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Solusi Model Transportasi dengan Program Komputer Pertemuan 13 : Mata kuliah : K0164/ Pemrograman Matematika Tahun: 2008

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

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Outline Materi: Masalah Transportasi Pembuatan program komputer Contoh & Penyelesaian..

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

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Transportation Problem Network Representation 1 1 2 2 3 3 1 1 2 2 c 11 c 12 c 13 c 21 c 22 c 23 d1d1d1d1 d2d2d2d2 d3d3d3d3 s1s1s1s1 s2s2 SOURCESDESTINATIONS

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Transportation Problem LP Formulation The LP formulation in terms of the amounts shipped from the origins to the destinations, x ij, can be written as: Min c ij x ij i j s.t. x ij < s i for each origin i j x ij = d j for each destination j i x ij > 0 for all i and j

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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: x ij > L ij –Maximum route capacity from i to j: x ij < L ij –Unacceptable route: Remove the corresponding decision variable.

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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?

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Example: BBC n Delivery Cost Per Ton Northwood Westwood Eastwood Northwood Westwood Eastwood Plant 1 24 30 40 Plant 1 24 30 40 Plant 2 30 40 42 Plant 2 30 40 42

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Example: BBC n Partial Spreadsheet Showing Problem Data

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Example: BBC n Partial Spreadsheet Showing Optimal Solution

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n Optimal Solution From To Amount Cost From To Amount Cost Plant 1 Northwood 5 120 Plant 1 Westwood 45 1,350 Plant 1 Westwood 45 1,350 Plant 2 Northwood 20 600 Plant 2 Northwood 20 600 Plant 2 Eastwood 10 420 Plant 2 Eastwood 10 420 Total Cost = $2,490 Total Cost = $2,490 Example: BBC

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n Partial Sensitivity Report (first half)

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Example: BBC n Partial Sensitivity Report (second half)

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Linear Programming Example 5 Transportation Problem.

Linear Programming Example 5 Transportation Problem.

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