Question

Joey works at a interarrival times (in minutes) .chocolate store. Starting at time 0, we have the following 4 customer Bill Angie Ursula Tom 2 2 Customers are served in alphabetical order (though get displaced by a higher-priority customer). The 4 customers order the following numbers of chocolate products, respectively once you start service, you don't 6 2 3 1 Suppose it takes Joey 3 minutes to prepare each chocolate product. Further suppose that he charges $2/chocolate. Unfortunately, the customers are unruly and each customer causes $0.50 in damage for every minute the customer has to wait in line (a) When does the first customer leave? (b) What is the average number of customers in the system during the first 20 minutes? (c) How much money will Joey make or lose with the above 4 customers?

Answer 1

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AS FOR GIVEN DATA..

Joey works at a chocolate store. Starting at time 0, we have the following 4 customer interarrival times (in minutes):

Bill = 8

Tom = 2

Angie = 5

Ursula = 2

Customers are served in alphabetical order (though once you start service, you don’t get displaced by a higher-priority customer).

The 4 customers order the following numbers of chocolate products, respectively: 6 2 3 1

Suppose it takes Joey 3 minutes to prepare each chocolate product. Further suppose that he charges $2/chocolate. Unfortunately, the customers are unruly and each customer causes $0.50 in damage for every minute the customer has to wait in line.

(a) When does the first customer leave?

(b) What is the average number of customers in the system during the first 20 minutes?

(c) How much money will Joey make or lose with the above 4 customers?

EXPLANATION:

Service time of each customer = Number of chocolate products ordered * 3 minutes to prepare each chocholate product

Customers are served in alphabetical order. However, Bill arives the first. So, he is served first. It takes = 6*3 = 18 minutes to complete his order. His service end time = 8+18 = 26 minutes. By this time, the other three customers have also arrived. So, these customers are served in alphabetical order: Angie, Tom, Ursula

A C D E E G Interarrival Arrival Service start Service Service 1 Customer end time time time time time Bill 8 8 8 18 26 Angle 3 5 15 26 9 35 Tom 10 35 6 41 Ursula 41 5 2 17 3 44 6 7 8 9 10 st

FORMULAS:

Customer	Interarrival time	Arrival time	Service start time	Service time	Service end time
Bill	8	=B2	=C2	=6*3	=D2+E2
Angie	5	=C4+B3	=MAX(C3,F2)	=3*3	=D3+E3
Tom	2	=C2+B4	=MAX(C4,F3)	=2*3	=D4+E4
Ursula	2	=C3+B5	=MAX(C5,F4)	=1*3	=D5+E5

(a) First customer leaves at 26 minutes

(b)

During the first 20 minutes, Bill is there in system for 20-8 = 12 minutes

Angie is there in system for 20-15 = 5 minutes

Tom is there in system for 20-10 = 10 minutes

Ursula is there in system for 20-17 = 3 minutes

Average number of customers in the system = (12+5+10+3)/20 = 1.5

(c) Revenue earned = (6+2+3+1)*2 = $ 24

Waiting time for each customer = Service start time - Arrival time

Total waiting time = (8-8)+(26-15)+(35-10)+(41-17) = 60 minutes

Total cost of damage due to customer waiting = 60*0.5 = $ 30

Money made or lost with the above 4 customers = Revenue earned - Total damage due to customer waiting

= 24 - 30

= $ - 6 (loss)

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