The manager of a warehouse must decide on the number of loading docks to request

Question

The manager of a 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 $600 per day and that each dock plus loading crew represents a cost of $1,000 per day (or per 8 hours). The arrival and service rates in the output below are per day Arrival rate Service rate Increment Inte rarrival Time 0.1 increment 0.1 Service time 1/ 0.2000 10.3333 Number of servers (max 12) System Utilizati on Probability system is empty Probability arrival must wa it Average number in line Average number in system Average time in line Average time in system Average waiting time 0.6000 Po= 0.4000 0.6000 0.9000 Le= 1.5000 0.3000 0.5000 0.5000 0.2000 0.5479 0.0247 0.0062 0.6062 0.0021 0.2021 0.0833 0.1500 0.5487 0.0035 0.0006 0.6006 0.0002 0.2002 0.0588 0.1200 0.5488 0.0004 0.0001 0.6001 0.0000 0.2000 0.0455 0.1000 0.5488 0.0000 0.0000 0.6000 0.0000 0.2000 0.0370 0.3000 0.5385 0.1385 0.0593 0.6593 0.0198 0.2198 0.1429 100% 680% 60% 0.60 0.50 040 P 0.30 0.20 0.10 0.00 20% Numberof servers Num berof servers

Explanation / Answer

Ans 1) (b) multiple channel, exponential service time

Explanation: Please observe that the problem mentions a maximum of 12 servers, i.e more than 1 channels. So it is a multiple channel system. Now look at the service time bar chart given in your question. With increase in number of docks average wait time decreases, i.e it is an inverse relationship. If you plot the peaks of all the bars and join the peak points they will form an exponential (i.e. logarithmic) curve.

Ans 2) (c)

Explanation: Service pattern is NOT constant. If it were, service times would also be constant and you would get a flat trendline for the bar chart instead of an exponential one.

Ans 3) As per data given in the question, (column 2 last row), if 2 docks are built, average waiting time = 0.1429

Ans 4) Data in question shows that with 3 docks, average wait time = 0.0833 day = 0.0833 * 24 hrs = 1.9 hrs.

By increasing just 3 more dock we get average wait time = 0.0377 day = 0.0377*24 = 0.8 hr

So, to bring it below 1 hr. we need 6 docks.

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