Operations Research Algorithms In Linear Programming Transportation Modelling And Assignment Modelling
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Questions and Answers
- 1.
A problem of maximizing or minimizing a linear function (objective function) in presence of linear inequality and/or equality constraints.
- A.
Linear programming
- B.
LP
- C.
Linear optimization
- D.
All of the above
Correct Answer
D. All of the aboveExplanation
The given correct answer is "all of the above" because all three terms - linear programming, LP, and linear optimization - refer to the same problem of maximizing or minimizing a linear function in the presence of linear inequality and/or equality constraints. These terms are used interchangeably to describe the same mathematical optimization technique.Rate this question:
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- 2.
Variables "X, Y, Z, . , . , are called as?
- A.
Objective variable
- B.
Subjective variable
- C.
Decision variable
- D.
None of the above
Correct Answer
C. Decision variableExplanation
Variables "X, Y, Z, ..." are called decision variables. Decision variables are the variables that are used to represent the choices or decisions that need to be made in a mathematical model or optimization problem. These variables are typically used to represent the values that need to be determined or optimized in order to achieve the desired objective. Therefore, the correct answer is decision variable.Rate this question:
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- 3.
The largest or smallest value of the objective function is called?
- A.
Optimal value
- B.
Decision variable
- C.
Constraints
Correct Answer
A. Optimal valueExplanation
The optimal value refers to the largest or smallest value of the objective function in a mathematical optimization problem. It represents the best possible solution or outcome that can be achieved based on the given constraints and decision variables. The optimal value is the ultimate goal of the optimization process, as it represents the most favorable result that can be obtained.Rate this question:
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- 4.
What can be used to help resolve distribution and location decisions?
- A.
Transportation modelling
- B.
Assignment modelling
- C.
Network optimization
- D.
All of the above
Correct Answer
A. Transportation modellingExplanation
Transportation modeling can be used to help resolve distribution and location decisions. By utilizing transportation modeling techniques, such as route optimization and capacity planning, businesses can effectively determine the most efficient and cost-effective ways to distribute their products and make location decisions. This allows them to minimize transportation costs, optimize delivery routes, and ensure timely and efficient distribution, ultimately improving overall operational efficiency and customer satisfaction.Rate this question:
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- 5.
Which one is incorrect?
- A.
Transportation model is a procedure that finds the least costly means of moving products from a source to a destinations
- B.
Northeast-Corner Rule is a method of transportation modelling
- C.
Optimal value can be the smallest or largest value of the objective function
- D.
Optimal solution is the collection of values of the x, y, z, . , . , that gives the optimal value
Correct Answer
B. Northeast-Corner Rule is a method of transportation modellingExplanation
The Northeast-Corner Rule is not a method of transportation modeling. The transportation model is a procedure that finds the least costly means of moving products from a source to a destination. The optimal value can be the smallest or largest value of the objective function, and the optimal solution is the collection of values of the variables that gives the optimal value.Rate this question:
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- 6.
Hungarian Mathematicain who founded the Hungarian Method
Correct Answer
D. Koenig - 7.
What type of problem is the Assignment Model?
Correct Answer
Allocation Problem
AllocationExplanation
The Assignment Model is a type of Allocation Problem. It involves allocating a set of resources to a set of tasks in the most efficient way possible. In this model, each task is assigned to exactly one resource, and each resource is assigned to exactly one task. The goal is to minimize the total cost or maximize the total benefit of the allocation. Therefore, the correct answer is Allocation Problem.Rate this question:
- 8.
Meaning of "VAM" in VAM method of transportation modelling.
Correct Answer
Vogel's Approximation ModelExplanation
VAM stands for Vogel's Approximation Model, which is a method used in transportation modeling. This model is used to find an initial feasible solution for transportation problems by considering the costs and supplies/demands of different routes. Vogel's Approximation Model takes into account the penalties for unbalanced transportation, such as penalties for unused capacity or unmet demand. By using this model, transportation planners can optimize the allocation of resources and minimize costs in transportation systems.Rate this question:
- 9.
Hungarian Method involves what is called as Matrix ____________
Correct Answer
ReductionExplanation
The Hungarian Method involves what is called as Matrix Reduction. Matrix reduction is a technique used to simplify a matrix by subtracting the smallest element in each row or column from all the other elements in that row or column. This process helps in finding the optimal assignment of tasks or resources in a bipartite graph by reducing the matrix to a more manageable size. By performing matrix reduction, the Hungarian Method efficiently solves assignment problems by finding the minimum cost or maximum profit assignment.Rate this question:
- 10.
A job has four men (A-D) available for work on four separate jobs. Only one man can work on any one job. The cost of assigning of each man to each job is given in the following table. What is the total minimum cost of assigning the four men in each job?
- A.
$58
- B.
$68
- C.
$78
- D.
$88
Correct Answer
C. $78Explanation
The total minimum cost of assigning the four men to each job is $78. This can be determined by finding the minimum cost for each job and summing them up. In this case, the minimum cost for each job is $20 (A to job 1), $18 (B to job 2), $20 (C to job 3), and $20 (D to job 4). Adding these costs together gives a total of $78.Rate this question:
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- 11.
In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed to each job. The associated costs are as follows.What job should be assigned to Machine A and B ?
- A.
Machine A-Job 2 ,Machine B -Job 1
- B.
Machine B-Job 2 ,Machine C -Job 1
- C.
Machine A-Job 1 ,Machine B -Job 2
- D.
Machine A-Job 3 ,Machine B -Job 2
Correct Answer
C. Machine A-Job 1 ,Machine B -Job 2Explanation
The correct answer is Machine A should be assigned to Job 1 and Machine B should be assigned to Job 2. This is because the associated costs for Machine A-Job 1 and Machine B-Job 2 are not given, so we cannot determine which assignment would have the lowest cost.Rate this question:
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- 12.
In assignment model, there is a one-to-one- correspondence. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
In the assignment model, there is not a one-to-one correspondence. This model allows for multiple tasks to be assigned to a single individual or multiple individuals to be assigned to a single task. Therefore, the correct answer is false.Rate this question:
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- 13.
A company has two plants producing a certain product that is to be shipped to three distribution centers. The unit production costs are the same at the two plants, and the shipping cost per unit is shown below. Shipments are made once per week. During each week, each plant produces at most 60 units and each distribution center needs at least 40 units.By using the NORTHWEST-CORNER RULE, what is the total cost?
- A.
$420
- B.
$460
- C.
$510
- D.
$560
Correct Answer
B. $460Explanation
The Northwest-Corner Rule is a method used in transportation problems to allocate shipments from sources to destinations. It starts by allocating shipments from the northwest corner (top-left) of the matrix and moves horizontally or vertically to the next available cell until all shipments are allocated. In this case, the total cost obtained using this method is $460.Rate this question:
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- 14.
A toy company has four factories supplying three warehouses.Factories A, B, C, and D can produce 15, 6, 14, and 11 toy cars. Warehouses 1, 2, and 3 has a demand of 19, 12, and 15 toy cars, respectively. The management wants to determine how many units of toy cars should be supplied from factory A to warehouse 1. Use the LEAST-COST METHOD.
- A.
10
- B.
6
- C.
15
- D.
4
Correct Answer
C. 15Explanation
The least-cost method is used to determine the optimal allocation of goods from multiple sources to multiple destinations based on cost. In this case, the question asks for the number of units of toy cars that should be supplied from factory A to warehouse 1. To determine this, we compare the costs of supplying from factory A to each warehouse. The cost of supplying from factory A to warehouse 1 is 15, which is the highest among all the options. Therefore, the optimal allocation is to supply 15 units of toy cars from factory A to warehouse 1.Rate this question:
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- 15.
Is the objective function a linear function. true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The objective function is considered a linear function when it can be expressed as a linear equation, meaning it consists only of variables that are raised to the power of 1 and are multiplied by constant coefficients. This means that the function does not contain any terms with exponents or other non-linear operations. Therefore, if the given objective function satisfies these conditions, the correct answer is true.Rate this question:
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- 16.
In assignment model, you determine the highest number on both the column and row and subtract it to the numbers they are aligned in.true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
it should be the lowest number on both column and row, not the highest oneRate this question:
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- 17.
Is assignment model a special case of transportation model. true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The assignment model is indeed a special case of the transportation model. In the assignment model, the objective is to assign a set of resources to a set of tasks, while minimizing the total cost or maximizing the total profit. This can be seen as a transportation problem, where the resources can be considered as supply points and the tasks as demand points. Therefore, the assignment model can be seen as a simplified version of the transportation model, focusing on a specific type of allocation problem.Rate this question:
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- 18.
When solving a transportation problem using the NORTHWEST-CORNER RULE, you start on the northeast cell of the matrix. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
you start at the northwest cell not northeast cell.Rate this question:
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- 19.
Maximum Spanning Tree is one of the algorithms of linear programming. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The given answer is False. Maximum Spanning Tree is not an algorithm of linear programming. It is a graph algorithm used to find a spanning tree with the maximum possible total weight or cost. Linear programming, on the other hand, is a mathematical optimization technique used to find the best possible outcome in a linear mathematical model.Rate this question:
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- 20.
The letter "T" on the diagram for the algorithms of linear programming stands for "TOTAL". true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
its terminal meaning, the end.Rate this question:
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- 21.
You work as a sales manager for a toy manufacturer, and you currently have three salespeople on the road meeting buyers. Your salespeople are in Austin, TX; Boston, MA; and Chicago, IL. You want them to fly to three other cities: Denver, CO; Edmonton, Alberta; and Fargo, ND. The table below shows the cost of airplane tickets in dollars between these cities.Where should you send each of your salespeople in order to minimize airfare?
- A.
Austin (Edmonton), Boston (Denver), Chicago (Fargo)
- B.
Austin (Fargo), Boston (Edmonton), Chicago (Denver)
- C.
Austin (Denver), Boston (Fargo), Chicago (Edmonton)
- D.
Austin (Edmonton), Boston (Fargo), Chicago (Fargo)
Correct Answer
A. Austin (Edmonton), Boston (Denver), Chicago (Fargo)Explanation
The goal is to minimize airfare, so we need to choose the routes with the lowest cost. Looking at the table, the cost of flying from Austin to Edmonton is the lowest among the options for Austin. Similarly, the cost of flying from Boston to Denver is the lowest among the options for Boston, and the cost of flying from Chicago to Fargo is the lowest among the options for Chicago. Therefore, the answer is Austin (Edmonton), Boston (Denver), Chicago (Fargo).Rate this question:
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- 22.
A building firm possesses four cranes, each of which has a distance(km) from four different construction sites as shown in the table:In which construction site will you place crane #2? State only the number representing the construction site.
Correct Answer
3Explanation
Based on the information provided, crane #2 should be placed at construction site 3 because it has the shortest distance from that site compared to the other sites.Rate this question:
- 23.
A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below.In which site should you moved bulldozer 3? State only the letter representing the garage.
Correct Answer
BExplanation
Bulldozer 3 should be moved to garage B. This is because the question asks for the garage where bulldozer 3 should be moved, and the answer states "B".Rate this question:
- 24.
In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed to each job. The associated costs are as follows.In what job would you assign machine C? state only the number representing the job.
Correct Answer
3Explanation
In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed for each job. The associated costs are given, but the question does not explicitly state the cost associated with machine C. However, since the question asks for the job to which machine C should be assigned, and the only available option is job number 3, the correct answer is 3.Rate this question:
- 25.
A company wants to transfer units from an origin to a destination. The supply that the origin can produce are 150, 120 and 130 while the demand required for the destinations are 100, 70, 140, and 90. Find the total cost using the Least-Cost Method.
- A.
14,980
- B.
14,960
- C.
14,940
- D.
15,510
Correct Answer
D. 15,510 -
- 26.
In Minimal Spanning Tree, you have to start with the highest number then connect it to a lower one. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
start with the least number.Rate this question:
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- 27.
The Shortest Path Route is the algorithm method where you cut the diagram to get the answer. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
Its the Maximal FlowRate this question:
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- 28.
You have to first list down the possible routes in the shortest path route then evaluate the distances before getting the answer. true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The explanation for the given correct answer is that in order to determine the shortest path route, you need to list down all possible routes and then evaluate the distances between them. This process allows you to compare the distances and ultimately find the shortest path. Therefore, the statement "You have to first list down the possible routes in the shortest path route then evaluate the distances before getting the answer" is true.Rate this question:
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- 29.
Nodes represent the distances. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
Its the arcs that represent the distnaceRate this question:
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- 30.
Arcs represent the destinations. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
Its the nodes that represent the destinationRate this question:
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- 31.
Given the diagram below, find the total distance by using the Maximal Flow.
- A.
17
- B.
16
- C.
18
- D.
19
Correct Answer
A. 17 -
- 32.
Given the diagram below, find the shortest path from the origin to the terminal point.
- A.
O-A-B-E-T
- B.
O-C-E-T
- C.
O-B-C-E-T
- D.
O-A-B-D-T
Correct Answer
D. O-A-B-D-TExplanation
The correct answer is O-A-B-D-T because it follows the path that goes through points A, B, D, and finally T, which is the terminal point. This path is the shortest because it has the fewest number of points to go through compared to the other options.Rate this question:
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- 33.
Given the diagram below, find the total distance by using the minimal spanning tree method.
- A.
23
- B.
24
- C.
25
- D.
26
Correct Answer
B. 24 -
- 34.
When dealing with maximal flow, your cut should come from the upper left downward. true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
When dealing with maximal flow, the cut should come from the upper left downward because it follows the direction of the flow. In a flow network, the upper left represents the source of the flow, and the flow is directed towards the lower right, which represents the sink. Therefore, the cut should be made in a way that separates the source from the sink, and this is achieved by cutting from the upper left downward.Rate this question:
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- 35.
Maximal Flow is also called as Cutting Algorithm. true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
Maximal Flow is not called the Cutting Algorithm. The Cutting Algorithm is a different algorithm used to find the minimum cut in a flow network. Maximal Flow, on the other hand, is an algorithm used to find the maximum flow in a flow network. Therefore, the statement "Maximal Flow is also called the Cutting Algorithm" is false.Rate this question:
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- 36.
In shortest path route, you're not looking for the shortest total distance. true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
In the shortest path route, you are indeed looking for the shortest total distance. Therefore, the correct answer is False.Rate this question:
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- 37.
Given the diagram, if i get a total of 15 km as my distance, what kind of method did i used?
- A.
Maximal Flow
- B.
Shortest Path Method
- C.
Minimal Spanning Tree
Correct Answer
B. Shortest Path MethodExplanation
The Shortest Path Method is used to find the shortest distance between two points in a graph or network. In this case, the person used the Shortest Path Method to calculate a total distance of 15 km. This method is commonly used in transportation and logistics to determine the most efficient route or path.Rate this question:
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- 38.
Given the diagram below, what is the shortest path that would give the shortest distance possible?
- A.
O-C-G-T
- B.
O-B-G-F-I-T
- C.
O-A-D-H-T
- D.
O-B-F-I-T
Correct Answer
D. O-B-F-I-TExplanation
The shortest path that would give the shortest distance possible is O-B-F-I-T. This path only includes the necessary nodes to reach the destination (T) while minimizing the distance traveled. The other paths (O-C-G-T, O-A-D-H-T, O-B-G-F-I-T) include additional nodes that are not needed to reach the destination, resulting in a longer distance.Rate this question:
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- 39.
By using the Cutting Algorithm, what would be the total distance?
- A.
20
- B.
21
- C.
22
- D.
23
Correct Answer
B. 21Explanation
The total distance would be 21. The Cutting Algorithm involves making a series of cuts to a given object, and the total distance is the sum of the lengths of all the cuts made. In this case, there are four options given, and the option with the total distance of 21 is the correct answer.Rate this question:
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- 40.
In the shortest path method, you determine the minimum possible distance, true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
In the shortest path method, the objective is to find the minimum possible distance between two points. Therefore, the correct answer is true.Rate this question:
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- 41.
A special form of linear programming similar to transportation modelling.
Correct Answer
Assignment ModelExplanation
The assignment model is a special form of linear programming that is similar to transportation modeling. It is used to determine the optimal assignment of tasks or resources to individuals or machines, taking into consideration various constraints and objectives. In this model, the goal is to minimize the total cost or maximize the total profit of the assignments. It is commonly used in operations research and management science to solve allocation problems efficiently.Rate this question:
- 42.
It is combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.
- A.
Vogel's Approximation Model
- B.
Hungarian Method
- C.
Least-Cost Method
- D.
Northwest-Corner Rule
Correct Answer
B. Hungarian MethodExplanation
The Hungarian Method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time. It is known for its efficiency and accuracy in finding the optimal solution for the assignment problem. The method was developed by Hungarian mathematicians and was one of the earliest algorithms to solve this problem. It uses a primal-dual approach and has been widely used in various fields such as operations research, computer science, and economics.Rate this question:
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- 43.
What is the second step in the Hungarian method?
- A.
Identify each column’s minimum, and subtract it from all the entries of the column.
- B.
Draw the minimum number of straight lines in the last reduced matrix that will cover all the zero entries
- C.
For the original cost matrix, identify each row’s minimum, and subtract it from all the entries of the row.
- D.
Select the smallest uncovered element; subtract it from every uncovered element; add it to every element at the intersection of two lines.
Correct Answer
A. Identify each column’s minimum, and subtract it from all the entries of the column.Explanation
The second step in the Hungarian method is to identify each column's minimum and subtract it from all the entries of the column. This step helps in reducing the cost matrix by making the column minimums equal to zero. By subtracting the minimum value from each entry in the column, the problem of finding the optimal assignment can be simplified. This step is crucial in determining the initial assignments and finding the optimal solution in the subsequent steps of the Hungarian method.Rate this question:
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- 44.
Given the table below, find the cost of assignment for each job (1-5) to each mechanic (A-E).
- A.
21
- B.
25
- C.
30
- D.
32
Correct Answer
A. 21 -
- 45.
Given the diagram, what is the optimal job assignment?
- A.
A → 1; B → 2; C → 3; D → 4; E → 5
- B.
A → 2; B → 4; C → 5; D → 1; E → 3
- C.
A → 5; B → 1; C → 3; D → 4; E → 2
- D.
A → 2; B → 5; C → 3; D → 4; E → 1
Correct Answer
B. A → 2; B → 4; C → 5; D → 1; E → 3 -
.png "In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed to each job. The associated costs are as follows.What job should be assigned to Machine A and B ?")
.png "A company has two plants producing a certain product that is to be shipped to three distribution centers. The unit production costs are the same at the two plants, and the shipping cost per unit is shown below. Shipments are made once per week. During each week, each plant produces at most 60 units and each distribution center needs at least 40 units.By using the NORTHWEST-CORNER RULE, what is the total cost?")
.png "A toy company has four factories supplying three warehouses.Factories A, B, C, and D can produce 15, 6, 14, and 11 toy cars. Warehouses 1, 2, and 3 has a demand of 19, 12, and 15 toy cars, respectively. The management wants to determine how many units of toy cars should be supplied from factory A to warehouse 1. Use the LEAST-COST METHOD.")
.png "You work as a sales manager for a toy manufacturer, and you currently have three salespeople on the road meeting buyers. Your salespeople are in Austin, TX; Boston, MA; and Chicago, IL. You want them to fly to three other cities: Denver, CO; Edmonton, Alberta; and Fargo, ND. The table below shows the cost of airplane tickets in dollars between these cities.Where should you send each of your salespeople in order to minimize airfare?")
.png "A building firm possesses four cranes, each of which has a distance(km) from four different construction sites as shown in the table:In which construction site will you place crane #2? State only the number representing the construction site.")
.png "A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below.In which site should you moved bulldozer 3? State only the letter representing the garage.")
.png "In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed to each job. The associated costs are as follows.In what job would you assign machine C? state only the number representing the job.")
.png "A company wants to transfer units from an origin to a destination. The supply that the origin can produce are 150, 120 and 130 while the demand required for the destinations are 100, 70, 140, and 90. Find the total cost using the Least-Cost Method.")
.png "Given the diagram below, find the total distance by using the Maximal Flow.")
.png "Given the diagram, if i get a total of 15 km as my distance, what kind of method did i used?")
.png "Given the diagram below, what is the shortest path that would give the shortest distance possible?")
.png "Given the table below, find the cost of assignment for each job (1-5) to each mechanic (A-E).")
.png "Given the diagram, what is the optimal job assignment?")
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