Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 64 views

    OR (Mech) Questions

    Uploaded by

    Nagamani Rajesh
    The document contains questions related to operations research techniques including: 1. Definitions for unbounded solution, general linear programming problem (LPP), feasible region, constraint, and optimal solution. 2. Questions asking to solve sample LPP problems using various methods like simplex, graphical, and Big-M. 3. Questions on transportation problem including determining initial basic feasible solutions using methods like Northwest Corner, Least Cost, and MODI and solving sample problems. 4. Questions involving calculation of economic order quantity, inventory costs, project scheduling using PERT/CPM, two-person zero-sum games and their solutions.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd

    OR (Mech) Questions

    Uploaded by

    Nagamani Rajesh
    64 views7 pages
    The document contains questions related to operations research techniques including: 1. Definitions for unbounded solution, general linear programming problem (LPP), feasible region, constraint, and optimal solution. 2. Questions asking to solve sample LPP problems using various methods like simplex, graphical, and Big-M. 3. Questions on transportation problem including determining initial basic feasible solutions using methods like Northwest Corner, Least Cost, and MODI and solving sample problems. 4. Questions involving calculation of economic order quantity, inventory costs, project scheduling using PERT/CPM, two-person zero-sum games and their solutions.

    Original Description:

    Original Title

    OR(Mech) Questions

    Copyright

    © © All Rights Reserved

    Available Formats

    DOC, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    The document contains questions related to operations research techniques including: 1. Definitions for unbounded solution, general linear programming problem (LPP), feasible region, constraint, and optimal solution. 2. Questions asking to solve sample LPP problems using various methods like simplex, graphical, and Big-M. 3. Questions on transportation problem including determining initial basic feasible solutions using methods like Northwest Corner, Least Cost, and MODI and solving sample problems. 4. Questions involving calculation of economic order quantity, inventory costs, project scheduling using PERT/CPM, two-person zero-sum games and their solutions.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    64 views7 pages

    OR (Mech) Questions

    Uploaded by

    Nagamani Rajesh
    The document contains questions related to operations research techniques including: 1. Definitions for unbounded solution, general linear programming problem (LPP), feasible region, constraint, and optimal solution. 2. Questions asking to solve sample LPP problems using various methods like simplex, graphical, and Big-M. 3. Questions on transportation problem including determining initial basic feasible solutions using methods like Northwest Corner, Least Cost, and MODI and solving sample problems. 4. Questions involving calculation of economic order quantity, inventory costs, project scheduling using PERT/CPM, two-person zero-sum games and their solutions.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    of 7

    Operation Research Techniques

    Part-A Questions

    1. Define unbounded solution


    If value of objective function decreases or increases indefinitely such a solution is
    called unbounded solution.

    2. What do you mean by a general LPP?


    The general LPP calls for optimizing (maximizing / minimizing) a linear function
    of variables called the ‘Objective function’ subject to a set of linear equations
    and / or inequalities called the ‘Constraints’ or ‘Restrictions’.

    3. Define feasible region.


    Feasible region is a collection of all feasible solutions (Feasible solution is a
    solution for which all constraints are satisfied).

    4. Define constraint

    5. State any three salient features of a LPP


    6. Define infeasible solution
    7. Define slack & surplus variable
    8. Define optimal solution
    9. Write the standard form of LPP in Matrix form.
    10. What is degeneracy in LPP?
    11. What is key column, key row? How is it selected?
    12. Stat the condition for an unbounded solution of a LPP?
    13. Define artificial variable.
    14. What is the use of artificial variable?
    15. Give mathematical formulation of assignment problem.
    16. List any three approaches used with transportation problem for determining the
    starting solution.
    17. What d you mean by transportation problem?
    18. What is the use of MODI method?
    19. Define degenerate and non-degenerate basic feasible solution of a transportation
    problem.
    20. What is unbalanced transportation problem? How to solve it?
    21. Define an assignment problem.
    22. How will you revise the opportunity cost matrix of a n assignment problem, if it does
    not give the optimal solution?
    23. What do you mean by a project?
    24. What do you mean by an activity of a project?
    25. Define network.
    26. Define EST & LFT.
    27. In inventory models, What is mean by q and C3.
    28. A Particular item has demand of 9,000 units/year. The cost of one procurement is
    Rs.100 and the holding cost per unit is Rs.2.40 per years. The replacement is
    instantaneous and no shortages are allowed. Determine the economic lot size.
    29. Define Value of the game?
    30. When Two-person zero sum game has a saddle point?
    31. Differentiate PERT and CPM
    32. Define pure strategy.
    33. Define group replacement.
    34. What is travelling salesman problem?
    35. Define assignment problem.
    36. What is an unbalanced transportation problem?
    Part-B Questions

    1. Solve the following LPP problem by simplex method


    Maximize 15 x1  6 x 2  9 x3  2 x 4
    Subject to
    2 x1  x 2  5 x3  6 x 4  20
    3 x1  x 2  3 x3  25 x 4  24
    7 x1  x 4  70
    x1 , x 2 , x3 , x 4  0

    2. Solve the following L.P.P by the graphical method.


    Maximize z  3 x1  2 x 2
    Subject to  2 x1  x 2  1
    x1  2
    x1  x 2  3, and x1 , x 2  0

    3. Solve the following LPP by Big-M method


    Minimize Z  3x  2y
    subject to 7x  2y  30
    5x  4y  20
    2x  8y  16 x, y  0

    4. Determine basic feasible solution to the following


    transportation problem using North West Corner Rule
    SinK
    A B C D E Supply
    P 2 11 10 3 7 4
    Origin Q 1 4 7 2 1 8
    R 3 9 4 8 12 9
    Demand 3 3 4 5 6

    5. Find the starting solution of the following transporation


    model by Least Cost method
    1 2 3 4 Supply
    I 21 16 25 13 11
    II 17 18 14 23 13
    6. Find an optimal solution by
    III 27 18 41 41 19
    MODI method of the following
    Demand 10 12 15 15
    matrix using VAM for finding the
    initial solution

    7. A machine operator has to perform two operations, turning and threading on a


    number of different jobs. The time required to perform these operations (in minutes) for
    each job is known. Determine the order in which the jobs should be processed in order
    to minimize the total time required to turn out all the jobs.
    Time for turning Time for threading
    Job
    (minutes) (minutes)
    1 3 8
    2 12 10
    3 5 9
    4 2 6
    5 9 3
    6 11 1

    7. Draw the network and determine the critical path for given data

    Jobs 1-2 1-3 2-4 3-4 3-5 4-5 4-6 5-6

    Duration 6 5 10 3 4 6 2 9

    8. Construct the 1 2 6 7 network for the project whose activities


    are given below and compute the total, free and
    0 4 2 12
    independent float of each avtivity and hence determine
    the critical path 3 1 5 11 and project duration.
    10 10 10
    Activity 0-1 1-2 1-3 2-4 2-5 3-4 3-6 4-7 5-7 6-7
    Duration 3 8 12 6 3 3 8 5 3 8
    (in weeks)
    9. A particular item has a demand of 9,000 units/year. The cost of one procurement
    is Rs.100 and the holding cost per unit is Rs.2.40 per year. The replacement is
    isntantaneous and no shortages are allowed. Determine
    i) the economic lot size.
    ii) the number of orders per year
    iii) the between orders
    iv) the total cost per year if the cost of one units is Re.1

    10. An item is produced at the rate of 50 items per day. The demand occurs at the
    rate of 25 items pr day. If the setup cost is Rs.100 per setup and holding cost is
    Re.0.01 per unit of item per day, find the economic lot size for one run, minimum
    total cost for one run.

    11. Using the principle of Dominance solve the following game


     8 10 9 14
    10 11 8 12
     
    13 12 14 13

    12. Solve the following game by graphical method


     6 4 1 2 7 
     7 5 2 5  6

    13. Reduce the game by dominance and find the game value

    I II III IV
    I 3 2 4 0
    II 3 4 2 4
    III 4 2 4 0
    IV 0 4 0 8

    14. Solve the transportation problem using VAM and find the
    optimal solution whose cost, demand, supply are given by the
    following table

    W1 W2 W3 W4 W5 Supply

    P1 20 28 32 55 70 50
    P2 48 36 40 44 25 100

    P3 35 55 22 45 48 150

    Demand 100 70 50 40 40

    15. An item is produced at the rate of 50 units per day. The demand is at the rate of
    25 units per day. The set up cost is 100 per unit per day. Find the EOQ and the
    minimum annual inventory cost. After how many days should production be
    stopped during each run?

    16. A manufacturer has a supply 12000 units of a product per year to his customer.
    Shortages are not permitted and there is no lead time. The inventory holding cost is
    Rs.0.20 per unit per month and the set up cost per run is Rs.350. Determine the
    economic lot size, the period of one run, the minimum annual inventory cost.

    17. In a game of matching coins with two players, suppose A wins one unit value when
    there are two heads, wins nothing there are two tails, and losses ½ units value when
    there are one head and one tail. Determine the payoff matrix, the best strategy for
    each palyer,and the value of the game.

    18. Use simplex method to


    Min Z=x2-3x3+2x5
    3 x 2  x3  2 x 5  7
     2 x 2  4 x3  12
     4 x 2  3x3  8 x5  10
    Subject to and x 2 , x3 , x5  0
    19. Solve the following game by graphical method
     6 7 
     4  5 

    1  2
     
     2 5 
     7  6 

     3 1 1 2
     2 3 2 3
    20. Solve the following game 
     2 2  1 1 
    21. Find the sequence for the following eight jobs that will minimize the total
    elapsed time for the completion of all the jobs. Each job is processed in the same
    order “C, A, B”. Entries give the time in hours on machines

    Jobs 1 2 3 4 5 6 7 8
    Times on Machine A 4 6 7 4 5 3 6 2
    Times on Machine B 8 10 7 8 11 8 9 13
    Times on Machine C 5 6 2 3 4 9 15 11

    22. A project consists of the tasks A, B, C,D,E ,F,G, H, I with the following data

    Activity A B C D E F G H I

    Preceding -- -- -- A A B,D C B F,G


    activity

    Duration 23 8 20 16 24 18 19 4 10

    Construct network. Find critical path. Also find Total, Independent and Free
    floats

    23. Solve the following traveling salesman problem. A salesman is planning to tour cities
    B,C, D,E starting from his home city A.
    The inter-city distances are shown in the following table

    City A B C D E

    A -- 103 188 136 38

    B 103 -- 262 176 52

    C 188 262 -- 85 275

    D 136 176 85 -- 162

    E 38 52 275 162 --

    You might also like