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Learning Outcomes

Learning Outcomes. Mahasiswa dapat menghitung solusi model transportasi dengan menggunakan program komputer. Outline Materi:. Masalah Transportasi Pembuatan program komputer Contoh & Penyelesaian. Transportation Problem.

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Learning Outcomes

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  1. Learning Outcomes • Mahasiswa dapat menghitung solusi model transportasi dengan menggunakan program komputer..

  2. Outline Materi: • MasalahTransportasi • Pembuatan program komputer • Contoh & Penyelesaian..

  3. Transportation Problem • The transportation problem seeks to minimize the total shipping costs of transporting goods from m origins (each with a supply si) to n destinations (each with a demand dj), when the unit shipping cost from an origin, i, to a destination, j, is cij. • The network representation for a transportation problem with two sources and three destinations is given on the next slide.

  4. Transportation Problem • Network Representation 1 d1 c11 1 c12 s1 c13 2 d2 c21 c22 2 s2 c23 3 d3 SOURCES DESTINATIONS

  5. Transportation Problem • LP Formulation The LP formulation in terms of the amounts shipped from the origins to the destinations, xij , can be written as: Min cijxij i j s.t. xij<si for each origin i j xij = dj for each destination j i xij> 0 for all i and j

  6. Transportation Problem • LP Formulation Special Cases The following special-case modifications to the linear programming formulation can be made: • Minimum shipping guarantee from i to j: xij>Lij • Maximum route capacity from i to j: xij<Lij • Unacceptable route: Remove the corresponding decision variable.

  7. Example: BBC Building Brick Company (BBC) has orders for 80 tons of bricks at three suburban locations as follows: Northwood -- 25 tons, Westwood -- 45 tons, and Eastwood -- 10 tons. BBC has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is shown on the next slide. How should end of week shipments be made to fill the above orders?

  8. Example: BBC • Delivery Cost Per Ton NorthwoodWestwoodEastwood Plant 1 24 30 40 Plant 2 30 40 42

  9. Example: BBC • Partial Spreadsheet Showing Problem Data

  10. Example: BBC • Partial Spreadsheet Showing Optimal Solution

  11. Example: BBC • Optimal Solution FromToAmountCost Plant 1 Northwood 5 120 Plant 1 Westwood 45 1,350 Plant 2 Northwood 20 600 Plant 2 Eastwood 10 420 Total Cost = $2,490

  12. Example: BBC • Partial Sensitivity Report (first half)

  13. Example: BBC • Partial Sensitivity Report (second half)

  14. Terima kasih, Semoga berhasil

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