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Transportation Pbm. Transportation Problem. The Transportation Model Solution of a Transportation Problem North west corner solution Least cost solution. The Transportation Model Characteristics.

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Presentation Transcript
transportation problem
Transportation Problem
  • The Transportation Model
  • Solution of a Transportation Problem
  • North west corner solution
  • Least cost solution
the transportation model characteristics
The Transportation Model Characteristics
  • A product is transported from a number of sources to a number of destinations at the minimum possible cost.
  • Each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product.
  • The linear programming model has constraints for supply at each source and demand at each destination.
  • All constraints are equalities in a balanced transportation model where supply equals demand.
  • Constraints contain inequalities in unbalanced models where supply does not equal demand.
example of a transportation model1
Example of a Transportation Model

- Problem: how many tons of wheat to transport from each grain elevator to each mill on

a monthly basis in order to minimize the total cost of transportation ?

- Data: Grain ElevatorSupplyMill Demand

1. Kansas City 150 A. Chicago 200

2. Omaha 175 B. St.Louis 100

3. Des Moines 275 C. Cincinnati 300

Total 600 tons Total 600 tons

3 dcs and 3 customers
3 DCs and 3 customers.

You have 3 DCs, and need to deliver product to 3 customers.

Find cheapest way to satisfy all demand?

CH 200

KC 150

St 100

O 175

DM 275

CI 300

transportation model example lp model formulation
Transportation Model ExampleLP Model Formulation

minimize Z = 6x1A + 8x1B + 10x1C + 7x2A + 11x2B + 11x2C + 4x3A + 5x3B + 12x3C

subject to x1A + x1B + x1C = 150

x2A + x2B + x2C = 175

x3A + x3B+ x3C = 275

x1A + x2A + x3A = 200

x1B + x2B + x3B = 100

x1C + x2C + x3C = 300

xij  0

where xij = tons of wheat from each grain elevator, i, i = 1, 2, 3, to each mill j, j = A,B,C

Network of transportation routes for wheat shipments

solution of the transportation model tableau format
Solution of the Transportation ModelTableau Format
  • Transportation problems are solved manually within a tableau format.
  • Each cell in a transportation tableau is analogous to a decision variable that indicates the amount allocated from a source to a destination.

The Transportation Tableau

solution of the transportation model solution methods
Solution of the Transportation ModelSolution Methods
  • Transportation models do not start at the origin where all decision values are zero; they must instead be given an initial feasible solution.
  • Initial feasible solution determination methods include:
  • - northwest corner method
  • - Lowest cost method
  • - Vogel’s Approximation Method
  • Methods for solving the transportation problem itself include:
    • - Transportation Algorithm.
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