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 The company in question is being pressed by several of its customers to fulfill their orders faster.The company’s management estimates that the company stands to lose € 250,000 in revenue if they do not reduce their order fulfillment time below 40 working days. Adding one engineer to the existing team would reduce the time to design a hardware down to 14 working days (from 16 days). An additional engineer would cost the company € 50,000. On the other hand, hiring a second engineering team would cost € 250,000. Analyze these two scenarios and recommend an option to the company.

Analysing

While analysing the two scenarios, It costs around €50000 for each additional engineer to finish the work in 16 days but it costs €250000 for hiring a engineering team, so If we hire three additional engineers it costs around €150000,
For example.
For 16 days to reduce 14 day company can hire one staff it cost €50000 so it means one staff can reduce 2 days , and 16 days reduce to 10 days company need only 3 staff , it means company can finish the work within 10 days and total cost 3x €50000. So its better to hire 3 engineers and we can reduce the number of working days with less cost.

 We consider a Level-2 IT service desk with two staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment it is fulfilled?

Queueing theory gives us the following formulas for calculating the above parameters for M/M/1 models:

 Lq—The average number of jobs (e.g. customers) in the queue.
 Wq—The average time one job spends in the queue.
 W—The average time one job spends in the system. This includes both the time the customer spends in the queue but also the time the customer spends being serviced.
 L—The average number of jobs in the system

ρ=( λ/μ)
Lq = ρ2/(1 −ρ)
Wq = Lq/λ

Each staff can handle one work in 4 hrs so λ=0.25 (1/4)
One Request arrival is for 3 hrs so μ =0.33 (1/3)

So the occupation rate ρ=( λ/μ)

If we only 1 Staff , then the occupation rate ρ =0.25/0.33= 0.75 ,

Lq= ρ2/(1 − ρ) = 0.75^2/(1 − 0.75) = 2.25,

And Wq= Lq/λ = 2.25/0.25=9 hours
To conclude the average time taken by each staff is 9 hrs to fulfil the service request.