Question

2. A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of a = 9 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of u = 12 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $250 per day. The cost associated with lost productivity from the breakdown is estimated at $200 per vehicle per day (or any fraction thereof). a. What is the expected cost of this system? Which is cheaper, the existing system with one service crew, or a revised system with two service crews? [Given that the average number in the queue (Lq) is 0.1227 and the average number in the system (Ls) is 0.8727]

Answer 1

(2)

Given:

Arrival rate λ = 9 vehicles per day

Service rate µ = 12 vehicles per day

Crew cost = $250 per day

Cost associated with the lost productivity = $200 per vehicle per day

(a) Expected cost of the system:

Number of vehicles in the service is Ls

Ls 299 3 cars u-112-93

Cost associated with lost productivity = Number of vehicles waiting in the system * Cost per vehicle per day = 3 * 200 = 600 per day

Crew cost = 250 per day

Total cost = Cost associated with lost productivity + Crew cost = 600+250 = $850

(b) Cheaper system:

Two service crew system Ls = 0.8727

Cost associated with the lost productivity = 0.8727 * 200 = $174.54

Crew cost = 2 * 250 = 500

Total cost = 174.54 + 500 = 674.54

Revised system is cheaper as total cost is less for the new system.

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