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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.
Related posts:
- Operations Research approach of problem solving
- Introduction to Transportation Problem
- Procedure for finding an optimum solution for transportation problem
- Initial Basic Feasible Solution of a Transportation Problem
- Introduction to Decision Models
- Transportation Cost Elements
- Modes of Transportation in Logistics
- Factors Affecting Transportation in Logistics
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Copyright © 2003 by Robert Fourer, David M. Gay and Brian W. Kernighan
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CHAPTER 15 TRANSPORTATION AND ASSIGNMENT PROBLEMS
The formal definition of the assignment problem (or linear assignment problem) is . Given two sets, A and T, together with a weight function C : A × T → R.Find a bijection f : A → T such that the cost function: (, ())is minimized. Usually the weight function is viewed as a square real-valued matrix C, so that the cost function is written down as: , The problem is "linear" because the cost ...
Module 4: Transportation Problem and Assignment problem Prasad A Y, Dept of CSE, ACSCE, B'lore-74 Page 3 Since the supply from row O1 is completed cancel the row O1. The demand for column D2 remain 350 - 50 = 50. From the remaining table the north-west corner cell is (O2, D2). The minimum among the supply
model, the algorithm is actually rooted in the simplex method, just as the transportation model . 2. LP Representation An assignment problem is characterized by knowledge of the cost of assigning each supply point to each demand point: cij On the other hand, a 0-1 integer variable xij is defined as follows
This is particularly important in the theory of decision making. [4] The assignment models is a special state of a linear programming models and its similar to the transportation model. The different between the ... Model), International Journal of Science and Research (IJSR), 4 (2015), no. 3, 1446-1449.
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 ...
Assignment Models The linear programs in Chapters 1 and 2 are all examples of classical ''activity'' mod-els. In such models the variables and constraints deal with distinctly different kinds of activities — tons of steel produced versus hours of mill time used, or packages of food bought versus percentages of nutrients supplied.
total cost. The situation is known as the assignment problem. An assignment problem is a balanced transportation problem in which all supplies and demands equal to 1. In this model jobs represent supplies and machines represent demands. In the following table we can see the general representation of the assignment problem. Table 5.5.1 Jobs
F.F.K. AL-Abdulhameed, A linear Programming Formulation of Assignment Problems, Journal of Basrah Researches ((Sciences)), 37 (2011), no. 2, 21-26. Recommended publications Discover more
Decision Sciences. Volume 19, Issue 2 p. 306-321. MULTIDIMENSIONAL ASSIGNMENT PROBLEMS. Kenneth C. Gilbert, Kenneth C. Gilbert. Department of Management, University of Tennessee, Knoxville, TN 37931. ... This paper is a tutorial on these higher dimensional assignment models and their applications. It is a synthesis of a vast literature ...