Suppose you run a firm who processes mediation requests from

Suppose you run a firm who processes mediation requests from companies dealing with minor labor relations disputes. The number of requests received per day is well-modeled by a Poisson random variable with an average value of 40. All requests are processed by \"primary adjudicators\", who can process up to 10 requests per day. Primary adjudicators make $350 per day. If too many requests are received for the number of primary adjudicators on staff, the extra requests are sent to be processed at another firm at a cost of $150 each. Each request that undergoes primary adjudication internally has a 40% chance, independent of all other requests, of requiring attention from a \"secondary adjudicator\". Secondary adjudicators make $450 per day and can process up to 5 request per day. If there are more requests for secondary adjudication than your staff is able to handle, the extra requests are sent for secondary adjudication at another firm, at a cost of $225 each. You are considering having 3, 4, 5, or 6 primary adjudicators on staff, and 2, 3, or 4 secondary adjudicators. Of all 12 possible combinations of these options, which would give you the lowest average cost?

Solution

With fluctuating situation and conditions here, the most suitable option out of the given 12 options will be option with 5 primary adjudicators and 3 secondary adjudicators.

This is due to the fact that this is the most economical combination out of the given one(s).