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Solved assignment problems – algorithms and flowcharts.

An algorithm is defined as sequence of steps to solve a problem (task) . The steps must be finite, well defined and unambiguous. Writing algorithm requires some thinking. Algorithm can also be defined as a plan to solve a problem and represents its logic. Note that an algorithm is of no use if it does not help us arrive at the desired solution

Algorithm characteristics

  • It should have finite number of steps . No one can be expected to execute infinite number of steps.
  • The steps must be in order and simple
  • Each step should be defined clearly i.e. without un-ambiguity (without doubtfulness)
  • Must include all required information
  • Should exhibit at least one output

A flowchart is a pictorial (graphical) representation of an algorithm . A flowchart is drawn using different kinds of symbols. A symbol is used for a specific purpose. Each symbol has name.

An algorithm is defined as . .Set of instructions. Instruction is a command to the computer to do some task.
Algorithm can also be defined as a plan to solve a problem and represents its logic.A picture is worth of 1000 words. We can understand more from picture than words.Implementation of Algorithm or flowchart

Different algorithms have different performance characteristics to solve the same problem. Some algorithms are fast. Some are slow. Some occupy more memory space. Some occupy less memory space. Some are complex and some algorithms are simple.

Logically algorithm, flowchart and program are the same.

Q1 . Create a program to compute the volume of a sphere. Use the formula: V = (4/3) *pi*r 3 where pi is equal to 3.1416 approximately. The r is the radius of sphere.  Display the result.

assignment problem mcq questions

Q2 . Write a program the converts the input Celsius degree into its equivalent Fahrenheit degree. Use the formula: F = (9/5) *C+32.

assignment problem mcq questions

Q3 . Write a program that converts the input dollar to its peso exchange rate equivalent.  Assume that the present exchange rate is 51.50 pesos against the dollar. Then display the peso equivalent exchange rate.

assignment problem mcq questions

Q4 . Write a program that converts an input inch(es) into its equivalent centimeters. Take note that one inch is equivalent to 2.54cms.

assignment problem mcq questions

Q5 . Write a program that exchanges the value of two variables: x and y.  The output must be: the value of variable y will become the value of variable x, and vice versa.

assignment problem mcq questions

Q6 . Design a program to find the circumference of a circle. Use the formula: C=2πr, where π is approximately equivalent 3.1416.

assignment problem mcq questions

Q7 . Write a program that takes as input the purchase price of an item (P), its expected number of years of service (Y) and its expected salvage value (S). Then outputs the yearly depreciation for the item (D). Use the formula: D = (P – S) Y.

assignment problem mcq questions

Q8 . Swapping of 2 variables without using temporary (or 3 rd variable).

assignment problem mcq questions

Q9 . Determine the most economical quantity to be stocked for each product that a manufacturing company has in its inventory: This quantity, called economic order quantity (EOQ) is calculated as follows: EOQ=2rs/1 where: R= total yearly production requirement S=set up cost per order I=inventory carrying cost per unit.

assignment problem mcq questions

Q10 . Write a program to compute the radius of a circle. Derive your formula from the given equation: A=πr², then display the output.

assignment problem mcq questions

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Hey Engineers, welcome to the award-winning blog,Engineers Tutor. I'm Gopal Krishna. a professional engineer & blogger from Andhra Pradesh, India. Notes and Video Materials for Engineering in Electronics, Communications and Computer Science subjects are added. "A blog to support Electronics, Electrical communication and computer students".

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Operations Research

31. Using ______________ method, we can never have an unbounded solution

  • Dual simplex

32. The customers of high priority are given service over the low priority customers is ______________.

  • Pre emptive

33. A queuing system is said to be a ______________ when its operating characteristic are independent upon time

  • pure birth model
  • pure death model
  • transient state
  • steady state

34. An activity which does not consume neither any resource nor time is known as ______________.

  • predecessor activity
  • successor activity
  • dummy activity

35. The difference between total and free float is ______________.

  • independent
  • interference

36. The number of time estimates involved in Program Evaluation Review Technique problem is ______________.

37. The assignment problem is always a ______________matrix.

38. The slack variables indicate ______________.

  • excess resource available.
  • shortage of resource
  • nil resource
  • idle resource

39. If the net evaluation corresponding to any non -basic variable is zero, it is an indication of the existence of an ______________.

  • initial basic feasible solution
  • optimum basic feasible solution
  • optimum solution.
  • alternate optimum solution.

40. Mathematical model of linear programming problem is important because ______________.

  • it helps in converting the verbal description and numerical data into mathematical expression
  • decision makers prefer to work with formal models
  • it captures the relevant relationship among decision factors
  • it enables the use of algebraic technique

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Assignment Problem: Meaning, Methods and Variations | Operations Research

assignment problem mcq questions

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

assignment problem mcq questions

Mathematical Formulation of the Assignment Problem:

assignment problem mcq questions

Let us explore all approaches for this problem.

Solution 1: Brute Force  

We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O(n!).

Solution 2: Hungarian Algorithm  

The optimal assignment can be found using the Hungarian algorithm. The Hungarian algorithm has worst case run-time complexity of O(n^3).

Solution 3: DFS/BFS on state space tree  

A state space tree is a N-ary tree with property that any path from root to leaf node holds one of many solutions to given problem. We can perform depth-first search on state space tree and but successive moves can take us away from the goal rather than bringing closer. The search of state space tree follows leftmost path from the root regardless of initial state. An answer node may never be found in this approach. We can also perform a Breadth-first search on state space tree. But no matter what the initial state is, the algorithm attempts the same sequence of moves like DFS.

Solution 4: Finding Optimal Solution using Branch and Bound  

The selection rule for the next node in BFS and DFS is “blind”. i.e. the selection rule does not give any preference to a node that has a very good chance of getting the search to an answer node quickly. The search for an optimal solution can often be speeded by using an “intelligent” ranking function, also called an approximate cost function to avoid searching in sub-trees that do not contain an optimal solution. It is similar to BFS-like search but with one major optimization. Instead of following FIFO order, we choose a live node with least cost. We may not get optimal solution by following node with least promising cost, but it will provide very good chance of getting the search to an answer node quickly.

There are two approaches to calculate the cost function:  

  • For each worker, we choose job with minimum cost from list of unassigned jobs (take minimum entry from each row).
  • For each job, we choose a worker with lowest cost for that job from list of unassigned workers (take minimum entry from each column).

In this article, the first approach is followed.

Let’s take below example and try to calculate promising cost when Job 2 is assigned to worker A. 

jobassignment2

Since Job 2 is assigned to worker A (marked in green), cost becomes 2 and Job 2 and worker A becomes unavailable (marked in red). 

jobassignment3

Now we assign job 3 to worker B as it has minimum cost from list of unassigned jobs. Cost becomes 2 + 3 = 5 and Job 3 and worker B also becomes unavailable. 

jobassignment4

Finally, job 1 gets assigned to worker C as it has minimum cost among unassigned jobs and job 4 gets assigned to worker D as it is only Job left. Total cost becomes 2 + 3 + 5 + 4 = 14. 

jobassignment5

Below diagram shows complete search space diagram showing optimal solution path in green. 

jobassignment6

Complete Algorithm:  

Below is the implementation of the above approach:

Time Complexity: O(M*N). This is because the algorithm uses a double for loop to iterate through the M x N matrix.  Auxiliary Space: O(M+N). This is because it uses two arrays of size M and N to track the applicants and jobs.

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True
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True
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6
True
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7
12.
7.
13.
8.
8
the objective function only.
the constraints only.
both objective function and constraints.
neither objective function nor constraints.
9 denoting the amount shipped from supply point i (1 or 2) to demand point j (1, 2 or 3) the correct constraint to make sure that supply available in supply point #2 will be fully used is:


7 + 2 + 5 = 300
+ + = 300
7 + 2 + 5 ≥ 300
+ + ≥ 300
10
Dummy supply 300.
Dummy supply 2100.
Dummy demand 300.
Dummy demand 2100.
11
origins.
intermediate points.
either origins or intermediated points.
origins or external sources.
12
24.
9.
48.
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TRANSPORTATION PROBLEM Solved MCQs

  • RATIO, PROPORATION AND PERCENTAGE
  • PROFIT AND LOSS
  • LINEAR PROGRAMMING PROBLEM
  • MATICES AND DETERMINANTS
  • TRANSPORTATION PROBLEM
1.
A. economical
B. scientific
C. a and b both
D. artistic
Answer» B. scientific
2.
A. battle field
B. fighting
C. the opponent
D. both a and b
Answer» D. both a and b
3.
A. morse and kimball (1946)
B. p.m.s. blackett (1948)
C. e.l. arnoff and m.j. netzorg
D. none of the above
Answer» A. morse and kimball (1946)
4.
A. programme evaluation
B. review technique (pert)
C. both a and b
D. deployment of resources
Answer» C. both a and b
5.
A. increases infinitely
B. basic variables are nonzero
C. decreases infinitely
D. one or more basic variables are zero
Answer» D. one or more basic variables are zero
6.
A. scientists
B. mathematicians
C. academics
D. all of the above
Answer» D. all of the above
7.
A. only constraints
B. only non-negative restriction
C. [a] and [b] both
D. [a],[b] and optimum solution
Answer» C. [a] and [b] both
8.
A. balanced
B. unbalanced
C. degenerate
D. none of the above
Answer» A. balanced
9.
A. least cost method
B. vogel’s approximation method
C. modified distribution method
D. all of the above
Answer» A. least cost method
10.
A. dummy allocation(s) needs to be added
B. the problem has no feasible solution
C. the multiple optimal solution exist
D. a & b but not c
Answer» C. the multiple optimal solution exist
11.
A. satisfy rim conditions
B. prevent solution from becoming degenerate
C. ensure that total cost does not exceed a limit
D. none of the above
Answer» A. satisfy rim conditions
12.
A. total supply equals total demand
B. the solution so obtained is not feasible
C. the few allocations become negative
D. none of the above
Answer» B. the solution so obtained is not feasible
13.
A. positive & greater than zero
B. positive with at least one equal to zero
C. negative with at least one equal to zero
D. none of the above
Answer» B. positive with at least one equal to zero
14.
A. it is complicated to use
B. it does not take into account cost of transportation
C. it leads to a degenerate initial solution
D. all of the above
Answer» B. it does not take into account cost of transportation
15.
A. m+n
B. m*n
C. m+n-1
D. m+n+1
Answer» C. m+n-1
16.
A. equal to zero
B. most negative number
C. most positive number
D. any value
Answer» B. most negative number
17.
A. it represents per unit cost reduction
B. it represents per unit cost improvement
C. it ensure no rim requirement violation
D. none of the above
Answer» A. it represents per unit cost reduction
18.
A. it improve the total cost
B. it does not disturb rim conditions
C. it ensure feasible solution
D. all of the above
Answer» C. it ensure feasible solution
19.
A. logical approach
B. rational approach
C. scientific approach
D. all of the above
Answer» C. scientific approach
20.
A. experience
B. judgement
C. intuition
D. all of the above
Answer» D. all of the above

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  1. Assignment MCQ [Free PDF]

    Assignment Question 10. An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes.

  2. MCQ Assignment

    Chapter 1: Assignment Problem. Multiple Choice Questions (MCQ) The application of assignment problems is to obtain _____. a. only minimum cost. b. only maximum profit. c. minimum cost or maximum profit. d. assign the jobs. The assignment problem is said to be unbalanced if _____. a. number of rows is greater than number of columns.

  3. 270+ Operations Research solved MCQs with PDF download

    When a maximization assignment problem is converted in minimization problem, the resulting matrix is called matrix. A. cost: B. regret: C. profit: D. dummy: Answer» B. regret ... Operations Research multiple choice questions and answers, Operations Research Important MCQs, Solved MCQs for Operations Research, ...

  4. Solved Assignment Problems

    Program. An algorithm is defined as sequence of steps to solve a problem (task). A flowchart is pictorial (graphical) representation of an algorithm. Set of instructions. Instruction is a command to the computer to do some task. Algorithm can also be defined as a plan to solve a problem and represents its logic. A picture is worth of 1000 words.

  5. Problem Solving MCQ [Free PDF]

    Problem Solving Question 1: Arrange the stages of the problem-solving process in the correct order: A. Identifying the problem. B. Generating potential solutions. C. Implementing the chosen solution. D. Evaluating the outcomes. E. Analyzing the available information.

  6. PDF OPERATIONS RESEARCH Multiple Choice Questions

    a, b, and c are independent. a, b, and d are independent. d c. are independentb and d are i. dependent38. Consider the linear equation 2 x1 + 3 x2 - 4 x3 + 5 x4 = 10 How many basic and non. One variable is basic, three variables are non-basic. Two variables are basic, two variables are non-basic. e i.

  7. PDF ASSIGNMENT PROBLEM

    MCQ QUESTIONS WITH ANSWER K.BHARATHI,SCSVMV. ASSIGNMENT PROBLEM 2 / 55 ... An assignment problem is a particular case of transportation problem. The objective is to assign a number of resources to an equal number of activities . So as to minimize total cost or maximize total pro t of allocation.

  8. Operations Research MCQ [Free PDF]

    Get Operations Research Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. Download these Free Operations Research MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. ... A linear programming problem typically involves an objective function that needs to be maximized or minimized ...

  9. Operations Research Multiple choice Questions and Answers. Page 1

    Multiple choice Questions on Operations Research. Practice for BBA or MBA exams using these MCQ. Page 1. ... A feasible solution to a linear programming problem _____. ... An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost should be equal to the number of _____.

  10. PDF OPERATIONS RESEARCH Multiple Choice Questions

    Multiple Choice Questions 1. Operations research is the application of _____methods to arrive at the optimal Solutions to the problems. A. economical B. scientific C. a and b both D. artistic 2. In operations research, the -----are prepared for situations. A. mathematical models B. physical models diagrammatic

  11. Assignment problems

    Multiple Choice Questions: An assignment problem will have the following solution: (a) optimal (b) unique (c) multiple (d) all of the above. Maximisation assignment problem is transformed into minimization problem by (a) adding each entry in a column from the maximum value in that column

  12. Operations Research Multiple choice Questions and Answers. Page 3

    Multiple choice Questions on Operations Research. Practice for BBA or MBA exams using these MCQ. Page 3. ... An assignment problem is a particular case of _____. transportation Problem; assignment Problem; travelling salesman problem; replacement Problem; View answer. Correct answer: (A)

  13. Operations Research Multiple choice Questions and Answers. Page 4

    Multiple choice Questions on Operations Research. Practice for BBA or MBA exams using these MCQ. Page 4. ... The assignment problem is always a _____matrix. circle; square; rectangle; triangle; View answer. Correct answer: (B) ... Mathematical model of linear programming problem is important because _____.

  14. Assignment Problem: Meaning, Methods and Variations

    After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations. Meaning of Assignment Problem: An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total ...

  15. Hungarian Algorithm for Assignment Problem

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  16. Transportation and assignment MCQs

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  17. Job Assignment Problem using Branch And Bound

    Solution 1: Brute Force. We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O (n!). Solution 2: Hungarian Algorithm. The optimal assignment can be found using the Hungarian algorithm.

  18. Multiple Choice Quiz

    Multiple Choice Quiz. Transportation and assignment problems can be solved by simplex method though special purpose algorithms offer an easier solution procedure. The total supply must equal total demand in a transportation problem in order to solve it by the transportation algorithm. XYZ Inc. manufactures desks and chairs in all its four ...

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    Multiple Choice Questions. Operations research is the application of _____methods to arrive at the optimal Solutions to the problems. A. economical B. scientific C. a and b both D. artistic. In operations research, the -----are prepared for situations. ... An assignment problem is a special case of transportation problem, where A. Number of ...

  21. Transportation Model MCQ [Free PDF]

    Get Transportation Model Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. Download these Free Transportation Model MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. ... The assignment problem is a special case of transportation problem when each origin is associated with one ...

  22. TRANSPORTATION PROBLEM Solved MCQs with PDF Download

    An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is: A. positive & greater than zero. B. positive with at least one equal to zero. C. negative with at least one equal to zero. D.

  23. MCQ Assignment

    Chapter 1: Assignment Problem. Multiple Choice Questions (MCQ) The application of assignment problems is to obtain _____. a. only minimum cost. b. only maximum profit. c. minimum cost or maximum profit. d. assign the jobs. The assignment problem is said to be unbalanced if _____. a. number of rows is greater than number of columns.