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Chapter 6

Chapter 6. Transportation and Assignment Problems. The Transportation Problem. Given: Capacity of each source; Demand of each destination; Transportation cost to ship one unit from a source to a destination.

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Chapter 6

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  1. Chapter 6 Transportation and Assignment Problems

  2. The Transportation Problem • Given: • Capacity of each source; • Demand of each destination; • Transportation cost to ship one unit from a source to a destination. • To find the most economical way of satisfying the demands of the destinations by using the resources.

  3. Solving Transportation Problem • The solution method (algorithm) is elegant. But, as business people, we do not need to know the details since computers can help us solve it. • Use the ‘transportation module’ in QM.

  4. Total Supply and Total Demand • Total supply is not necessary equal to total demand. • A dummy source or a dummy destination appears in the QM result if total supply is not equal to total demand.

  5. Dummy Source or Destination • A dummy source in the result of QM indicates an overall shortage, and at which destinations shortages will occur. • A dummy destination in the result of QM indicates an overall surplus, and which sources will have surpluses.

  6. Prohibited Route • If a route is prohibited to use, just set the unit transportation cost of that route to a very large number.

  7. The Assignment Problem • Given • The cost (or efficiency index) for a person to a job. • To assign Y persons to Y jobs so that the total cost is minimized or total efficiency is maximized.

  8. Solving Assignment Problem • It is a special transportation problem (why?), so it can be solved by using ‘Transportation Module’ in QM. • More conveniently, we use the ‘Assignment Module’ in QM.

  9. Assignment Problem vs. Transportation Problem • The assignment problem is a special case of the transportation problem in which demands of all destinations are 1, and capacities of all sources are 1.

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