# Difference: CosmicComputersSolverStudio (3 vs. 4)

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 META TOPICPARENT name="SubmitCaseStudy"
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|*FORM FIELD Conclusions*|Conclusions|As with the Brewery Problem, the solution to the Cosmic Computers Problem can be presented in many ways. Figure 1 gives a graphical solution to the Cosmic Computers Problem.

Figure 1 Solution to the Cosmic Computers Problem

| |*FORM FIELD ExtraForExperts*|ExtraForExperts|Another form of branch and bound implements branches on constraints that should take integer values. For example, in the Cosmic Computers Problem the sum of any subset of Build variables should be integer. Consider the LP relaxation solution:

The sum of the three non-zero Build variables is 2.82 (2 dp), but it should be integer. We can remove the fractional part by forcing this sum to be either 3 or 2. First, let's branch up:

Our solution is integer so we can fathom this node. Now let's drop the Up constraint and branch down:

This solution still has fractional Build variables. We can add further constraint branches to continue searching from this node:

1. Solve the Cosmic Computers Problem. Write a management summary of your solution.

What to hand in Your management summary.

2. Experts Only Complete the branch-and-bound process using constraint branches on fractional sums of the Build variables. Draw your branch-and-bound tree as shown above (in the Extra for Experts section). Be sure to indicate what branches you used. Briefly (1 paragraph) compare your experience with constraint branching to the variable branching used in CPLEX.

What to hand in Hand in your drawing of your branch-and-bound tree along with your conclusions about the effectiveness of constraint branching compared with variable branching.

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