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I am working on an optimization problem where I want to find resource-activity assignment based on skill restrictions (not all resources have all skills), resource restrictions (resources have a limited presence) and an assignment restriction limiting the number of resources assigned to an activity. I want to maximize the sum of weights of all selected activities. The model is depicted here:

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Now I fed this into CPlex and it solves gigantic instances in a very short amount of time as long as I allow heuristics (1000 activities, 50 resources, 5 skills within about 10 sec).

Why is this problem so easy for CPlex? Is there some kind of easily solvable underlying problem that I am missing?

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    How long would you expect brute forcing it to take? – 2017-02-26
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    A gigantic amount of time since I'd have to check all the subsets of activities to be selected and then all the subsets of resources with the right cardinality to be assigned to these activities. – 2017-02-27

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