phase1 - OR&IE 320/520 10/16/07 Prof. Bland...

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Unformatted text preview: OR&IE 320/520 10/16/07 Prof. Bland Initialization of the Simplex Method: An Example Using Ar- tificial Variables cf. BHM Chapter 2 sections 2,4,5. Recall (from Rec Exercise/Problem Set 4) the AluMinimum Corp. problem concern- ing the production of a low-cost aluminum alloy from scrap (recycled beer cans). For the current production period AluMinimum Corp has orders for 100 tons of an alloy that must contain at least 1% silicon and at most 1% manganese . There are four sources of scrap aluminum available (in plentiful supply). The ta- ble below shows the cost per ton (including processing costs) and the silicon and manganese content for each of the four kinds of scrap. Scrap 1 Scrap 2 Scrap 3 Scrap 4 Cost (US dollars per ton) 350 300 250 200 Percentage Silicon 1.9 1.3 .4 Percentage Manganese 1.2 1.1 1 .7 We came up with the following linear programming formulation: minimize 350 x 1 + 300 x 2 + 250 x 3 + 200 x 4 subject to: 1 x 1 + 1 x 2 + 1 x 3 + 1 x 4 = 100 . 9 x 1 + . 3 x 2 +- . 6 x 3 +- 1 x 4 . 2 x 1 + . 1 x 2 + x 3 +- . 3 x 4 x 1 , x 2 , x 3 , x 4 . We produced AMPL model and data files for this problem and solved it using AMPL. But I am wondering how AMPL got started. In some of our examples (e.g., making beer and sausages) it was easy to get an initial feasible simplex tableau, because the...
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phase1 - OR&IE 320/520 10/16/07 Prof. Bland...

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