Estochastic models: heavy tails in stochastic systems.

A Pulp Company is planning the expansion of its processing plant. It has been determined that the monthly volume of raw materials that it will demand is equivalent to the load of 24,000 trucks; being the discharge of these one of the critical points of operation. Trucks arrive at the plant randomly, and unloading yard protocols are that: arriving trucks park in the unloading team (crane) queue, choosing the smallest queue; each crane has its own row, and the service obeys the FIFO discipline. Consider that there is enough space to park the trucks that arrive and the cranes that you determine. The costs while they are in the plant are 25,000 CLP per hour of stopped truck. The costs of each unloading equipment are 100,000 CLP per hour of equipment; being the Unloading times Exponential at a rate of 6 trucks per hour. Finally, consider that the plant operates 25 days per month, for 16 hours per day.

a) Determine the number of cranes needed to balance the unloading costs (minimize costs).

b) Determine the waiting costs (queue plus unloading), service costs and the total costs for each hour of operation.