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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Transportation Problem | Assignment Problem | |
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 |
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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