Suppose you run a firm who processes mediation requests from companies dealing w

Question

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?

Explanation / Answer

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).

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