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Excel Solver Problem and Maximum Flows

Problem 1
The network below shows the product flows possible between pairs of six locations. Formulate a Solver model to find the maximal flow possible from Node 1 to Node 6. Caution: The arrows indicate which flows are possible, e.g. product could flow from Node 2 to Node 4 but cannot flow from Node 4 to Node 2.

Question: What is the maximal flow through this network?
Define the decision variables, the objective function, and the constraints within your answer to this question in your Word report. Then, solve the model using Excel Solver and list the value of the objective function and the values for the decision variables in your Word report.

Please take a look at the diagram attached for this problem.


Solution Preview

Please see the attached Excel file and Word document.

The decision variables are the amounts of flow through each edge of the given graph. The objective function is to maximize the flow to and from the source to sink, which we calculate as the total flow emanating from node 1.

There are two sets of constraints: first, each decision variable value must be less than or ...

Solution Summary

The solution determines the maximum flows in the Excel Solver problem.