difference between assignment problem and transportation problem in tabular form

Difference between transportation and assignment problems?

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February 11, 2023
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lets understand the Difference between transportation and assignment problems?

Transportation problems and assignment problems are two types of linear programming problems that arise in different applications.

The main difference between transportation and assignment problems is in the nature of the decision variables and the constraints.

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Assignment Problem	Minimization or maximization of the cost of transporting goods from one source to another	Maximization of the total profit or minimization of the total cost in assigning tasks to individuals
Nature of problem	Involves transporting goods from sources to destinations	Involves assigning tasks to individuals
Number of sources and destinations	Multiple sources and destinations	An equal number of sources and destinations
Availability and demand	Each source and destination have a supply or demand value	Each task has only one individual who can perform it
Decision variables	Amount of goods transported from each source to each destination	Binary variables indicate whether an individual is assigned a task or not
Constraints	Capacity constraints on sources and demand constraints on destinations	Each individual can only perform one task
Solution method	Transportation simplex method, northwest corner rule, Vogel’s approximation method	Hungarian algorithm, brute force method
Example	Transporting goods from factories to warehouses	Assigning tasks to employees or jobs to machines

Difference between transportation and assignment problems

Additional Different between Transportation and Assignment Problems are as follows :

Decision Variables:

In a transportation problem, the decision variables represent the flow of goods from sources to destinations. Each variable represents the quantity of goods transported from a source to a destination.

In contrast, in an assignment problem, the decision variables represent the assignment of agents to tasks. Each variable represents whether an agent is assigned to a particular task or not.

Constraints:

In a transportation problem, the constraints ensure that the supply from each source matches the demand at each destination and that the total flow of goods does not exceed the capacity of each source and destination.

In contrast, in an assignment problem, the constraints ensure that each task is assigned to exactly one agent and that each agent is assigned to at most one task.

Objective function:

The objective function in a transportation problem typically involves minimizing the total cost of transportation or maximizing the total profit of transportation.

In an assignment problem, the objective function typically involves minimizing the total cost or maximizing the total benefit of assigning agents to tasks.

In summary,

The transportation problem is concerned with finding the optimal way to transport goods from sources to destinations,

while the assignment problem is concerned with finding the optimal way to assign agents to tasks.

Both problems are important in operations research and have numerous practical applications.

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Operations Research/Transportation and Assignment Problem

The Transportation and Assignment problems deal with assigning sources and jobs to destinations and machines. We will discuss the transportation problem first.

Suppose a company has m factories where it manufactures its product and n outlets from where the product is sold. Transporting the product from a factory to an outlet costs some money which depends on several factors and varies for each choice of factory and outlet. The total amount of the product a particular factory makes is fixed and so is the total amount a particular outlet can store. The problem is to decide how much of the product should be supplied from each factory to each outlet so that the total cost is minimum.

Let us consider an example.

Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D and E. The capacities of the three plants during the next quarter are 1000, 1500 and 1200 cars. The quarterly demands of the two distribution centers are 2300 and 1400 cars. The transportation costs (which depend on the mileage, transport company etc) between the plants and the distribution centers is as follows:

Cost Table	Dist Center D	Dist Center E
Plant A	80	215
Plant B	100	108
Plant C	102	68

Which plant should supply how many cars to which outlet so that the total cost is minimum?

The problem can be formulated as a LP model:

$x_{ij}$

The whole model is:

subject to,

$x_{11}+x_{12}=1000$

The problem can now be solved using the simplex method. A convenient procedure is discussed in the next section.

Book:Operations Research

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Difference Between Assignment and Transportation Model

1.1 Comparison Between Assignment and Transportation Model With Tabular Form
1.2 Comparison Chart
1.3 Similarities
2 More Difference

Comparison Between Assignment and Transportation Model With Tabular Form

The Major Difference Between Assignment and Transportation model is that Assignment model may be regarded as a special case of the transportation model. However, the Transportation algorithm is not very useful to solve this model because of degeneracy.

Comparison Chart


The problem may have a rectangular matrix or a square matrix.	The assignment algorithm can not be used to solve the transportation model.
The rows and columns may have any number of allocations depending on the rim conditions.	The rows and columns must have one-to-one allocation. Because of this property, the matrix must be a square matrix.
The basic feasible solution is obtained by the northwest corner method or LCM method or VAM	The basic feasible solution is obtained by the Hungarian method or Flood’s technique or by Assignment algorithm.
The optimality test is given by the stepping stone method or by the MODI method.	The optimality test is given by drawing a minimum number of horizontal and vertical lines to cover all the zeros in the matrix.
The rim requirement may have any positive numbers.	The optimality test is given by drawing a minimum number of horizontal and vertical lines to cover all the zeros in the matrix.
The transportation algorithm can be used to solve the assignment model.	The assignment algorithm can not be used to solve the transportation model.

Similarities

Both are special types of linear programming problems.
Both have an objective function, structural constraints, and non-negativity constraints. And the relationship between variables and constraints is linear.
The coefficients of variables in the solution will be either 1 or zero in both cases.
Both are basically minimization problems. For converting them into maximization problems same procedure is used.

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Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized. It is also sometimes called as Hitchcock problem.

Types of Transportation problems: Balanced: When both supplies and demands are equal then the problem is said to be a balanced transportation problem.

Unbalanced: When the supply and demand are not equal then it is said to be an unbalanced transportation problem. In this type of problem, either a dummy row or a dummy column is added according to the requirement to make it a balanced problem. Then it can be solved similar to the balanced problem.

Methods to Solve: To find the initial basic feasible solution there are three methods:

NorthWest Corner Cell Method.
Least Cost Method.
Vogel’s Approximation Method (VAM).

difference between assignment problem and transportation problem in tabular form

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Assignment Problem

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The problem of optimally assigning m individuals to m jobs, so that each individual is assigned to one job, and each job is filled by one individual. The problem can be formulated as a linear-programming problem with the objective function measuring the (linear) utility of the assignment as follows:

The problem is a special form of the transportation problem and, as such,...

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Burkard, R., Dell’Amico, M., & Marterllo, S. (2009). Assignment problems . Philadelphia: SIAM.

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Kuhn, H. W. (1995). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2 , 83–97.

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Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

Saul I. Gass

Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD, USA

Michael C. Fu

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(2013). Assignment Problem. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_200965

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What is the difference between Assignment Problem and Transportation Problem? - Business Mathematics and Statistics

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What is the difference between Assignment Problem and Transportation Problem?

Solution Show Solution

The assignment problem is a special case of the transportation problem.

The differences are given below:


This is about reducing the cost of transportation merchandise	This is about assigning finite sources to finite destinations where only one destination is allotted for one source with a minimum cost
Number of sources and number of demand need not be equal	Number of sources and the number of destinations must be equal
If total demand and total supply are not equal then the problem is said to be unbalanced.	If the number of rows is not equal to the number of columns then problems are unbalanced.
It requires 2 stages to solve: Getting initial basic feasible solution, by NWC, LCM, VAM and optimal solution by MODI method	It has only one stage. Hungarian method is sufficient for obtaining an optimal solution

RELATED QUESTIONS

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

Jobs	Machines
	P	Q	R	S
	Processing Cost (Rs.)
A	31	25	33	29
B	25	24	23	21
C	19	21	23	24
D	38	36	34	40

How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Solve the following minimal assignment problem and hence find the minimum value :


2	10	9	7
13	2	12	2
3	4	6	1
4	15	4	9

Determine `l_92 and l_93, "given that" l_91 = 97, d_91 = 38 and q_92 = 27/59`

Solve the following maximal assignment problem :



11	11	9	9
13	16	11	10
12	17	13	8
16	14	16	12

In a factory there are six jobs to be performed each of which should go through two machines A and B in the order A - B. The processing timing (in hours) for the jobs arc given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T. What is the value of T? Also find the idle time for machines · A and B.

Jobs	J	J	J	J	J	J
Machine A	1	3	8	5	6	3
MAchine B	5	6	3	2	2	10

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job for each machine is given in the following table:



A	31	25	33	29
B	25	24	23	21
C	19	21	23	24
D	38	36	34	40

Find the optimal assignment to minimize the total processing cost.

Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at 5 stations I, II, III, IV, and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?


10	5	9	18	11
13	9	6	12	14
3	2	4	4	5
18	9	12	17	15
11	6	14	19	10

Five different machines can do any of the five required jobs, with different profits resulting from each assignment as shown below:



30	37	40	28	40
40	24	27	21	36
40	32	33	30	35
25	38	40	36	36
29	62	41	34	39

Find the optimal assignment schedule.

The assignment problem is said to be unbalance if ______

The assignment problem is said to be balanced if ______.

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

The objective of an assignment problem is to assign ______.

Fill in the blank :

An _______ is a special type of linear programming problem.

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

State whether the following is True or False :

It is not necessary to express an assignment problem into n x n matrix.

Solve the following problem :

A plant manager has four subordinates, and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This estimate of the time each man would take to perform each task is given in the effectiveness matrix below.


7	25	26	10
12	27	3	25
37	18	17	14
18	25	23	9

How should the tasks be allocated, one to a man, as to minimize the total man hours?

A dairy plant has five milk tankers, I, II, III, IV and V. These milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.


150	120	175	180	200
125	110	120	150	165
130	100	145	160	175
40	40	70	70	100
45	25	60	70	95

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

Choose the correct alternative:

The assignment problem is generally defined as a problem of ______

Choose the correct alternative:

Assignment Problem is special case of ______

When an assignment problem has more than one solution, then it is ______

The assignment problem is said to be balanced if ______

If the given matrix is ______ matrix, the assignment problem is called balanced problem

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

State whether the following statement is True or False:

In assignment problem each worker or machine is assigned only one job

What is the Assignment problem?

Give mathematical form of Assignment problem

Find the optimal solution for the assignment problem with the following cost matrix.

		Area
		1	2	3	4
	P	11	17	8	16
Salesman	Q	9	7	12	6
	R	13	16	15	12
	S	14	10	12	11

Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.

	1	2	3	4
A	4	7	3	7
B	8	2	5	5
C	4	9	6	9
D	7	5	4	8
E	6	3	5	4
F	6	8	7	3

Number of basic allocation in any row or column in an assignment problem can be

If number of sources is not equal to number of destinations, the assignment problem is called ______

The purpose of a dummy row or column in an assignment problem is to

In an assignment problem involving four workers and three jobs, total number of assignments possible are

A car hire company has one car at each of five depots a, b, c, d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

	a	b	c	d	e
A	160	130	175	190	200
B	135	120	130	160	175
C	140	110	155	170	185
D	50	50	80	80	110
E	55	35	70	80	105

How should the cars be assigned to the customers so as to minimize the distance travelled?

A natural truck-rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

		To
		7	8	9	10	11	12
From	1	31	62	29	42	15	41
	2	12	19	39	55	71	40
	3	17	29	50	41	22	22
	4	35	40	38	42	27	33
	5	19	30	29	16	20	33
	6	72	30	30	50	41	20

How should the truck be dispersed so as to minimize the total distance travelled?

A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.


150	120	175	180	200
125	110	120	150	165
130	100	145	160	170
40	40	70	70	100
45	25	60	70	95

A department store has four workers to pack goods. The times (in minutes) required for each worker to complete the packings per item sold is given below. How should the manager of the store assign the jobs to the workers, so as to minimize the total time of packing?


Books	Toys	Crockery	Cutlery
3	11	10	8
13	2	12	12
3	4	6	1
4	15	4	9

A job production unit has four jobs P, Q, R, S which can be manufactured on each of the four machines I, II, III and IV. The processing cost of each job for each machine is given in the following table :



31	25	33	29
25	24	23	21
19	21	23	24
38	36	34	40

Complete the following activity to find the optimal assignment to minimize the total processing cost.

Step 1: Subtract the smallest element in each row from every element of it. New assignment matrix is obtained as follows :



6	0	8	4
4	3	2	0
0	2	4	5
4	2	0	6

Step 2: Subtract the smallest element in each column from every element of it. New assignment matrix is obtained as above, because each column in it contains one zero.

Step 3: Draw minimum number of vertical and horizontal lines to cover all zeros:

Step 4: From step 3, as the minimum number of straight lines required to cover all zeros in the assignment matrix equals the number of rows/columns. Optimal solution has reached.

Examine the rows one by one starting with the first row with exactly one zero is found. Mark the zero by enclosing it in (`square`), indicating assignment of the job. Cross all the zeros in the same column. This step is shown in the following table :



6		8	4
4	3	2
	2	4	5
4	2		6

Step 5: It is observed that all the zeros are assigned and each row and each column contains exactly one assignment. Hence, the optimal (minimum) assignment schedule is :


P	II	`square`
Q	`square`	21
R	I	`square`
S	III	34

Hence, total (minimum) processing cost = 25 + 21 + 19 + 34 = ₹`square`

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Difference Between Transportation Problem and Assignment Problem
Transportation Problem deals with the optimal distribution of goods or resources from multiple sources to multiple destinations. While Assignment Problem deals with allocating tasks, jobs, or resources one-to-one. These LPP methods are used for cost minimization, resource allocation, supply chain management, workforce planning, facility ...
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7. Identify the relationship between assignment problems and transportation problems. 8. Formulate a spreadsheet model for an assignment problem from a description of the problem. 9. Do the same for some variants of assignment problems. 10. Give the name of an algorithm that can solve huge assignment problems that are well
Difference between transportation and assignment problems?
In summary, The transportation problem is concerned with finding the optimal way to transport goods from sources to destinations, while the assignment problem is concerned with finding the optimal way to assign agents to tasks. Both problems are important in operations research and have numerous practical applications.
PDF Module 4: Transportation Problem and Assignment problem
Prasad A Y, Dept of CSE, ACSCE, B'lore-74. Page 33. Module 4: Transportation Problem and Assignment problem. This means that programmer 1 is assigned programme C, programmer 2 is assigned programme A, and so on. The minimum time taken in developing the programmes is = 80 + 80 + 100 + 90 = 350 min.
PDF 9 Transportation and Assignment Problems
It turns out that transportation problems already capture the full expressiveness of minimum cost ﬂow problems. Theorem 9.1. Every minimum cost ﬂow problem with ﬁnite capacities or non-negative costs has an equivalent transportation problem. Proof. Consider a minimum cost ﬂow problem on a network G =(V,E)with supplies or demands b i ...
PDF Transportation and Assignment Problems
disguised form of the dual simplex algorithm of 4§2. Assignment problems, which are special cases of transportation problems, pose difficulties for the transportation algorithm and require the development of an algorithm which takes advantage of the simpler nature of these problems. § 1. An Example; The Balanced Transportation Problem
Transportation and Related Problems
Transportation and Related Problems. In this section, we will discuss several special types of linear programs. These are the transportation problems, the assignment problems, and the transshipment problems. The standard scenario where a transportation problem arises is that of sending units of a product across a network of highways that ...
Transportation and Assignment Problems
Describe the characteristics of assignment problems. Identify the relationship between assignment problems and transportation problems. Formulate a spreadsheet model for an assignment problem from a description of the problem. Do the same for some variants of assignment problems. Give the name of an algorithm that can solve huge assignment ...
PDF Transportation, Assignment, and Transshipment Problems
Transportation, Assignment, and Transshipment Problems In this chapter, we discuss three special types of linear programming problems: transporta-tion, assignment, and transshipment. Each of these can be solved by the simplex algorithm, but specialized algorithms for each type of problem are much more efﬁcient. 7.1 Formulating Transportation ...
The Transportation and Assignment Problems
Definition of the Transportation Problem. Properties of the A Matrix. Representation of a Nonbasic Vector in Terms of the Basic Vectors. The Simplex Method for Transportation Problems. Illustrative Examples and a Note on Degeneracy. The Simplex Tableau Associated with a Transportation Tableau. The Assignment Problem: (Kuhn's) Hungarian Algorithm
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The second type of problem is assignment problem. It involves such applications as assigning people to tasks. Although its applications appear to be quite different from those for the transportation, we shall see the assignment problem can be viewed as a special type of transportation problem. Application of the transportation and assignment ...
Operations Research/Transportation and Assignment Problem
The Transportation and Assignment problems deal with assigning sources and jobs to destinations and machines. We will discuss the transportation problem first. Suppose a company has m factories where it manufactures its product and n outlets from where the product is sold. Transporting the product from a factory to an outlet costs some money ...
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154 Chapter5. Thetransportationproblemandtheassignmentproblem min z = (8 , 6 , 10 , 10 , 4 , 9) x11 x12 x13 x21 x22 x23 subjectto
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Transportation, Transshipment, and Assignment Problems Learning Objectives After completing this chapter, you should be able to: Describe the nature of transportation transshipment and assignment problems. Formulate a transportation problem as a linear programming model. Use the transportation method to solve problems with Excel.
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Figure 8: Constructing a transportation problem 4.3.2 Mathematical model of a transportation problem Before we discuss the solution of transportation problems we will introduce the notation used to describe the transportation problem and show that it can be formulated as a linear programming problem. We use the following notation; x
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Comparison Between Assignment and Transportation Model With Tabular Form. The Major Difference Between Assignment and Transportation model is that Assignment model may be regarded as a special case of the transportation model. However, the Transportation algorithm is not very useful to solve this model because of degeneracy.
Transportation Problem
An introduction to the transportation problem has been discussed in this article. In this article, the method to solve the unbalanced transportation problem will be discussed. Below transportation problem is an unbalanced transportation problem. The problem is unbalanced because the sum of all the supplies i.e. O1 , O2 , O3 and O4 is not equal to t
Assignment Problem
The problem is a special form of the transportation problem and, as such, has an optimal solution in which each variable is either zero or one. The problem can be solved by the simplex method, but special assignment problem algorithms tend to be computationally more efficient.
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Transportation Problem: Definition, Formulation, and Types
Transportation problems are broadly classified into balanced and unbalanced, depending on the source's supply and the requirement at the destination. Balanced Transportation Problem. Unbalanced Transportation Problem. Example - 1: Check which types of Transportation Problem it is. Answer - 1: From the above, we have.
Difference between transportation and assignment problem in tabular
Difference between transportation and assignment problem in tabular form Doors, partitions, stairways, etc. Therefore, the next step is to actually split the chain, i.
What is the difference between Assignment Problem and Transportation
When an assignment problem has more than one solution, then it is _____ Choose the correct alternative: The assignment problem is said to be balanced if _____ If the given matrix is _____ matrix, the assignment problem is called balanced problem. In an assignment problem if number of rows is greater than number of columns, then dummy _____ is added
Chapter 6a Flashcards
1) Costs appear in the objective function only. 2) All decision variable values are either 0 or 1. 3) All constraint left-hand-side coefficient values are 1. In an assignment problem, one agent can be assigned to several tasks. A dummy origin in a transportation problem is used when supply exceeds demand.

difference between assignment problem and transportation problem in tabular form

Difference Between Assignment and Transportation Model

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Transportation Problem | Set 1 (Introduction)

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Difference between transportation and assignment problems?

lets understand the Difference between transportation and assignment problems?

Additional Different between Transportation and Assignment Problems are as follows :

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Operations Research/Transportation and Assignment Problem

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Difference Between Assignment and Transportation Model

Comparison Between Assignment and Transportation Model With Tabular Form

Comparison Chart

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More Difference

Transportation Problem | Set 1 (Introduction)

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Assignment Problem

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What is the difference between Assignment Problem and Transportation Problem? - Business Mathematics and Statistics

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