Final answer:
The warehouse manager must calculate the optimal number of loading docks to handle the arrival of trucks at a cost-effective rate. By analyzing the Poisson process truck arrival rate and each dock's capacity, an ideal balance of dock and driver-truck costs can be determined.
Step-by-step explanation:
The regional warehouse manager needs to determine the number of loading docks to minimize the total costs consisting of dock costs and driver-truck costs. With trucks arriving at a rate of three per day and each dock being able to handle up to five trucks per day, and considering Poisson distribution rates, the manager must calculate the balance point where the cost of adding an additional dock exceeds the savings from reducing driver-truck wait times.
Since the cost for each driver-truck combination is $300 per day and each dock plus loading crew costs $1,100 per day, the optimal number of loading docks would be the one that minimizes the sum of these two costs while handling the arrival rate of trucks efficiently.
To optimize the number of docks to request, the manager must analyze the expected arrival rate of trucks (given as a Poisson process) alongside the processing rate of docks, accounting for cost per day. Apportioning the dock's working capacity to the truck arrival rate (three trucks per dock, per day), and considering the daily costs, will help the manager reach the most cost-effective solution.
For example, one dock handling up to five trucks per day would mean a lowered need for more drivers and trucks waiting, thus less driver-truck cost but potentially more dock cost if the number of docks requested is more than necessary for the three trucks that arrive per day.