difference between transportation and assignment problem with example

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 Models in Operations Research

Transportation and assignment models are special purpose algorithms of the linear programming. The simplex method of Linear Programming Problems(LPP) proves to be inefficient is certain situations like determining optimum assignment of jobs to persons, supply of materials from several supply points to several destinations and the like. More effective solution models have been evolved and these are called assignment and transportation models.

The transportation model is concerned with selecting the routes between supply and demand points in order to minimize costs of transportation subject to constraints of supply at any supply point and demand at any demand point. Assume a company has 4 manufacturing plants with different capacity levels, and 5 regional distribution centres. 4 x 5 = 20 routes are possible. Given the transportation costs per load of each of 20 routes between the manufacturing (supply) plants and the regional distribution (demand) centres, and supply and demand constraints, how many loads can be transported through different routes so as to minimize transportation costs? The answer to this question is obtained easily through the transportation algorithm.

Similarly, how are we to assign different jobs to different persons/machines, given cost of job completion for each pair of job machine/person? The objective is minimizing total cost. This is best solved through assignment algorithm.

Uses of Transportation and Assignment Models in Decision Making

The broad purposes of Transportation and Assignment models in LPP are just mentioned above. Now we have just enumerated the different situations where we can make use of these models.

Transportation model is used in the following:

• To decide the transportation of new materials from various centres to different manufacturing plants. In the case of multi-plant company this is highly useful.
• To decide the transportation of finished goods from different manufacturing plants to the different distribution centres. For a multi-plant-multi-market company this is useful.
• To decide the transportation of finished goods from different manufacturing plants to the different distribution centres. For a multi-plant-multi-market company this is useful. These two are the uses of transportation model. The objective is minimizing transportation cost.

Assignment model is used in the following:

• To decide the assignment of jobs to persons/machines, the assignment model is used.
• To decide the route a traveling executive has to adopt (dealing with the order inn which he/she has to visit different places).
• To decide the order in which different activities performed on one and the same facility be taken up.

In the case of transportation model, the supply quantity may be less or more than the demand. Similarly the assignment model, the number of jobs may be equal to, less or more than the number of machines/persons available. In all these cases the simplex method of LPP can be adopted, but transportation and assignment models are more effective, less time consuming and easier than the LPP.

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Exclussive dff. And easy understude

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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

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

• Practice Mathematical Algorithm
• Mathematical Algorithms
• Pythagorean Triplet
• Fibonacci Number
• Euclidean Algorithm
• LCM of Array
• GCD of Array
• Binomial Coefficient
• Catalan Numbers
• Sieve of Eratosthenes
• Euler Totient Function
• Modular Exponentiation
• Modular Multiplicative Inverse
• Stein's Algorithm
• Juggler Sequence
• Chinese Remainder Theorem
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Transportation Problem | Set 1 (Introduction)

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).

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Transportation and Assignment Problems

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• James K. Strayer 2  

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Transportation and assignment problems are traditional examples of linear programming problems. Although these problems are solvable by using the techniques of Chapters 2–4 directly, the solution procedure is cumbersome; hence, we develop much more efficient algorithms for handling these problems. In the case of transportation problems, the algorithm is essentially a 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.

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Strayer, J.K. (1989). Transportation and Assignment Problems. In: Linear Programming and Its Applications. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1009-2_7

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The Geography of Transport Systems

The spatial organization of transportation and mobility

Traffic Assignment Problem

Traffic assignment problems usually consider two dimensions.

• Generation and attraction . A place of origin generates movements that are bound (attracted) to a place of destination. The relationship between traffic generation and attraction is commonly labeled as spatial interaction. The above example considers one origin/generation and destination/attraction, but the majority of traffic assignment problems consider several origins and destinations.
• Path selection . Traffic assignment considers which paths are to be selected and the amount of traffic using these paths (if more than one unit). For simple problems, a single path will be selected, while for complex problems, several paths could be used. Factors behind the choice of traffic assignment may include cost, time, or the number of connections.

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Assignation or Assignment – Difference, Meaning & Examples

Marcus Froland

July 15, 2024

When learning English, it’s natural to find words that seem very similar, but have entirely different meanings. That’s just one of the many challenges that language learners face. Two such words are assignation and assignment . They sound so alike, you might think they’re interchangeable. Yet, they are not.

In this article, we are going to put these two under the spotlight. Our focus is to help you understand the difference between assignation and assignment , provide their meanings, and offer clear examples. It’s about getting you comfortable with these words and helping you use them correctly in your English journey. So, let’s get started!

The critical difference between Assignation and Assignment lies in their usage and context. Assignation primarily refers to an agreement or appointment for a meeting. For instance, “They had an assignation at the coffee shop.” On the other hand, an Assignment refers to a task or duty assigned to someone. For instance, “He completed his math assignment.”

Both terms originate from the verb ‘assign’ but are utilized differently. Assignation is more often used in legal or formal settings, but assignment is common in educational or work contexts. So, if you’re scheduling a secretive meeting, use assignation. But if you’re handing out tasks or duties, use assignment.

Understanding the Meaning of Assignation

The word assignation is rich in meaning, covering everything simple to secret. At its basic level, it means assigning tasks or property. But, it has a more exciting side in stories. Here it often means secret meetings , tied to love or forbidden activities.

Definition of Assignation

Traditionally, assignation is about giving out duties or rights. It’s used in law and history to talk about dividing up or handing out responsibilities. This is like using the word assign in everyday situations. But add a dash of mystery or love, and assignation takes on a new life. It then means secret meetings or private moments.

Examples of Assignation in Sentences

Let’s look at some examples of assignation to get a clear picture:

• In books, an assignation can mean secret meetings between lovers, adding mystery.
• News stories might hint at illicit relationships by mentioning assignation, adding a thrill.
• Old documents might talk about assignation when they discuss dividing land rights, in a more straightforward sense.
• In romantic stories today, a secret meeting in a cafe could be an assignation, hinting at hidden love.

Understanding the Meaning of Assignment

The word assignment holds great importance in various areas. These include education, work, and law. Exploring its meanings helps us understand its wide use and importance.

Definition of Assignment

In schools, an assignment is the work teachers give to students. It helps to check how much students understand and how they perform. At work, assignments are tasks given to employees. These tasks keep the business running smoothly and productively.

In the legal world, an assignment means transferring rights or property . This is key to understand how people can give or receive ownership and duties legally.

Examples of Assignment in Sentences

• For their big project, the students got an academic work challenging them to research and present their findings.
• The boss gave a hard task to the new employee to test how well they manage work under pressure.
• With the contract signed, the ownership officially changed hands through a property transfer .

Understanding assignment in its various forms is crucial. It allows us to be more effective in school, at work, and in legal matters. Recognizing these differences ensures we communicate and act clearly and confidently.

Assignation or Assignment: Key Differences

It’s vital to understand the difference between assignation and assignment for clear communication. The term assignation brings to mind secret or romantic meetings. It can also mean the act of assigning something. Meanwhile, assignment is about giving out tasks, duties, or responsibilities. This is common in school or work.

Assignation and assignment have different uses. Assignation suggests secrecy and is linked with private meetings. On the opposite side, assignment talks about clear duties or legal handovers. It doesn’t have the secret flavor that assignation does.

To avoid confusion, it’s key to know when to use each term. Calling a work task an assignation could suggest something secret or wrong. So, choosing the right word matters:

• Use assignation for secret or love meetings done quietly.
• Use assignment when you mean work tasks or handing over property, in formal or work settings.

Using the right term, assignation or assignment, makes your meaning clear. This way, you won’t confuse anyone.

Using Assignation and Assignment Correctly

It’s key to know how assignation and assignment differ. Each word has its own meaning. Using them right is key to avoid mix-ups.

When to Use Assignation

The word assignation is about secret meetings. These are often for romantic reasons. Books use it to talk about meetings held in private.

It hints at something hidden or confidential. This makes it perfect for talks that need to stay under wraps.

When to Use Assignment

Assignment , on the other hand, is about giving tasks. It’s used in schools, work, and law. For example, it can mean homework or handing over property rights.

This word doesn’t suggest secrets like assignation does. It’s all about structured, formal tasks.

Knowing these differences helps you communicate clearly. Use assignment for tasks, and assignation for secret meet-ups. This keeps your meaning clear and stops any confusion. It’s especially important in professional settings to avoid the wrong idea about secret meetings.

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