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Difference between transportation and assignment problems?

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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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:

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:

{\displaystyle x_{ij}}

The whole model is:

subject to,

{\displaystyle x_{11}+x_{12}=1000}

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

the similarity between assignment problem and transportation problem is

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AllDifferences

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.

Assignment Model and Transportation Model Comparison

Comparison Chart

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.

More Difference

  • Difference between Lagrangian and Eulerian Approach
  • Difference between Line Standards and End Standards

Book cover

Introduction to Transportation Analysis, Modeling and Simulation pp 109–137 Cite as

Traffic Assignments to Transportation Networks

  • Dietmar P. F. Möller 3  
  • First Online: 01 January 2014

1862 Accesses

Part of the book series: Simulation Foundations, Methods and Applications ((SFMA))

This chapter begins with a brief overview of traffic assignment in transportation systems. Section 3.1 introduces the assignment problem in transportation as the distribution of traffic in a network considering the demand between locations and the transport supply of the network. Four trip assignment models relevant to transportation are presented and characterized. Section 3.2 covers traffic assignment to uncongested networks based on the assumption that cost does not depend on traffic flow. Section 3.3 introduces the topic of traffic assignment and congested models based on assumptions from traffic flow modeling, e.g., each vehicle is traveling at the legal velocity, v , and each vehicle driver is following the preceding vehicle at a legal safe velocity. Section 3.4 covers the important topic of equilibrium assignment which can be expressed by the so-called fixed-point models where origin to destination (O-D) demands are fixed, representing systems of nonlinear equations or variational inequalities. Equilibrium models are also used to predict traffic patterns in transportation networks that are subject to congestion phenomena. Section 3.5 presents the topic of multiclass assignment, which is based on the assumption that travel demand can be allocated as a number of distinct classes which share behavioral characteristics. In Sect. 3.6, dynamic traffic assignment is introduced which allows the simultaneous determination of a traveler’s choice of departure time and path. With this approach, phenomenon such as peak spreading in response to congestion dynamics or time-varying tolls can be directly analyzed. In Sect. 3.7, transportation network synthesis is introduced which focuses on the modification of a transportation road network to fit a required demand. Section 3.8 covers a case study involving a diverging diamond interchange (DDI), an interchange in which the two directions of traffic on a nonfreeway road cross to the opposite side on both sides of a freeway overpass. The DDI requires traffic on the freeway overpass (or underpass) to briefly drive on the opposite side of the road. Section 3.9 contains comprehensive questions from the transportation system area. A final section includes references and suggestions for further reading.

  • Road Network
  • Traffic Flow
  • Route Choice
  • Travel Demand
  • Traffic Assignment

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References and Further Readings

Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995) Dynamic model of traffic congestion and numerical simulation. Phys Rev E 51(2):1035–1042

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Bliemer MCJ (2001) Analytical dynamic traffic assignment with interacting user-classes: theoretical advances and applications using a variational inequality approach. PhD thesis, Delft University of Technology, The Netherlands

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Bliemer MCJ, Castenmiller RJ, Bovy PHL (2002) Analytical multiclass dynamic traffic assignment using a dynamic network loading procedure. In: Proceedings of the 9th meeting EURO Working Group on Transportation. Tayler & Francis Publication, pp 473–477

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Chiu YC, Bottom J, Mahut M, Paz A, Balakrishna R, Waller T, Hicks J (2011) Dynamic Traffic Assignment, A Primer for the Transportation Network Modeling Committee, Transportation Research Circular, Number E-C153, June 2011

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Correa ER, Stier-Moses NE (2010) Wardrop equilibria. In: Cochran JJ (ed) Encyclopedia of operations research and management science. Wiley, Hoboken

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Inman V, Williams J, Cartwright R, Wallick B, Chou P, Baumgartner M (2010) Drivers’ evaluation of the diverging diamond interchange. TECHBRIEF FHWA-HRT-07-048, U.S. Department of Transportation, Federal Highway Administration, Washington, DC. FHWA contact: J. Bared, 202-493-3314

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Möller, D.P.F. (2014). Traffic Assignments to Transportation Networks. In: Introduction to Transportation Analysis, Modeling and Simulation. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-5637-6_3

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