The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver-truck costs. the manager has learned that each driver-truck combination represents a cost of $300 per day and that each dock plus loading crew represents a cost of $100 per day. how many docks should be requested if trucks arrive at the rate of three per day on average and each dock can handle five trucks per day on average. arrival of trucks follows a poisson distribution and loading time follows exponential distribution. (hint: in this problem, the average service rate, μ, is directly given to you)

Question

Business

Terrence Benson

26 October, 07:35

The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver-truck costs. the manager has learned that each driver-truck combination represents a cost of $300 per day and that each dock plus loading crew represents a cost of $100 per day. how many docks should be requested if trucks arrive at the rate of three per day on average and each dock can handle five trucks per day on average. arrival of trucks follows a poisson distribution and loading time follows exponential distribution. (hint: in this problem, the average service rate, μ, is directly given to you)

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Answers (1)

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Kamila Villa · Answer 1

Only 1 dock is required since its overall cost is lower than having two docks

Explanation:

Solution

Given that:

let us consider the data given for the warehouse:

the cost per day/driver truck = $300

Cost per day/Dock plus loading crew = $100

Arrival rate λ = 3 per day

Service rate μ = 5 per day

Now,

we compute the utilization of the ware house

Utilization = λ/μ

= 3/5

ρ = 0.6

Only 1 dock is required since its overall cost is lower than having two docks