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DochEvi [55]
3 years ago
13

Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins

working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days with a standard deviation of 2.7 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of 1. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.)
Business
1 answer:
Degger [83]3 years ago
7 0

Answer:

12.55 days

Explanation:

<em><u>Provided information </u></em>

Number of employees 2

Average production time=1.8 days

Standard deviation=2.7 days

Inter-arrival time= 1 day

Coefficient of variation= 1 day

Standard deviation of inter-arrival time= 1 day

The coefficient of variations

<u>Inter-arrival coefficient of variation </u>

C_{vi}=\frac {\sigma}{T} where \sigma is standard deviation of inter-arrival time, T is inter-arrival time and C_v is coefficient of variation of inter-arrival time

C_{vi}=\frac {1 day}{1 day}=1

<u>Production time coefficient of variation </u>

C_{vp}=\frac {2.7}{1.8}=1.5

<u><em>Total utilization time </em></u>

U=\frac {T}{n*T_i} where T is the time of production, n is number of employees, U is utilization, T_i is inter-arrival time

U=\frac {1.8}{2*1}=0.9

Therefore, utilization time by 2 employees is 0.9

<u>Expected average waiting time </u>

T_e=(\frac {T}{n*T_i})*0.5(C_{vi}^{2}+C_{vp}^{2})*(\frac{U^{\sqrt{2(n+1)}-1}}{1-U})

Where T_e is expected average waiting time and the other symbols as already defined

Substituting 1.5 for C_{vp}, 1 for C_{vi}, 0.9 for U, 2 for n, 1 for T_iand 1.8 for T

T_e=(\frac {1.8}{2*1})*0.5(1^{2}+1.5^{2})*(\frac{0.9^{\sqrt{2(2+1)}-1}}{1-0.9})

T_e=0.9*1.625*8.583709=12.55367 days  and rounding off to 2 decimal places we obtain 12.55 days

Therefore, expected duration between order received and beginning of production is approximately 12.55 days

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