Question

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 $1,100 per day.

How many docks should be requested if trucks arrive at the rate of three per day, each dock can handle five trucks per day, and both rates are Poisson?

Answer 1

Solution:

Consider the following data

Cost of driver an truck =$300

Cost of dock and loading crew = $1,100

Arrival rate (λ) =3

Service rate (μ) = 5

Calculate the total number of Servers (M) required for minimizing the total cost.

Calculate the r vale tor mentioned data using given formula:

R= λ / μ

= 3/5

   = 0.6

Prepare an excel sheet as shown below:

The costs are analyzed to both a single server as well as a dual server model. The L_q value is taken from the infinite source value tablet for L_q and P_o for M and λ / μ.

It gives the following below values:

Hence it is concluded that manager should request 1 dock to accomplish his objective.