assignment model mcq

Test: Transportation & Assignment Model - Mechanical Engineering MCQ

10 questions mcq test - test: transportation & assignment model, which of the following is needed to use the transportation model.

Capacity of the sources

Demand of the destinations

Unit shipping cost

All of these

Which method usually gives a very good solution to the assignment problem?

Northwest corner rule

Vogel's approximation method

MODI method

Stepping-stone method

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In applying Vogel’s approximation method to a profit maximation problem, row and column penalties are determined by

finding the largest unit cost in each row or column.

finding the sum of the unit costs in each row or column.

finding the difference between the two highest unit costs in each row and column.

finding the difference between the two lowest unit costs in each row and column.

The concept of Vogel’s Approximation Method can be well understood through an illustration given below :

 The difference between two least cost cells are calculated for each row and column, which can be seen in the iteration given for each row and column.

Which one of the following is riot the solution method of transportation method?

Hungarian method

North west corner method

Least cost method

Vogel’s approximate method

The matrix in assignment model is

square maxtrix

rectangular matrix

diagonal matrix

unit matrix

Assignment model can be solved by conventional linear programming approach or transportation model approach, it is square matrix, having equal number of rows and columns. The objective is to assign one item from row to one item from column so that total cost of assignement is minimum.

In order for a transportation matrix which has six rows and four columns not to degenerate, what is the number of occupied cells, in the matrix?

Number of cells for non-degenerate solution  = 6 + 4 - 1 = 9

Consider the following statements: 1. For the application of optimally test in case of transportation model, the number of allocations should be equal to (m + n) where m is the number of rows and n is the number of columns. 2. Transportation problem is a special case of a linear programming problem. 3. In case of assignment problem, the first step is to dummy row or a matrix by adding a dummy row or a dummy column.

Which of these statements is/are correct?

1 and 2 only

2 and 3 only

Consider the following statements on transportation problem: 1. In Vogel’s approximation method, priority allotment is made in the cell with the lowest cost. 2. The North-west corner method ensures faster optimal solution. 3. If the total demand is higher than the supply, transportation problem cannot be solved. 4. A feasible solution may not be an optimal solution.

Which of these statements are correct?

Penalty cost method is

North West corner method

Vogel’s approximation method

None of the above

One disadvantage of using North-West Corner Rule to find initial solution to the transportation problem is that

it is complicated to use

it does not ’take into account cost of transportation

it leads to a degenerate initial solution

all of the above

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Important Questions for Transportation & Assignment Model

Transportation & assignment model mcqs with answers, online tests for transportation & assignment model.

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270+ Operations Research Solved MCQs

1.
A.	objective function
B.	decision variable
C.	constraints
D.	opportunity cost
Answer» A. objective function

2.
A.	infeasible region
B.	unbounded region
C.	infinite region
D.	feasible region
Answer» D. feasible region

3.
A.	outgoing row
B.	key row
C.	basic row
D.	interchanging row
Answer» C. basic row

4.
A.	dummy
B.	epsilon
C.	penalty
D.	regret
Answer» B. epsilon

5.
A.	ncwr
B.	lcm
C.	vam
D.	hungarian
Answer» D. hungarian

6.
A.	head path
B.	sub path
C.	critical path
D.	sub critical path
Answer» C. critical path

7.
A.	7
B.	10
C.	18
D.	8
Answer» B. 10

8.
A.	interfering float = total float – free float
B.	total float =free float + independent float
C.	total float ≥ free float ≥ independent float
D.	free float = total float – head event slack
Answer» B. total float =free float + independent float

9.
A.	expected
B.	pessimitic
C.	optimistic
D.	most likely
Answer» C. optimistic

10.
A.	processing order
B.	idle time
C.	processing time
D.	elapsed time
Answer» D. elapsed time

11.
A.	physical
B.	symbolic
C.	deterministic
D.	probabilistic
Answer» C. deterministic

12.
A.	physical
B.	symbolic
C.	deterministic
D.	probabilistic
Answer» D. probabilistic

13.
A.	cpm and pert
B.	assignment & transportation
C.	game theory
D.	decision theory & inventory models
Answer» A. cpm and pert

14.
A.	objective function
B.	decision variables
C.	constraints
D.	opportunity cost
Answer» B. decision variables

15.
A.	objective function
B.	decision variables
C.	constraints
D.	opportunity cost
Answer» A. objective function

16.
A.	objective function
B.	variables
C.	constraints
D.	profit
Answer» C. constraints

17.
A.	infeasible
B.	unbounded
C.	improper
D.	unknown
Answer» A. infeasible

18.
A.	less than or equal to
B.	greater than or equal to
C.	mixed
D.	equal to
Answer» D. equal to

19.
A.	infeasible
B.	infinite
C.	unique
D.	degenerate
Answer» B. infinite

20.
A.	key column
B.	incoming column
C.	important column
D.	variable column
Answer» A. key column

21.
A.	vital element
B.	important element
C.	basic element
D.	key element
Answer» D. key element

22.
A.	surplus
B.	artificial
C.	slack
D.	additional
Answer» C. slack

23.
A.	null resource
B.	scarce resource
C.	abundant resource
D.	zero resource
Answer» B. scarce resource

24.
A.	either zero or positive
B.	either zero or negative
C.	only positive
D.	only negative
Answer» A. either zero or positive

25.
A.	vogel’s approximat ion method
B.	nwcr
C.	lcm
D.	modi
Answer» C. lcm

26.
A.	infeasible solution
B.	feasible solution
C.	optimum solution
D.	degenerate solution
Answer» B. feasible solution

27.
A.	infeasible solution
B.	feasible solution
C.	non degenerate solution
D.	degenerate solution
Answer» C. non degenerate solution

28.
A.	vam
B.	nwcr
C.	modi
D.	lcm
Answer» A. vam

29.
A.	balanced
B.	unbalanced
C.	infeasible
D.	unbounded
Answer» B. unbalanced

30.
A.	vam
B.	nwcr
C.	modi
D.	hungarian
Answer» D. hungarian

31.
A.	cost
B.	regret
C.	profit
D.	dummy
Answer» B. regret

32.
A.	critical
B.	sub-critical
C.	best
D.	worst
Answer» A. critical

33.
A.	tentative
B.	definite
C.	latest
D.	earliest
Answer» C. latest

34.
A.	machines order
B.	job order
C.	processing order
D.	working order
Answer» C. processing order

35.
A.	processing
B.	waiting
C.	free
D.	idle
Answer» D. idle

36.
A.	objective function
B.	decision variables
C.	constraints
D.	opportunity cost
Answer» C. constraints

37.
A.	less than
B.	greater than
C.	not greater than
D.	not less than
Answer» A. less than

38.
A.	infeasible
B.	infinite
C.	unbounded
D.	feasible
Answer» D. feasible

39.
A.	multiple constraints
B.	infinite constraints
C.	infeasible constraints
D.	mixed constraints
Answer» D. mixed constraints

40.
A.	outgoing row
B.	key row
C.	interchanging row
D.	basic row
Answer» B. key row

41.
A.	null resource
B.	scarce resource
C.	abundant resource
D.	zero resource
Answer» C. abundant resource

42.
A.	unit price
B.	extra price
C.	retail price
D.	shadow price
Answer» D. shadow price

43.
A.	either zero or positive
B.	either zero or negative
C.	only positive
D.	only negative
Answer» B. either zero or negative

44.
A.	vogel’s approximat ion method
B.	nwcr
C.	lcm
D.	modi
Answer» A. vogel’s approximat ion method

45.
A.	dummy
B.	penalty
C.	regret
D.	epsilon
Answer» D. epsilon

46.
A.	there is no degeneracy
B.	degeneracy exists
C.	solution is optimum
D.	problem is balanced
Answer» A. there is no degeneracy

47.
A.	dummy
B.	non-critical
C.	important
D.	critical
Answer» D. critical

48.
A.	one
B.	zero
C.	highest
D.	equal to duration
Answer» B. zero

49.
A.	optimistic
B.	pessimistic
C.	expected
D.	most likely
Answer» A. optimistic

50.
A.	processing time
B.	waiting time
C.	elapsed time
D.	idle time
Answer» C. elapsed time

51.
A.	invitees
B.	players
C.	contestants
D.	clients
Answer» B. players

52.
A.	income
B.	profit
C.	payoff
D.	gains
Answer» C. payoff

53.
A.	choices
B.	strategies
C.	options
D.	actions
Answer» B. strategies

54.
A.	centre point
B.	saddle point
C.	main point
D.	equal point
Answer» B. saddle point

55.
A.	2
B.	3
C.	1
D.	4
Answer» B. 3

56.
A.	parallel to x axis
B.	parallel to y axis
C.	passes through the origin
D.	intersects both the axis
Answer» A. parallel to x axis

57.
A.	qualitative
B.	quantitative
C.	judgmental
D.	subjective
Answer» B. quantitative

58.
A.	exact
B.	earliest
C.	latest
D.	approximate
Answer» B. earliest

59.
A.	alternate
B.	feasible solution
C.	critical
D.	sub-critical
Answer» D. sub-critical

60.
A.	degenerate
B.	prohibited
C.	infeasible
D.	unbalanced
Answer» B. prohibited

61.
A.	Research
B.	Decision – Making
C.	Operations
D.	None of the above
Answer» B. Decision – Making

62.
A.	J.F. McCloskey
B.	F.N. Trefethen
C.	P.F. Adams
D.	Both A and B
Answer» D. Both A and B

63.
A.	1950
B.	1940
C.	1978
D.	1960
Answer» B. 1940

64.
A.	Civil War
B.	World War I
C.	World War II
D.	Industrial Revolution
Answer» C. World War II

65.
A.	Battle field
B.	Fighting
C.	War
D.	Both A and B
Answer» D. Both A and B

66.
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)

67.
A.	E.L. Arnoff
B.	P.M.S. Blackett
C.	H.M. Wagner
D.	None of the above
Answer» C. H.M. Wagner

68.
A.	C. Kitte
B.	H.M. Wagner
C.	E.L. Arnoff
D.	None of the above
Answer» A. C. Kitte

69.
A.	Scientists
B.	Mathematicians
C.	Academics
D.	All of the above
Answer» A. Scientists

70.
A.	Economists
B.	Administrators
C.	Statisticians and Technicians
D.	All of the above
Answer» D. All of the above

71.
A.	System Orientation
B.	System Approach
C.	Interdisciplinary Team Approach
D.	none
Answer» D. none

72.
A.	Answers
B.	Solutions
C.	Both A and B
D.	Decisions
Answer» C. Both A and B

73.
A.	Quality
B.	Clarity
C.	Look
D.	None of the above
Answer» A. Quality

74.
A.	Scientific
B.	Systematic
C.	Both A and B
D.	Statistical
Answer» C. Both A and B

75.
A.	Two or more
B.	One or more
C.	Three or more
D.	Only One
Answer» B. One or more

76.
A.	Conducting experiments on it
B.	Mathematical analysis
C.	Both A and B
D.	Diversified Techniques
Answer» C. Both A and B

77.
A.	Policies
B.	Actions
C.	Both A and B
D.	None of the above
Answer» C. Both A and B

78.
A.	Science
B.	Art
C.	Mathematics
D.	Both A and B
Answer» D. Both A and B

79.
A.	Scientific Models
B.	Algorithms
C.	Mathematical Models
D.	None of the above
Answer» C. Mathematical Models

80.
A.	Quailing Theory
B.	Waiting Line
C.	Both A and B
D.	Linear Programming
Answer» D. Linear Programming

81.
A.	Inventory Control
B.	Inventory Capacity
C.	Inventory Planning
D.	None of the above
Answer» C. Inventory Planning

82.
A.	Inventory Control
B.	Inventory
C.	Inventory Planning
D.	None of the above
Answer» B. Inventory

83.
A.	Game Theory
B.	Network Analysis
C.	Decision Theory
D.	None of the above
Answer» C. Decision Theory

84.
A.	Game Theory
B.	Network Analysis
C.	Decision Theory
D.	None of the above
Answer» B. Network Analysis

85.
A.	Simulation
B.	Integrated Production Models
C.	Inventory Control
D.	Game Theory
Answer» A. Simulation

86.
A.	Search Theory
B.	Theory of replacement
C.	Probabilistic Programming
D.	None of the above
Answer» B. Theory of replacement

87.
A.	Probabilistic Programming
B.	Stochastic Programming
C.	Both A and B
D.	Linear Programming
Answer» C. Both A and B

88.
A.	Programme Evaluation
B.	Review Technique (PERT)
C.	Both A and B
D.	Deployment of resources
Answer» C. Both A and B

89.
A.	Schedule
B.	Product Mix
C.	Both A and B
D.	Servicing Cost
Answer» C. Both A and B

90.
A.	Men and Machine
B.	Money
C.	Material and Time
D.	All of the above
Answer» D. All of the above

91.
A.	Three
B.	Four
C.	Five
D.	Two
Answer» A. Three

92.
A.	Sequencing
B.	Allocation Models
C.	Queuing Theory
D.	Decision Theory
Answer» B. Allocation Models

93.
A.	Linear Programming Technique
B.	Non – Linear Programming Technique
C.	Both A and B
D.	None of the above
Answer» C. Both A and B

94.
A.	Deterministic Models
B.	Probabilistic Models
C.	Both A and B
D.	None of the above
Answer» A. Deterministic Models

95.
A.	Deterministic Models
B.	Probabilistic Models
C.	Both A and B
D.	None of the above
Answer» B. Probabilistic Models

96.
A.	Iconic Models
B.	Analogue Models
C.	Symbolic Models
D.	None of the above
Answer» A. Iconic Models

97.
A.	Optimum
B.	Perfect
C.	Degenerate
D.	None of the above
Answer» A. Optimum

98.
A.	Research
B.	Operation
C.	Both A and B
D.	None of the above
Answer» B. Operation

99.
A.	Decision Theory
B.	Simulation
C.	Game Theory
D.	None of the above
Answer» B. Simulation

100.
A.	Queuing Theory
B.	Decision Theory
C.	Both A and B
D.	None of the above
Answer» A. Queuing Theory

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Operations Research

101. All the basis for a transportation problem is ______________.

102. In the transportation table, empty cells will be called ______________.

103. ______________ is a completely degenerate form of a transportation problem

• Transportation Problem
• Assignment Problem
• Travelling salesman problem
• Replacement Problem

104. The linear function to be maximized or minimized is called ______________ function.

105. The coefficient of an artificial variable in the objective function of penalty method are always assumed to be ______________.

106. The process that performs the services to the customer is known as ______________.

• service channel

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

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

108. Slack is also known as ______________.

109. What type of distribution does a time follow in program evaluation review technique model?

• Exponential

110. A activity in a network diagram is said to be ______________ if the delay in its start will further delay the project completion time.

• critical path
• non critical

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Assignment Problem: Meaning, Methods and Variations | Operations Research

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:

Hungarian Method for Solving Assignment Problem:

The Hungarian method of assignment provides us with an efficient method of finding the optimal solution without having to make a-direct comparison of every solution. It works on the principle of reducing the given cost matrix to a matrix of opportunity costs.

Opportunity cost show the relative penalties associated with assigning resources to an activity as opposed to making the best or least cost assignment. If we can reduce the cost matrix to the extent of having at least one zero in each row and column, it will be possible to make optimal assignment.

The Hungarian method can be summarized in the following steps:

Step 1: Develop the Cost Table from the given Problem:

If the no of rows are not equal to the no of columns and vice versa, a dummy row or dummy column must be added. The assignment cost for dummy cells are always zero.

Step 2:  Find the Opportunity Cost Table:

(a) Locate the smallest element in each row of the given cost table and then subtract that from each element of that row, and

(b) In the reduced matrix obtained from 2 (a) locate the smallest element in each column and then subtract that from each element. Each row and column now have at least one zero value.

Step 3: Make Assignment in the Opportunity Cost Matrix:

The procedure of making assignment is as follows:

(a) Examine rows successively until a row with exactly one unmarked zero is obtained. Make an assignment single zero by making a square around it.

(b) For each zero value that becomes assigned, eliminate (Strike off) all other zeros in the same row and/ or column

(c) Repeat step 3 (a) and 3 (b) for each column also with exactly single zero value all that has not been assigned.

(d) If a row and/or column has two or more unmarked zeros and one cannot be chosen by inspection, then choose the assigned zero cell arbitrarily.

(e) Continue this process until all zeros in row column are either enclosed (Assigned) or struck off (x)

Step 4: Optimality Criterion:

If the member of assigned cells is equal to the numbers of rows column then it is optimal solution. The total cost associated with this solution is obtained by adding original cost figures in the occupied cells.

If a zero cell was chosen arbitrarily in step (3), there exists an alternative optimal solution. But if no optimal solution is found, then go to step (5).

Step 5: Revise the Opportunity Cost Table:

Draw a set of horizontal and vertical lines to cover all the zeros in the revised cost table obtained from step (3), by using the following procedure:

(a) For each row in which no assignment was made, mark a tick (√)

(b) Examine the marked rows. If any zero occurs in those columns, tick the respective rows that contain those assigned zeros.

(c) Repeat this process until no more rows or columns can be marked.

(d) Draw a straight line through each marked column and each unmarked row.

If a no of lines drawn is equal to the no of (or columns) the current solution is the optimal solution, otherwise go to step 6.

Step 6: Develop the New Revised Opportunity Cost Table:

(a) From among the cells not covered by any line, choose the smallest element, call this value K

(b) Subtract K from every element in the cell not covered by line.

(c) Add K to very element in the cell covered by the two lines, i.e., intersection of two lines.

(d) Elements in cells covered by one line remain unchanged.

Step 7:  Repeat Step 3 to 6 Unlit an Optimal Solution is Obtained:

The flow chart of steps in the Hungarian method for solving an assignment problem is shown in following figures:

ADVERTISEMENTS:

Assignment problem is a special type of linear programming problem which deals with the allocation of the various resources to the various activities on one to one basis. It does it in such a way that the cost or time involved in the process is minimum and profit or sale is maximum. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems.

In a factory, a supervisor may have six workers available and six jobs to fire. He will have to take decision regarding which job should be given to which worker. Problem forms one to one basis. This is an assignment problem.

1. Assignment Model :

Suppose there are n facilitates and n jobs it is clear that in this case, there will be n assignments. Each facility or say worker can perform each job, one at a time. But there should be certain procedure by which assignment should be made so that the profit is maximized or the cost or time is minimized.

In the table, Co ij is defined as the cost when j th job is assigned to i th worker. It maybe noted here that this is a special case of transportation problem when the number of rows is equal to number of columns.

Mathematical Formulation:

Any basic feasible solution of an Assignment problem consists (2n – 1) variables of which the (n – 1) variables are zero, n is number of jobs or number of facilities. Due to this high degeneracy, if we solve the problem by usual transportation method, it will be a complex and time consuming work. Thus a separate technique is derived for it. Before going to the absolute method it is very important to formulate the problem.

Suppose x jj is a variable which is defined as

1 if the i th job is assigned to j th machine or facility

0 if the i th job is not assigned to j th machine or facility.

Now as the problem forms one to one basis or one job is to be assigned to one facility or machine.

The total assignment cost will be given by

The above definition can be developed into mathematical model as follows:

Determine x ij > 0 (i, j = 1,2, 3…n) in order to

Subjected to constraints

and x ij is either zero or one.

Method to solve Problem (Hungarian Technique):

Consider the objective function of minimization type. Following steps are involved in solving this Assignment problem,

1. Locate the smallest cost element in each row of the given cost table starting with the first row. Now, this smallest element is subtracted form each element of that row. So, we will be getting at least one zero in each row of this new table.

2. Having constructed the table (as by step-1) take the columns of the table. Starting from first column locate the smallest cost element in each column. Now subtract this smallest element from each element of that column. Having performed the step 1 and step 2, we will be getting at least one zero in each column in the reduced cost table.

3. Now, the assignments are made for the reduced table in following manner.

(i) Rows are examined successively, until the row with exactly single (one) zero is found. Assignment is made to this single zero by putting square □ around it and in the corresponding column, all other zeros are crossed out (x) because these will not be used to make any other assignment in this column. Step is conducted for each row.

(ii) Step 3 (i) in now performed on the columns as follow:- columns are examined successively till a column with exactly one zero is found. Now , assignment is made to this single zero by putting the square around it and at the same time, all other zeros in the corresponding rows are crossed out (x) step is conducted for each column.

(iii) Step 3, (i) and 3 (ii) are repeated till all the zeros are either marked or crossed out. Now, if the number of marked zeros or the assignments made are equal to number of rows or columns, optimum solution has been achieved. There will be exactly single assignment in each or columns without any assignment. In this case, we will go to step 4.

4. At this stage, draw the minimum number of lines (horizontal and vertical) necessary to cover all zeros in the matrix obtained in step 3, Following procedure is adopted:

(iii) Now tick mark all the rows that are not already marked and that have assignment in the marked columns.

(iv) All the steps i.e. (4(i), 4(ii), 4(iii) are repeated until no more rows or columns can be marked.

(v) Now draw straight lines which pass through all the un marked rows and marked columns. It can also be noticed that in an n x n matrix, always less than ‘n’ lines will cover all the zeros if there is no solution among them.

5. In step 4, if the number of lines drawn are equal to n or the number of rows, then it is the optimum solution if not, then go to step 6.

6. Select the smallest element among all the uncovered elements. Now, this element is subtracted from all the uncovered elements and added to the element which lies at the intersection of two lines. This is the matrix for fresh assignments.

7. Repeat the procedure from step (3) until the number of assignments becomes equal to the number of rows or number of columns.

Related Articles:

• Two Phase Methods of Problem Solving in Linear Programming: First and Second Phase
• Linear Programming: Applications, Definitions and Problems

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Transportation Models And Network Models MCQs

By By Team EasyExamNotes

1. Which transportation model is used to determine the most efficient allocation of resources between multiple origins and destinations? a) Traveling Salesman Problem b) Shortest Route Problem c) Transportation Assignment Model d) Minimal Spanning Tree Answer: c) Transportation Assignment Model Explanation: The Transportation Assignment Model is specifically designed to optimize the allocation of resources (such as goods or services) from multiple origins to multiple destinations, taking into account various constraints like costs and capacities.

2. What does the Traveling Salesman Problem seek to minimize? a) Time taken to travel between cities b) Cost of traveling between cities c) Number of cities visited d) Distance traveled between cities Answer: d) Distance traveled between cities Explanation: The Traveling Salesman Problem aims to find the shortest possible route that visits each city exactly once and returns to the original city.

3. Which network model is used to find the shortest path between two nodes in a network? a) Minimal Spanning Tree b) Maximum Flow Model c) Shortest Route Problem d) Critical Path Method Answer: c) Shortest Route Problem Explanation: The Shortest Route Problem deals with finding the most efficient path between two specific nodes in a network, minimizing distance, time, or other relevant metrics.

4. What is the primary objective of a Minimal Spanning Tree in network models? a) Maximizing the flow between nodes b) Minimizing the number of connections c) Minimizing the total cost of connections d) Maximizing the number of nodes Answer: c) Minimizing the total cost of connections Explanation: A Minimal Spanning Tree seeks to connect all the nodes in a network with the minimum possible total cost, ensuring that every node is reachable while minimizing the sum of edge weights.

5. In which type of network model is the concept of “flow” central to its optimization? a) Shortest Route Problem b) Maximum Flow Model c) Transportation Assignment Model d) Critical Path Method Answer: b) Maximum Flow Model Explanation: The Maximum Flow Model aims to determine the maximum amount of flow that can pass through a network from a source to a sink, subject to capacity constraints on edges and nodes.

6. Which network model is commonly used for project management to schedule and organize tasks? a) Shortest Route Problem b) Critical Path Method c) Minimal Spanning Tree d) Transportation Assignment Model Answer: b) Critical Path Method Explanation: The Critical Path Method (CPM) is a project management tool used to schedule and organize tasks in a project, identifying the critical path – the longest sequence of dependent tasks – and determining the project’s overall duration.

7. What does PERT stand for in the context of project management networks? a) Project Evaluation and Review Technique b) Project Efficiency and Resource Tracking c) Program Evaluation and Resource Timeframe d) Project Execution and Resource Tracking Answer: a) Project Evaluation and Review Technique Explanation: PERT (Project Evaluation and Review Technique) is a method used in project management to analyze and represent the tasks involved in completing a project, incorporating uncertainty into the project’s schedule.

8. Which sequencing model aims to optimize the order of tasks to minimize total completion time? a) Traveling Salesman Problem b) Critical Path Method c) Shortest Route Problem d) Sequencing Model Answer: d) Sequencing Model Explanation: Sequencing models focus on determining the optimal order or sequence of tasks or jobs to minimize total completion time, cost, or other specified criteria.

9. What does CPM identify in a project management network? a) Maximum flow path b) Critical path c) Minimal spanning tree d) Shortest route Answer: b) Critical path Explanation: In a project management network, the Critical Path Method (CPM) identifies the critical path, which is the longest sequence of dependent tasks and determines the project’s minimum duration.

10. Which transportation model is concerned with the allocation of resources to minimize the total transportation cost? a) Shortest Route Problem b) Transportation Assignment Model c) Maximum Flow Model d) Traveling Salesman Problem Answer: b) Transportation Assignment Model Explanation: The Transportation Assignment Model focuses on allocating resources (such as goods or services) from multiple origins to multiple destinations in a way that minimizes the total transportation cost.

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Assignment Method

Published on :

21 Aug, 2024

Blog Author :

Edited by :

Reviewed by :

Dheeraj Vaidya

What Is The Assignment Method?

The assignment method is a strategic approach to allocating organizational resources, including tasks and jobs to various departments like people, machines, or teams. It aims to minimize total costs or completion time and gain maximum efficiency, by assigning resources to corresponding units.

The assignment procedure's importance stems from its capacity to optimize resource allocation procedures in a business. Organizations may guarantee that resources are used optimally, reducing waste and increasing productivity by implementing a systematic method. It facilitates the decision-making process for the efficient and economical use of resources by helping to make well-informed choices.

Table of contents

Assignment method explained, methodology, advantages & disadvantages, frequently asked questions (faqs), recommended articles.

• The assignment method strategically allocates resources to tasks, jobs or teams to minimize costs or completion time. It optimizes resource utilization, reduces waste, and improves operational efficiency.
• It involves using methods like complete enumeration, simplex, transportation, or the Hungarian method. It involves using the assignment method of linear programming .
• The   Hungarian assignment method efficiently solves assignment problems by determining optimal assignments using a cost matrix.
• Advantages include structured resource allocation, enhanced resource utilization, and improved operational effectiveness. Limitations include data accuracy requirements and limited flexibility for dynamic changes.

The assignment method in operation research is a strategy for allocating organizational resources to tasks to increase profit via efficiency gains, cost reductions , and improved handling of operations that might create bottlenecks . It is an operations management tool that, by allocating jobs to the appropriate individual, minimizes expenses , time, and effort.

The technique is an essential tool for project management and cost accounting . It assists in allocating indirect expenses , such as overhead, to objects or cost centers according to predetermined standards, such as direct labor hours or required machine hours. The method helps determine the overall cost of every good or service, which helps with pricing, output, and resource distribution decisions. It also guarantees effective work allocation, on-time project completion, and economical use of resources. In short, it solves assignment problems.

Assignment problems involve assigning workers to specific roles, such as office workers or trucks on delivery routes, or determining which machines or products should be used in a plant during a specific period. Transportation problems involve distributing empty freight cars or assigning orders to factories. Allocation problems also involve determining which machines or products should be used to produce a given product or set of products. Unit costs or returns can be independent or interdependent, and if allocations affect subsequent periods, the problem is dynamic, requiring consideration of time in its solution.

The assignment problem can be solved using four methods: The complete enumeration method, the simplex method, the transportation method, and the Hungarian method.

The complete enumeration approach generates a list of potential assignments between resources and activities, from which the best option is chosen based on factors like cost, distance, time, or optimum profit. If the minimum cost, time, or distance for two or more assignments is the same, then this approach offers numerous optimal solutions. However If there are a lot of assignments, it is no longer appropriate for manual calculations. Assignment method calculators, if reliable, can be used for the same.

The simplex method can be solved as a linear programming problem using the simplex algorithm. The transportation method is a special case of the assignment problem. The method is, however, computationally inefficient for solving the assignment problem due to the solution's degeneracy problem.

The Hungarian assignment method problem, developed by mathematician D. Konig, is a faster and more efficient approach to solving assignment problems. It involves determining the cost of making all possible assignments using a matrix. Each problem has a row representing the objects to be assigned and columns representing assigned tasks. The cost matrix is square, and the optimum solution is to have only one assignment in a row or column. This method is a variation of the transportation problem, with the cost matrix being square and the optimum solution being one assignment in a row or column of the cost matrix.

Let us look into a few examples to understand the concept better.

TechLogistics Solutions, an imaginary delivery company, employs the assignment method to optimize the distribution of its delivery trucks. They meticulously consider distance, traffic conditions, and delivery schedules. TechLogistics efficiently allocates trucks to routes through strategic assignments, effectively reducing fuel costs and ensuring punctual deliveries. This method significantly enhances the company's operational efficiency and optimizes the utilization of its delivery resources.

Suppose XYZ Inc., a manufacturing company, is challenged to efficiently assign tasks to its machines (A, B, and C). Using the assignment method, XYZ calculates the cost matrix, reflecting the cost associated with each task assigned to each machine. Leveraging advanced algorithms like the Hungarian method, the company identifies optimal task-machine assignments, minimizing overall costs. This approach enables XYZ to streamline its production processes and enhance cost-effectiveness in manufacturing operations .

Advantages of the assignment method include:

• Resource allocation is carried out in a structured and organized manner.
• Enhancement of resource utilization to achieve optimal outcomes.
• Facilitation of efficient distribution of tasks.
• Improvement in operational effectiveness and productivity.
• Economical allocation of resources.
• Reduction in project completion time.
• Consideration of multiple factors and constraints for informed decision-making.

The disadvantages of the assignment method are as follows:

• Dependence on accurate and up-to-date data for effective decision-making.
• Complexity when dealing with resource allocation on a large scale.
• Subjectivity is involved in assigning values to the resource-requirement matrix.
• Limited flexibility in accommodating dynamic changes or unforeseen circumstances.
• Applicable primarily to quantitative tasks, with limitations in addressing qualitative aspects.

Johnson's rule is an operations research method that aims to estimate the optimal sequence of jobs in two work centers to reduce makespan. It optimizes the overall efficiency of the process. In contrast, the assignment method is useful for resource allocation, matching resources to specific tasks or requirements to optimize efficiency.

The study assignment method refers to the process of allocating students to specific courses or study programs based on their preferences, skills etc. It involves matching students with appropriate courses or programs to ensure optimal utilization of educational resources and meet individual student needs.

The assignment method is frequently employed when there is a requirement to allocate restricted resources like personnel, equipment, or budget to particular tasks or projects. It aids in enhancing resource utilization operational efficiency, and enables informed decision-making regarding resource allocation considering various factors and constraints.

This article has been a guide to what is Assignment Method. Here, we explain its methodologies, examples, advantages, & disadvantages. You may also find some useful articles here -

• Cost Allocation Methods
• Propensity Score Matching
• Regression Discontinuity Design