO-SUMGAME] means that FALL-2015 Get solved assignments at nominal price of Rs.125 each. Visit www.instamojo.com/subjects4u search for your code pay and download fully solved assignments. Any issues mail us at: [email protected] or contact at 09882243490