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Check 'Make Unconstrained Variables Non-Negative' and select 'Simplex LP'.Ĭonclusion: the path SADT with a flow of 2. Click Add to enter the following constraint.ħ. Click Add to enter the following constraint.Ħ. Enter Flow for the Changing Variable Cells.ĥ. You have the choice of typing the range names or clicking on the cells in the spreadsheet.Ĥ. The result should be consistent with the picture below. Note: can't find the Solver button? Click here to load the Solver add-in.Įnter the solver parameters (read on). On the Data tab, in the Analyze group, click Solver. To find the optimal solution, execute the following steps.ġ. We shall describe next how the Excel Solver can be used to quickly find the optimal solution. It is not necessary to use trial and error. For example, the path SADT with a flow of 2. With this formulation, it becomes easy to analyze any trial solution.ġ. Because node A, B, C, D and E have a Net Flow of 0, Flow Out of node S will equal Flow In of node T. Maximum Flow equals the value in cell I4, which is the flow out of node S. The second SUMIF function sums the values in the Flow column with an "A" in the To column (Flow In).
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For node A, the first SUMIF function sums the values in the Flow column with an "A" in the From column (Flow Out). Range NameĮxplanation: The SUMIF functions calculate the Net Flow of each node. To make the model easier to understand, create the following named ranges. The maximum flow equals the Flow Out of node S.Ģ. What is the overall measure of performance for these decisions? The overall measure of performance is the maximum flow, so the objective is to maximize this quantity. The flow on each arc should be less than this capacity.Ĭ. What are the constraints on these decisions? The Net Flow (Flow Out - Flow In) of node A, B, C, D and E should be equal to 0. For example, if the flow on SB is 2, cell D5 equals 2.ī.
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What are the decisions to be made? For this problem, we need Excel to find the flow on each arc. To formulate this maximum flow problem, answer the following three questions.Ī.
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