Transportation and Assignment


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Transportation and Assignment

  1. 1. GYAN GANGA INSTITUTE OF TECHNOLOGY AND MANAGEMENT, BHOPAL GROUP NAME:- ELITE Guided by: Prof. Lokesh Payasi Presented by: Krati Barman Poonam Patel Nisha Johari Tikaram Sahu Ankit Jain Prathrna Yadav TRANSPORTATION MODEL & ASSIGNMENT MODEL
  2. 2. CONCEPT <ul><li>The Transportation problems are one of the type of LPP. </li></ul><ul><li>The objective is to minimize the cost of distribution a product from a no. of sources or origins to a number of destinations in such a manner that the cost of transportation is minimum. </li></ul>
  3. 3. DEFINITION <ul><li>“ The transportation problem is to transport various amounts of a single homogenous commodity, which are initially stored at various origins , to different destinations in such a way that the total transportation cost is a minimum”. </li></ul>
  4. 4. Terminology Used <ul><li>Feasible Solution. </li></ul><ul><li>Basic Feasible Solution. </li></ul><ul><li>Optimal Feasible Solution. </li></ul><ul><li>Balanced Transportation Problem. </li></ul><ul><li>Unbalanced Transportation Problem. </li></ul><ul><li>Matrix Terminology. </li></ul>
  5. 5. Assumptions of the Model <ul><li>Availability of the quantity. </li></ul><ul><li>Transportation of items. </li></ul><ul><li>Cost per unit. </li></ul><ul><li>Independent cost. </li></ul><ul><li>Objective. </li></ul>
  6. 6. Steps to solve a Transportation Model <ul><li>Formulate the problem and setup in the matrix form. </li></ul><ul><li>Obtain the Initial Basic Feasible solution. </li></ul><ul><li>Test the initial solution for optimality. </li></ul><ul><li>Updating the solution. </li></ul>
  7. 7. Methods of Transportation <ul><li>North-West corner Method </li></ul><ul><li>Row Minima Method </li></ul><ul><li>Column Minima Method </li></ul><ul><li>Least-Cost Method </li></ul><ul><li>Vogel’s Approximation Method </li></ul>
  8. 8. North- West Corner Method (NWCM) <ul><li>The simplest of the procedures, used to generate an initial feasible solution is, NWCM. It is so called because we begin with the North West or upper left corner cell of our transportation table. </li></ul>
  9. 9. Row Minima Method <ul><li>Row minima method consists in allocation as much as possible in the lowest cost cell of the first row so that either the capacity of the first plant is exhausted or the requirement at distribution centre is satisfied or both. </li></ul>
  10. 10. Column Minima Method <ul><li>Column Minima Method consist in allocating as much as possible in the lowest cost cell of the first column so that either the demand of the first distribution centre is satisfied or the capacity of the plant is exhausted or both. </li></ul>
  11. 11. Least-Cost Method <ul><li>Least-Cost Method consist in allocating as much as possible in the lowest cost cell and then further allocation is done in th cell with second lowest cost cell and so on. </li></ul>
  12. 12. Vogel’s Approximation Method (VAM) <ul><li>In this method, each allocation is made on the basis of the opportunity (or penalty or extra) cost that would have been incurred if allocations in certain cells with minimum unit transportation cost were missed. In this method allocations are made so thet the penalty cost is minimized. </li></ul>
  13. 13. Meaning <ul><li>The assignment problem which finds many allocation in allocation and scheduling. </li></ul><ul><li>For example : In assigning salesman to different regions vehicles and drives to different routes. Products to bidders and research problem to teams etc. </li></ul>
  14. 14. Assignment <ul><li>The Name “assignment problem” originates from the classical problem where the objective is to assign a number of origins (Job) to the equal number of destinations (Persons) at a minimum cast (or maximum profit). </li></ul>
  15. 15. Application areas of Assignment Problem <ul><li>In assignment machines to factory orders. </li></ul><ul><li>In assigning sales/marketing people to sales territories. </li></ul><ul><li>In assignment contracts to bidders by systematic bid evaluation. </li></ul><ul><li>In assignment teachers to classes. </li></ul><ul><li>In assigning accountants to account of the clients. </li></ul><ul><li>In assignment police vehicles to patrolling areas. </li></ul>
  16. 16. Method for solving assignment problem <ul><li>Enumeration Method </li></ul><ul><li>Simplex Method </li></ul><ul><li>Transportation Method </li></ul><ul><li>Hungarian Method </li></ul>
  17. 17. Steps for Solving the problems (By Hungarian method ) <ul><li>Balancing the problem. </li></ul><ul><li>Find the opportunity cost table. </li></ul><ul><li>Make assignment in the opportunity cost matrix. </li></ul><ul><li>Optimality criterion. </li></ul><ul><li>Revise the opportunity cost table. </li></ul><ul><li>Develop the new revised opportunity cost table. </li></ul><ul><li>Repeat steps. </li></ul>
  18. 18. Difference Between Transportation problem and Assignment problem <ul><li>Transportation Problem </li></ul><ul><li>Assignment Problem </li></ul><ul><li>Number of sources and number of destinations need not be equal. Hence, the cost matrix is not necessarily a square matrix. </li></ul><ul><li>The problem is unbalanced if the total supply and total demand are not equal. </li></ul><ul><li>Since assignment is done one basis, the number of sources and the number of destinations are equal. Hence, the cost matrix must be a square matrix. </li></ul><ul><li>The problem is unbalanced if the cost matrix is not a square matrix. </li></ul>