I have a huge number of polygons that contain attribute field that represent number of offices inside each polygon. Now I want to merge all adjacent polygons which count (sum) of offices values is between 1000 and 2000. I want to do that using ArcGIS. I have idea to use Dissolve tool, Integrate tool and Merge tool, but I am not sure about steps in order to solve this.
I took your polygons and converted them to single parts. For each part I recomputed number of offices pro rata of parts count in parent polygon. I applied procedure and script from the post mentioned in my comments with tolerance 0.05 and 316 groups, i.e. I tried to create 316 groups from 3059 original polygons with each group containing 1500 offices (total of offices=475169 ):
This is statistics of dissolved:
And these are results. Note I removed islands because they have no neighbours in your definition.
For more information on algorithm, see this post.