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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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Presentation Transcript
learning outcomes
Learning Outcomes
  • Mahasiswa dapat menghitung solusi model transportasi dengan menggunakan program komputer..
outline materi
Outline Materi:
  • MasalahTransportasi
  • Pembuatan program komputer
  • Contoh & Penyelesaian..
transportation problem
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.
transportation problem1
Transportation Problem
  • Network Representation

1

d1

c11

1

c12

s1

c13

2

d2

c21

c22

2

s2

c23

3

d3

SOURCES

DESTINATIONS

transportation problem2
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

transportation problem3
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.

slide7

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?

slide8

Example: BBC

  • Delivery Cost Per Ton

NorthwoodWestwoodEastwood

Plant 1 24 30 40

Plant 2 30 40 42

slide9

Example: BBC

  • Partial Spreadsheet Showing Problem Data
slide10

Example: BBC

  • Partial Spreadsheet Showing Optimal Solution
slide11

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

slide12

Example: BBC

  • Partial Sensitivity Report (first half)
slide13

Example: BBC

  • Partial Sensitivity Report (second half)
slide14

Terima kasih,

Semoga berhasil