The Seaboard Shipping Company has a warehouse terminalin Spartanburg, South Carolina. The capacity of each terminal dock is three trucks. As trucks enter the terminal, the drivers receive numbers, and when one of the three dock spacesbecomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, andthe unloading and loading times (service times) are exponentially distributed. The average arrival rate at the terminalis five trucks per hour, and the average service rate per dockis two trucks per hour (30 minutes per truck).a. Compute L, Lq, W, and Wq.b. The management of the shipping company is considering adding extra employees and equipment to improvethe average service time per terminal dock to 25 minutes per truck. It would cost the company $18,000 peryear to achieve this improved service. Managementestimates that it will increase its profit by $750 per yearfor each minute it is able to reduce a truck’s waitingtime. Determine whether management should makethe investment.c. Now suppose that the managers of the shipping company have decided that truck waiting time is excessiveand they want to reduce the waiting time. They havedetermined that there are two alternatives available forreducing the waiting time. They can add a fourth dock,or they can add extra employees and equipment at theexisting docks, which will reduce the average servicetime per location from the original 30 minutes per truckto 23 minutes per truck. The costs of these alternativesare approximately equal. Management desires to implement the alternative that reduces waiting time by thegreatest amount. Which alternative should be selected?
The Seaboard Shipping Company has a warehouse terminal
in Spartanburg, South Carolina. The capacity of each terminal dock is three trucks. As trucks enter the terminal, the drivers receive numbers, and when one of the three dock spaces
becomes available, the truck with the lowest number enters
the vacant dock. Truck arrivals are Poisson distributed, and
the unloading and loading times (service times) are exponentially distributed. The average arrival rate at the terminal
is five trucks per hour, and the average service rate per dock
is two trucks per hour (30 minutes per truck).
a. Compute L, Lq, W, and Wq.
b. The management of the shipping company is considering adding extra employees and equipment to improve
the average service time per terminal dock to 25 minutes per truck. It would cost the company $18,000 per
year to achieve this improved service. Management
estimates that it will increase its profit by $750 per year
for each minute it is able to reduce a truck’s waiting
time. Determine whether management should make
the investment.
c. Now suppose that the managers of the shipping company have decided that truck waiting time is excessive
and they want to reduce the waiting time. They have
determined that there are two alternatives available for
reducing the waiting time. They can add a fourth dock,
or they can add extra employees and equipment at the
existing docks, which will reduce the average service
time per location from the original 30 minutes per truck
to 23 minutes per truck. The costs of these alternatives
are approximately equal. Management desires to implement the alternative that reduces waiting time by the
greatest amount. Which alternative should be selected?
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