What I thought was right:

The joint business venture will increase employee satisfaction and "will" improve relations between upper management and staff.

Parallelism is an interesting thing. Sometimes you have to repeat the exact words and sometimes you do not.

In this case you should focus on the "and" and what two items it joins.

The "and" joins the verbs "increase" and "improve." Because the "will" comes before the first of these items it carries over to the second of the two as well without it having to be repeated.

Here is and example:

"You cooking has thrilled and amused me." You do not need to say "has thrilled and has amused."

So it is acceptable to say "will increase employee satisfaction and improve relations." The second will is implied...

Does that make sense?