Introduction: The manager of a regional warehouse is tasked with the important decision of determining the optimal number of loading docks to request for the new facility to minimize the overall costs associated with driver-truck combinations and dock operations. With trucks arriving at the rate of four per day, the manager must carefully consider all factors to make the best decision.
Problem Statement: The manager has been informed that each driver-truck combination costs $300 per day and that each dock, along with its loading crew, costs $1,100 per day. The manager must determine the number of docks to request in order to minimize the overall costs while still ensuring an efficient loading process for drivers.
Assumptions: It is assumed that trucks arrive at the rate of four per day and that the arrival rate follows a Poisson distribution. Additionally, it is assumed that each dock can handle five trucks per day and that the loading rate follows an exponential distribution.
The manager has approached you as a consultant to provide recommendations and insights based on the case study above. Your task is to analyze the available data and provide a comprehensive report on the following questions: a), b), and c).
a) Determining the Optimal Number of Docks: Determine the optimal number of docks to request in order to minimize the sum of dock costs and driver-truck costs. Assuming the loading rate of five trucks per day per dock, calculate the number of docks needed to minimize the overall costs.