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:
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:
The whole model is:
subject to,
The problem can now be solved using the simplex method. A convenient procedure is discussed in the next section.
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Transportation and Assignment Problems
Mathematics.
10 questions
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In applying Vowgel's approximation method to a profit maximization problem, row and column penalties are determined by:
finding the smallest 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 lowest unit costs in each row and column.
finding the difference between the two highest unit costs in each row and column.
In a transportation problem, when the number of occupied cells is less than the number of rows plus the number of columns -1, we say that the solution is:
Non-Degenerate
In a transportation problem, we must make the number of __________ and __________ equal.
destinations; sources
units supplied; units demanded
columns; rows
warehouses; suppliers
In case of an unbalanced problem, shipping cost coefficients of ____________ are assigned to each created dummy factory or warehouse.
high positive costs
high negative costs
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 ___________.
∞ \infty ∞ ; ∞ \infty ∞
In a transportation problem, a single source may supply the units to any number of destinations.
The cell evaluation d ij = C ij - ( u i + v j ) is used to calculate __________.
Opportunity costs for using a particular route
MODI cost values ( u i , v j )
Degeneracy index
Optimality test
It is possible to find an optimal solution for a transportation problem that is degenerate.
Always a transportation problem possess unique solution.
Which is true for assignment problem?
The number of rows equals the number of columns
One assignment for each row and each column
All rim requirements are one
All are true
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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
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, welcome back, create your account for free.
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Difference between transportation and assignment problems?
- Engineeringbro
- February 11, 2023
- March 10, 2024
- 3 mins read
- Post author: Engineeringbro
- Post published: February 11, 2023
- Post category: Blog
- Post comments: 0 Comments
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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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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Related MCQs
- The assignment problem is a special case of transportation problem in which ______.
- The transportation problem deals with the transportation of ________.
- Maximization assignment problem is transformed into a minimization problem by_________.
- In an assignment problem involving 5 workers and 5 jobs, total number of assignments possible are _______.
- While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to_________.
- To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are___________.
- Every basic feasible solution of a general assignment problem having a square pay-off matrix of order n should have assignments equal to___________.
- An assignment problem can be solved by______.
- The Hungarian method used for finding the solution of the assignment problem is also called ___________.
- An assignment problem is a particular case of ____________.
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a. total supply must equal total demand in the transportation problem. b. the number of origins must equal the number of destinations in the transportation problem. c. each supply and demand value is 1 in the assignment problem. d. there are many differences between the transportation and assignment problem.
A transportation problem with three sources and four destinations will have seven decision variables. The difference between the transportation and assignment problems is that each supply and demand value is 1 in the assignment problem.
Transportation problem is basically a ( a) Maximisation model ( b) Minimisation model ( c) Trans-shipment problem ( d) Iconic model. The column, which is introduced in the matrix to balance the rim requirements, is known as: ( a) Key column ( b) Idle column ( c) Slack column ( d) Dummy Column. The row, which is introduced in the matrix to balance the rim requirement, is known as: ( a) Key row ...
The difference between the transportation and assignment problems is that A. total supply must equal total demand in the transportation problem: B. the number of origins must equal the number of destinations in the transportation problem: C. each supply and demand value is 1 in the assignment problem: D. there are many differences between the ...
X14+X24-X45-X46=0. what goes in must come out. Assignment Model. Special form of transportation problem in which all supply and demand values equal 1. Three Types of Network Flow Models. Transportation, Transshipment, Assignment. Study with Quizlet and memorize flashcards containing terms like Transportation Model, Where are the constraints for ...
Business; Operations Management; Operations Management questions and answers; The difference between the assignment and the transportation problem is that Select one: A. the number of origins must equal the number of destinations in the transportation problem B. the supply and demand value at each node must equal1 in the assignment problem C. the number of origins must equal the number of ...
The difference between the assignment and the transportation problem is that:A) the number of origins must equal the number of destinations in the transportation problem.B) total supply must equal total demand in the assignment problem.C) each supply and demand value is 1 in the assignment problem.D) both A and B
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 ...
Transportation and Assignment Problems. 1. Multiple Choice. finding the smallest 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 lowest unit costs in each row and column. finding the difference between the two highest unit costs in each row and column.
Transportation Problem: Assignment Problem: 1. This is about reducing cost of transportation merchandise: 1. This is about assigning finite sources to finite destinations where only one destination is allotted for one source with minimum cost
Test: Transportation & Assignment Model - Question 8. Save. 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.
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 ...
Question: The difference between the transportation and assignment problems is thatQuestion 5 options:total supply must equal total demand in the transportation problemthe number of origins must equal the number of destinations in the transportation problemeach supply and demand value is 1 in the assignment problemthere are many differences between the
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.
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
The difference between the transportation and assignment problems is that _____. a. each supply and demand value is 1 in the assignment problem b. total supply must equal total demand in the transportation problem c. the number of origins must equal the number of destinations in the transportation problem d. there are many differences between the transportation and assignment problems
Transportation Model MCQ Quiz - Objective Question with Answer for Transportation Model - Download Free PDF ... stocked for sale or the are in process of manufacturing or in the form of material yet to be utilized is known as an assignment problem. ... the difference between the smallest and next to it in each row and column are computed and ...
Login to comment. An assignment problem is considered as a particular case of a transportation problem because. An assignment problem is a special case of transportation problem, where. A solution to a transportation problem that has less than m + n − 1 cells with positive allocations in the transportation table is.
In assignment problem of maximization, the objective is to maximise A. Profit B. optimization C. cost D. None of the above. What is the difference between minimal cost network flows and transportation problems? A. The minimal cost network flows are special cases of transportation problems B.
Study with Quizlet and memorize flashcards containing terms like A solution to a transportation problem that has less than m + n − 1 cells with positive allocations in the transportation tableau is, The optimal solution is found in an assignment matrix when the minimum number of straight lines needed to cover all the zeros equals, The stepping-stone method requires that one or more ...
The transportation problem is commonly approached through simplex methods, and the assignment problem is addressed using specific algorithms like the Hungarian method. In this article, we will learn the difference between transportation problems and assignment problems with the help of examples.
The assignment problem is a special case of transportation problem in which _____. The transportation problem deals with the transportation of _____. Maximization assignment problem is transformed into a minimization problem by_____. In an assignment problem involving 5 workers and 5 jobs, total number of assignments possible are _____.
differences between transportation and transshipment model. transportation has one set of supply locations and one set of demand locations and transshipment has more than 2. transshipment is more complicated. transshipment requires more control by the supply chain and transportation is decision controlled by one firm.