Homework SourseTrucks arrive at the loading dock of a wholesale grocer at t
Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per hour. A single crew consisting of two workers can load a truck in about 30 minutes. Crew members receive $10 per hour in wages and fringe benefits, and trucks and drivers reflect an hourly cost of $69. The manager is thinking of adding another member to the crew. The service rate would then be 2.4 trucks per hour. Assume rates are Poisson.
What would the total cost for a fourth member if the resulting service capacity were 2.6 trucks per hour?
| Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per hour. A single crew consisting of two workers can load a truck in about 30 minutes. Crew members receive $10 per hour in wages and fringe benefits, and trucks and drivers reflect an hourly cost of $69. The manager is thinking of adding another member to the crew. The service rate would then be 2.4 trucks per hour. Assume rates are Poisson. |
Solution
Rate of arrival = 1.2 trucks =
When crew members = 2
Mean service rate = = 2/ hour
Mean number of trucks in system = / ( - ) = 1.2/(2-1.2)
= 1.5
Total Cost = 2*10 + 1.5*69 = 123.5
Crew members = 3
Mean service rate = = 2.4/ hour
Mean number of trucks in system = / ( - ) = 1.2/(2.4-1.2) = 1
Total Cost = 3*10 + 1*69 = 99
Crew members = 4
Mean service rate = = 2.6/ hour
Mean number of trucks in system = / ( - ) = 1.2/(2.6-1.2) = .8571
Total Cost = 4*10 + .8571*69 = 99.1399
It is better to use 3 crew members.
