an investment planning n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
An Investment Planning PowerPoint Presentation
Download Presentation
An Investment Planning

Loading in 2 Seconds...

play fullscreen
1 / 17

An Investment Planning - PowerPoint PPT Presentation


  • 87 Views
  • Uploaded on

An Investment Planning. In a barber shop business Paxton Zhou Paul Kim. Basic parameters. Customers arrives according to a Poisson distribution Male and female has the same arrival rate of 3 customers per hour Processing time for each customer is uniformly distributed

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'An Investment Planning' - turner


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
an investment planning

An Investment Planning

In a barber shop business

Paxton Zhou

Paul Kim

basic parameters
Basic parameters
  • Customers arrives according to a Poisson distribution
    • Male and female has the same arrival rate of 3 customers per hour
  • Processing time for each customer is uniformly distributed
    • Male: [15, 75] min per customer
    • Female: [21, 81] min per customer
  • 5 barbers; 2 only handle male hair, 2 only handle female hair, the fifth barber (the master) can handle both male and female hair and is 2x faster than the other barbers
the no queue scenario
The no-queue scenario

Male

Baber 1

Male Barber 2

Master

Customers arrive Poisson (λ=3) for both male and female

Female Barber 3

Female Barber 4

  • We assume that customers have no patience—if no barber is free they will just leave and go to another barber shop near by
  • As a result, we assume immediate blocking when all “machines” are busy
slide4

List scheduling (L-S) method:

  • FCFS
  • When a customer arrives
    • If male, assigned to male only barbers (B1, B2) first
      • If no male barber available, assign to master barber (B5)
      • If master barber is busy, the customer leaves for another barber shop
    • If Female, assign to female only barbers first (B3, B4)
      • If no female barber available, assign to master barber
      • If master barber is busy, the customer leaves for another barber shop
  • The barber shop opens for 8 hours. Any customer who arrives after 8 is not admitted. But barbers still need to work overtime to serve, for example, a customer who arrives at 7:50 and still need an hour to process
run simulation 10 000 times and take average
Run simulation 10,000 times and take average

Result of List-scheduling (L-S)

  • The Average make span is (in hours): 8.666184804397565
  • The Average # of Male customer served: 17.578
  • The Average # Female Customer Served: 16.978
  • The Average # of Total Customer Served: 34.556
let s think of how to improve the system to serve more customers while minimizing the makespan
Let’s think of how to improve the system to serve more customers, while minimizing the makespan
  • The list-scheduling method assign customers to gender constrained barbers (barbers who only handle male or female)
  • Can we improve the system by prioritizing the master barber, who is 2x faster and can handle both male and female?
slide7

Fastest Barber First (FBF) method:

  • FCFS
  • When a customer arrives
    • If male, assigned to B5
      • If B5 is busy, assign to B1 or B2, whoever is available
      • If B1 and B2 are busy, the customer leaves for another barber shop
    • If Female, assigned to B5
      • If B5 is busy, assign to B3 or B4, whoever is available
      • If B3 and B4 are busy, the customer leaves for another barber shop
  • Same as above, the barber shop opens for 8 hours only
run fbf 10 000 times and take average compare with l s method
Run FBF 10,000 times and take average, compare with L-S method
  • There seems to be a very minor improvement
  • We introduce another master barber B6 and see whether prioritizing fastest machines would improve the system
slide9

Compare Fastest Barber First with 2 master barbers(FBF-2) to List Scheduling with 2 master barbers (L-S-2)

  • FCFS
  • FBF-2: Assign new arrivals to B5 or B6 first, then to gender constraint barbers B1~4
  • L-S-2: Assign new arrivals to B1~4, if these gender constraint barbers are busy, assign to B5 or B6
  • Same as above, the barber shop opens for 8 hours only
run l s 2 fbf 2 10 000 times and take average compare with previous methods
Run L-S-2, FBF-2 10,000 times and take average, compare with previous methods
  • There is no improvement in terms of # of customers served, actually, fewer (very little) customers are served
  • There very limited reduction in makespan
  • Hiring more barbers does not reduce makespan!
the queue scenario
The queue scenario

Male

Baber 1

Male Barber 2

Master

Customers arrive Poisson (λ=3) for both male and female

Waitingseats

Female Barber 1

Female Barber 2

  • We assume that customers are willing to wait for at most 30 minutes—if no barber is free then they will just leave and go to another barber shop near by
introducing a queue waiting area
Introducing a Queue/ waiting area
  • We compare the performance of L-S, FBF. L-S-2, FBF-2
  • Having the queue does not make FBF any better compared to L-S
  • FBF results in 2% less customers being served
should we have a queue build a waiting area
Should we have a queue/ build a waiting area?
  • Having a queue does not substantially increases makespan, but we can serve more customers  keep the queue!
  • Do not hire one more master barber: only to serve 3~4 more customers is not worth it as an average barber serves more than 8 under the 5 barber system
  • Having a queue improves the system by serving more customers, while not dramatically increasing the makespan!.
slide14

If the Poission arrival rate is very low, then whether or not do we have a queue does not make a big difference

  • When a customer came in, one barber maybe idle and probably have been waiting for a long time
  • But if the arrival rate is high (much higher than λ=3 per hour, i.e a holiday),:
    • Having a queue will allow the barber shop to serve more customers (more arrivals will be “stored “ in the queue for later processing)
    • The only drawback is that the makespan could be higher (customers in the queue may force barbers to work longer)
  • We run a simulation under λ=10, and see if having a queue will benefit us. We also compare L-S to FBF
slide15

λ=10

  • Having a queue allows us to serve 5 more customers per day by increasing 30mins makespan this is desirable as each customer has an average processing time of more than 30min
  • L-S-2 is not desirable
  • Hiring an extra master barber allows us to serve 12 more customers. This may be desirable, as originally, a master barber processes more than 12 customers we now serve more customers without suffering form diminishing return

A growing queue!

under low arrival rate
Under low arrival rate
  • This is intuitive
  • A queue is not required
  • No need to hire an extra master barber not many customers out there to serve
  • FBF is optimal (example: the shop is quite empty and most of the barbers idle, a customer arrives at t=7:50 you want to assign him/her to the available fastest barber to reduce makespan)
our conclusion
Our conclusion:
  • Under normal arrival rate; we need to implement a queue; we do not hire an extra master barber; and either L-S or FBF is optimal
  • Under high arrival rate, we need a queue; we may hire an extra barber; FBF-2 is optimal
  • Under low arrival rate, a queue is not necessary; we do not need to hire an extra master barber; FBF is optimal