BA5201 APPLIED OPERATIONS RESEARCH - ANNA UNIVERSITY(MBA- 2017 Reg)

OBJECTIVE: 

 To learn the concepts of operations research applied in business decision making.

UNIT I INTRODUCTION TO LINEAR PROGRAMMING (LP) 9 

Introduction to applications of operations research in functional areas of management. Linear Programming-formulation, solution by graphical and simplex methods (Primal - Penalty, Two Phase), Special cases. Dual simplex method. Principles of Duality. Sensitivity Analysis.

 UNIT II LINEAR PROGRAMMING EXTENSIONS 9 

Transportation Models (Minimising and Maximising Problems) – Balanced and unbalanced Problems – Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel’s approximation methods. Check for optimality. Solution by MODI / Stepping Stone method. Case of Degeneracy. Transhipment Models. Assignment Models (Minimising and Maximising Problems) – Balanced and Unbalanced Problems. Solution by Hungarian and Branch and Bound Algorithms. Travelling Salesman problem. Crew Assignment Models.

UNIT III INTEGER PROGRAMMING AND GAME THEORY 9 

Solution to pure and mixed integer programming problem by Branch and Bound and cutting plane algorithms. Game Theory-Two person Zero sum games-Saddle point, Dominance Rule, Convex Linear Combination (Averages), methods of matrices, graphical and LP solutions.

UNIT IV INVENTORY MODELS, SIMULATION AND DECISION THEORY 9 

Inventory Models – EOQ and EBQ Models (With and without shortages), Quantity Discount Models. Decision making under risk – Decision trees – Decision making under uncertainty. Monte-carlo simulation.

UNIT V QUEUING THEORY AND REPLACEMENT MODELS 9 

Queuing Theory - single and Multi-channel models – infinite number of customers and infinite calling source. Replacement Models-Individuals replacement Models (With and without time value of money) – Group Replacement Models.

 TOTAL: 45 PERIODS 

OUTCOME: 

 To facilitate quantitative solutions in business decision making under conditions of certainty, risk and uncertainty.

REFERENCES : 

1. Paneerselvam R., Operations Research, Prentice Hall of India, Fourth Print, 2008.

2. N. D Vohra, Quantitative Techniques in Management,Tata Mcgraw Hill, 2010.

3. Hamdy A Taha, Introduction to Operations Research, Prentice Hall India, Ninth Edition, 2010.

4. Anderson , Sweeney Williams Solutions Manual to Accompany AnIntroduction to Management Science Quantitative Approaches To Decision, Cengage , 12th edition , 2012

5. G. Srinivasan, Operations Research – Principles and Applications, II edition , PHI, 2010.

6. Bernard W.Taylor ,Introduction to Management Science , 12 th edition, 2012

INTERNAL ASSESMENT TEST – I, FEBRUARY / 2018 Master of Business Administration    Semester   II   BA 5201 – Applied Operations Research (Regulation 2017)
Time : 3 hrs	Answer all Questions	Max.Marks : 100
PART- A (10 x 2 = 20 Marks) 1.      What is key row and how is it selected? 2.      What is meant by an optimal solution? 3.      Define non-degenerate solution. 4.      Define Slack, Surplus variables. 5.      State the objective of the transportation problem? 6.      Define an assignment problem? 7.       Write down basic steps involved in solving transportation problem? 8.       Write the matrix form of LPP to apply simplex method : Maximize Z = 3x1 + 2x2    subject to the constraints  2x1 + x2 £ 2, 3x1 + 4x2 ³ 12 & x1,x2 ³ 0. 9.      List any three approaches used in a transportation problem? 10.  What is unbalanced transportation problem?
PART- B (5 x 13 = 65 Marks) 11.  Solve by North-west corner method and Least cost Method. Justify the solutions.              [13] From / To A B C D Supply P 5 4 2 6 20 Q 8 3 5 7 30 R 5 9 4 6 50 Demand 10 40 20 30 100 12.  A company has three plants A,B and C, three ware houses X,Y and Z. The number of units available at the plants is 60,70,80 and demand at X,Y and Z are 50,80,80 respectively. The unit cost of the transportation is given in the following table                                                       [13] X Y Z A 8 7 3 B 3 8 9 C 11 3 5 Find the allocation so that the total transportation cost is minimum? 13.  Solve by Simplex Method :  Maximize Z = 2x1 + 4x2              subject to the constraints       x1 + 2x2 £ 5                                                             x1 + x2 £ 4  & x1,x2 ³ 0.                                                           [13] 14.  Use Big-M(Penalty) Method to Minimize Z = 4x1 + 3x2 subject to the constraints       2x1 + x2 ³ 10 -3x1 + 2x2£ 6,  x1 + x2 ³ 6 & x1,x2 ³ 0.                                                [13] 15.  A company is faced with the problem of assigning five jobs to five machines; each job must be done on only one machine; the cost processing each job on each machine is given below(in Rs.)The problem is to determine the assignment of jobs to machines so that it will result in minimum cost.                                                                                                             [13] Jobs /  Machines M1            M2      M3        M4      M5 J1 J2 J3 J4 J5 7           5          9          8        11 9         12          7        11        10 8           5          4          6          9 7           3          6          9          5 4           6          7          5        11
PART- C (1 x 15 = 15 Marks) 16.  a) Solve graphically : Maximize Z = 3x1 + 2x2 subject to the constraints  2x1 + x2 £ 2                            3x1 + 4x2 ³ 12 & x1,x2 ³ 0.                                                                                       [8]             b) Solve the following travelling problem so as to minimize the cost per cycle.                    [7] A B C D E A - 3 6 2 3 B 3 - 5 2 3 C 6 5 - 6 4 D 2 2 6 - 6 E 3 3 4 6 -   BA 5201 – Applied Operations Research INTERNAL ASSESSMENT TEST - II    Year/Sem : II/IV                     Max : 100 Marks                Time:  2 Hrs   CO3: Able to understand the concept of integer programming problem and integer solutions of LPP. CO4: Able to understand and apply the concepts of EOQ. Part – A (20*2 = 40 Marks) Q.NO QUESTIONS Cos 1.        Draw graph for the following 2x3 game   I II III I 1 3 11 II 8 5 2 CO 3 2.        When do you say a game is stable? CO 3 3.        What is dominance property? CO 3 4.        Write the characteristics of games? CO 3 5.        What are the methods of solving an integer programming problem? CO 3 6.        What is use of Gomory’s constraint in integer programming problem? CO 3 7.        What is mean by payoff matrix? CO 3 8.        What is mean by strategy? CO 3 9.        What are the two types of games? CO 3 10.    Explain the difference between pure strategy and mixed strategy? CO 3 11.    Define economic order quantity. CO 4 12.    What is inventory holding cost? CO 4 13.    What is shortage cost? CO 4 14.    What is setup cost? CO 4 15.    What are the advantages of inventory control? CO 4 16.    What are the two main decisions to be made in inventory control? CO 4 17.    what are the variables in an inventory problems? CO 4 18.    Discuss briefly the reasons for maintaining inventory in business management and inventory? CO 4 19.    What are the different forms of inventory? CO 4 20.    Explain the various types of inventory? CO 4         Part B (5*12=60 marks) Q.NO QUESTIONS 21. Solve the following transportation problem to maximize the profit.                                                              Destination A B C D Supply 1 15 1 42 33 23 2 80 42 26 81 44 3 90 40 66 60 33 Demand 23 31 16 30 100 22. Solve the following assignment problem. A B C D E A - 3 6 2 3 B 3 - 5 2 3 C 6 5 - 6 4 D 2 2 6 - 6 E 3 3 4 6 - 23. Find the optimal integer solution of the following all integer programming problems: 24. Solve the following game whose payoff matrix is given below. Player B                                                 B1       B2       B3       B4             A1       5          -10       9          0 Player A          A2       6          7          8          1                                     A3       8          7          15        2                                     A4       3          4          -1         4 25. The annual demand of an item is 3200 units. The unit cost is Rs 6/- and inventory carrying cost 25% per annum. If the cost of one procurement is Rs 150. Determine                                                         i.            EOQ                                                       ii.            No. of orders per year                                                     iii.            Time between two consecutive orders                                                     iv.            The optimal cost.                              BA 5201 – Applied Operations Research INTERNAL ASSESSMENT TEST - II    Year/Sem : II/IV                     Max : 100 Marks                Time:  2 Hrs   CO3: Able to understand the concept of integer programming problem and integer solutions of LPP. CO4: Able to understand and apply the concepts of EOQ. Part – A (20*2 = 40 Marks) Q.No. QUESTIONS Cos Draw graph for the following 2x3 game   I II III I 2 6 10 II 8 6 2 CO 3 What is mean by payoff matrix? CO 3 What is mean by strategy? CO 3 Write the characteristics of games? CO 3 What are the methods of solving an integer programming problem? CO 3 What is the value of the game? CO 3 What are the two types of games? CO 3 Explain the difference between pure strategy and mixed strategy? CO 3 When do you say a game is stable? CO 3 What is dominance property? CO 3 What are the different forms of inventory? CO 4 Explain the various types of inventory? CO 4 Discuss briefly the reasons for maintaining inventory in business management and inventory? CO 4 What are the advantages of inventory control? CO 4 What are the two main decisions to be made in inventorycontrol? CO 4 what are the variables in an inventory problems? CO 4 Define economic order quantity. CO 4 What is inventory holding cost? CO 4 What is shortage cost? CO 4 What is setup cost? CO 4   Part B (5*12=60 marks) Q.NO QUESTIONS Cos 21.    Find the optimal integer solution of the following all integer programming problems:   Co3 22.    Solve the following assignment problem. A B C D E A - 3 6 2 3 B 3 - 5 2 3 C 6 5 - 6 4 D 2 2 6 - 6 E 3 3 4 6 - Co3 23.    Reduce the following game by dominance property and solve it. Player B Player A 1 2 3 4 5 I 1 3 2 7 4 II 3 4 1 5 6 III 6 5 7 6 5 IV 2 1 6 3 1 Co3 24.    Solve the following game whose payoff matrix is given below. Player B                                                 B1       B2       B3       B4             A1       5          -10       9          0 Player A          A2       6          7          8          1                                     A3       8          7          15        2                                     A4       3          4          -1         4 C04 25.    The demand rate for an item in a company is 1800 units/year. The company can produce at the rate of 3000/month. The setup cost is Rs.500/ order and the holding cost is 0.15/ unit per month. Calculate                                                         i.            Optimum manufacturing quantity                                                       ii.            The maximum inventory                                                     iii.            Time between orders                                                     iv.            No. of orders per year                                                       v.            The time of manufacture.        C04