Hi, please answer the below question in Excel and please show how problem was an

Question

Hi, please answer the below question in Excel and please show how problem was answered and formulas that were used, (in any) ASAP for MBA 550.

The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 7.5 minutes, on average. The machine operator can process an average of 10 parts oer hour. Determine the average number of parts waiting to be worked on, the percentage of time the operator is working and the percentage of time the machine is idle.

Explanation / Answer

We assume that this is a queuing theory problem as per Kendall’s notation M/M/1 where arrival rate has a Poisson distribution and service rate has a negative exponential distribution

Given ,

Arrival rate of each unit ( @ once in every 7.5 minutes ) = a = 60/7.5 =    8 parts / hour

Processing rate = p = 10 parts / hour

Average number of parts waiting to be worked on

= a^2/ p x( p – a)

= 8 x 8 / 10 x ( 10 – 8 )

= 3.2

Percentage of time operator is working = a/p x 100 = 8/10 x 100 = 80%

Percentage of time machine is idle = 100% - Percentage of time operator is working = 100 – 80 = 20%

AVERAGE NUMBE ROF PARTS WAITING TO BE WORKD ON = 3.2

PERCENTAGE OF TIME OPERATOR IS WORKING = 80%

PERCENTAGE OF TIME MACHINE IS IDLE = 20%

AVERAGE NUMBE ROF PARTS WAITING TO BE WORKD ON = 3.2

PERCENTAGE OF TIME OPERATOR IS WORKING = 80%

PERCENTAGE OF TIME MACHINE IS IDLE = 20%

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