Operations Research Online MCQ Set 8

QN01. The transportation problem is balanced, if ______________.

  1. total demand and total supply are equal and the number of sources equals the number of destinations.
  2. none of the routes is prohibited
  3. total demand equals total supply irrespective of the number of sources and destinations
  4. number of sources matches with number of destinations
Answer

(C)total demand equals total supply irrespective of the number of sources and destinations

QN02. In an assignment problem involving 5 workers and 5 jobs, total number of assignments possible are ______________.

  1. 5
  2. 10
  3. 15
  4. 20
Answer

(A)5

QN03. All of the following are assumptions of the EOQ model except ______________

  1. the usage rate is reasonably constant
  2. replenishment is not instantaneous
  3. only one product is involved
  4. there are no quantity discount price
Answer

(B)replenishment is not instantaneous

QN04. Average number of trains spent in the yard is denoted by ______________.

  1. E(n)
  2. E(m)
  3. E(v)
  4. E(w)
Answer

(C)E(v)

QN05. Graphical method of linear programming is useful when the number of decision variable are ______________

  1. 2
  2. 3
  3. 4
  4. 5
Answer

(A)2

QN06. The cost of a surplus variable is ______________.

  1. 0
  2. 1
  3. 2
  4. -1
Answer

(A)0

QN07. The dual of the dual is ______________.

  1. dual-primal
  2. primal-dual
  3. dual
  4. primal
Answer

(D)primal

QN08. Solution of a Linear Programming Problem when permitted to be infinitely large is called ______________.

  1. unbounded
  2. bounded
  3. optimum solution
  4. no solution
Answer

(C)optimum solution

QN09. When the total demand is not equal to supply then it is said to be ______________.

  1. balanced
  2. unbalanced
  3. maximization
  4. minimization
Answer

(B)unbalanced

QN10. All equality constraints can be replaced equivalently by ______________ inequalities

  1. 1
  2. 2
  3. 3
  4. 4
Answer

(B)2

QN11. If the primal has an unbound objective function value then the dual has ______________.

  1. solution
  2. basic solution
  3. basic feasible solution
  4. no feasible solution
Answer

(D)no feasible solution

QN12. If there is no non-negative replacement ratio in a solution which is sought to be improved, then the solution is ______________.

  1. bounded
  2. unbounded
  3. no solution
  4. alternative solution
Answer

(B)unbounded

QN13. An activity is represented by a/an ______________.

  1. arrow
  2. straight line
  3. curve
  4. arc
Answer

(A)arrow

QN14. A project consists of a number of tasks which are called ______________.

  1. activities
  2. floats
  3. events
  4. paths
Answer

(A)activities

QN15. The similarity between assignment problem and transportation problem is ______________.

  1. both are rectangular matrices
  2. both are square matrices
  3. both can be solved y graphical method
  4. both have objective function and non-negativity constraints
Answer

(D)both have objective function and non-negativity constraints

QN16. The penalty for not taking correct decision is known as ______________.

  1. fine
  2. loss
  3. cost
  4. opportunity cost
Answer

(D)opportunity cost

QN17. In a given system of m simultaneous linear equations in n unknowns (m<n) there will be ______________.

  1. n basic variables
  2. m basic variables
  3. (n-m) basic variables
  4. (n+m) basic variables
Answer

(B)m basic variables

QN18. If all aij values in the entering variable column of the simplex table are negative, then ______________.

  1. solution is unbounded
  2. solution is degenerate
  3. there exist no solution
  4. there are multiple solutions
Answer

(A)solution is unbounded

QN19. An unoccupied cell in the transportation method is analogous to a______________.

  1. Zj-Cj value in the simplex table.
  2. variable in the B-column in the simplex table.
  3. variable not in the B-column in the simplex table.
  4. value in the XB column in the simplex table.
Answer

(B)variable in the B-column in the simplex table.

QN20. Every basic feasible solution of a general assignment problem having a square pay-off matrix of order n should have assignments equal to______________.

  1. 2n-1
  2. n
  3. n+1
  4. n-2
Answer

(A)2n-1

QN21. Which of the following is correct?

  1. Re-order quantity in a fixed order-interval system equals EOQ
  2. Review period of the item is always kept higher than its lead time
  3. Re-order level of an item is always more than its minimum stock
  4. Buffer stock is the total stock kept to meet the demand during lead time
Answer

(C)Re-order level of an item is always more than its minimum stock

QN22. The group replacement policy is suitable for identical low cost items which are likely to ______________.

  1. fail suddenly
  2. fail completely and suddenly
  3. fail over a period of time
  4. be progressive and retrogressive
Answer

(C)fail over a period of time

QN23. Identify the correct statement

  1. an assignment problem may require the introduction of both dummy row and dummy column
  2. an assignment problem with m rows and n columns will involves a total of m x n possible assignments
  3. an unbalanced assignment is one where the number of rows is more than, or less than the number of columns
  4. balancing any unbalanced assignment problem involves adding one dummy row or column
Answer

(C)an unbalanced assignment is one where the number of rows is more than, or less than the number of columns

QN24. A game is said to be fair if ______________.

  1. lower and upper values are zero
  2. only lower value to be zero
  3. only upper value to be zero
  4. lower and upper values are not equal to zero
Answer

(A)lower and upper values are zero

QN25. Which of the following is not a part of holding (or carrying) costs?

  1. Rent for storage space
  2. Extra expenses for an overnight express mail.
  3. Spoilage costs
  4. Electricity and heat for the buildings
Answer

(B)Extra expenses for an overnight express mail.

QN26. The area bounded by all the given constraints is called ______________.

  1. feasible region
  2. basic solution
  3. non feasible region
  4. optimum basic feasible solution
Answer

(A)feasible region

QN27. When D=18000, holding cost=Rs.1.20, set-up cost=Rs.400, EOQ = ______________

  1. 3465
  2. 3750
  3. 3500
  4. 4000
Answer

(A)3465

QN28. Given arrival rate = 15/hr, service rate = 20/hr, the value of traffic intensity is ______________.

  1. 3/4
  2. 4/3
  3. 3/5
  4. 4/5
Answer

(A)3/4

QN29. An activity is critical if its ______________ float is zero

  1. total
  2. free
  3. independent
  4. interference
Answer

(A)total

QN30. ______________ is employed in construction and business problems

  1. Queue
  2. Replacement
  3. CPM
  4. PERT
Answer

(D)PERT

QN31. __________ occurs when the number of occupied squares is less than the number of rows plus

  1. Degeneracy
  2. Infeasibility
  3. Unboundedness
  4. Unbalance
  5. Redundancy
Answer

(A)Degeneracy

QN32. __________ or __________ are used to “balance” an assignment or transportation problem.

  1. Destinations; sources
  2. Units supplied; units demanded
  3. Dummy rows; dummy columns
  4. Large cost coefficients; small cost coefficients
  5. Artificial cells; degenerate cells
Answer

(C)Dummy rows; dummy columns

QN33. A solution can be extracted from a model either by

  1. Conducting experiments on it
  2. Mathematical analysis
  3. Both A and B
  4. Diversified Techniques
Answer

(C)Both A and B

QN34. An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is:

  1. Positive & greater than zero
  2. Positive with at least one equal to zero
  3. Negative with at least one equal to zero
  4. None of the above
Answer

(B)Positive with at least one equal to zero

QN35. Which of these statements about the stepping-stone method is best?

  1. A dummy source and destination must be added if the number of rows plus columns minus 1 is not equal to the number of filled squares.
  2. Only squares containing assigned shipments can be used to trace a path back to an empty square.
  3. An improvement index that is a net positive means that the initial solution can be improved.
  4. Only empty squares can be used to trace a path back to a square containing an assigned shipment
Answer

(B)Only squares containing assigned shipments can be used to trace a path back to an empty square.

QN36. An assignment problem can be viewed as a special case of transportation problem in which the capacity from each source is __________ and the demand at each destination is __________.

  1. 1; 1
  2. Infinity; infinity
  3. 0; 0
  4. 1000; 1000
  5. -1; -1
Answer

(A)1; 1

QN37. Both transportation and assignment problems are members of a category of LP problems called __________.

  1. shipping problems
  2. logistics problems
  3. generalized flow problems
  4. routing problems
  5. network flow problems
Answer

(E)network flow problems

QN38. Consider the given vectors: a(2,0), b(0,2), c(1,1), and d(0,3). Which of the following vectors are linearly independent?

  1. a, b, and c are independent
  2. a, b, and d are independent
  3. a and c are independent
  4. b and d are independent
Answer

(C)a and c are independent

QN39. Consider the linear equation
2 x1 + 3 x2 – 4 x3 + 5 x4 = 10
How many basic and non-basic variables are defined by this equation?

  1. One variable is basic, three variables are non-basic
  2. Two variables are basic, two variables are non-basic
  3. Three variables are basic, one variable is non-basic
  4. All four variables are basic
Answer

(A)One variable is basic, three variables are non-basic

QN40. During an iteration while moving from one solution to the next, degeneracy may occur when

  1. The closed path indicates a diagonal move
  2. Two or more occupied cells are on the closed path but neither of them represents a corner of the path.
  3. Two or more occupied cells on the closed path with minus sign are tied for lowest circled value
  4. Either of the above
Answer

(C)Two or more occupied cells on the closed path with minus sign are tied for lowest circled value

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