Decision Analysis Lecture 7

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Decision Analysis - Lecture 7

• Crisis Help
• Queueing model problems and review

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Crisis Help
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Queueing review

• What are the assumptions underlying common
  queueing models?
• What are the important operating characteristics
  of a queueing system?
• Why must the average service time be greater than
  the average interarrival time for a single server
  queue?

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Queueing review

• When might a first-in-first-out rule not be
  applicable?
• What are situations in which there is a limited
  (finite) queue?
• Is the exponential distribution a good model for
  arrivals at
• 1) MBS Café 2) Dentist 3) Movie theatre 4)
  Hardware shop

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Juhn and Sons

• A wholesale fruit distributor, Juhn and Sons,
  employs one worker whose job it is to load fruit
  on outgoing company trucks. Trucks arrive at the
  loading gate at an average of 24 per day or 3 per
  hour, according to an exponential distribution.
  The worker loads them at a rate of 4 per hour
  (also exponential).

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Juhn and Sons

• On average, how many trucks are waiting to be
  loaded? How long do they wait on average?
• What is the probability that there will be more
  than three trucks either being loaded or waiting?

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Juhn and Sons (2)

• Juhn believes that adding a second loader will
  substantially improve the firms efficiency. With
  2 loaders the system would still operate as a
  single server queue with one truck being served
  at a time but the loading rate would increase to
  8 trucks per hour.
• What would be the effect on the queue?

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Juhn and Sons (3)

• Truck drivers working for Juhn and Sons are paid
  a salary of 15 per hour. Loaders receive 9 per
  hour. Drivers waiting in the queue or at the
  loading gate are earning a salary but are
  productively idle. What would be the hourly cost
  savings to the firm if they employed 2 loaders
  instead of 1?

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Economics of queues

• What are the costs of waiting?
• Product inventory versus Customer inventory

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Yacht rentals

• A yacht rental firm owns four identical yachts.
  The summer rental season runs for 150 days and
  during this time customers approach the firm
  every 2 days on average wanting to rent a yacht.
  The average rental period is 5.5 days (both
  arrivals and service are exponential). If no
  yachts are available, customers leave and dont
  wait in a queue.

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Yacht rentals

• Results for M/M/4/0
• At least 1 yacht rented 93 of the time
• At least 2 yachts rented 72 of the time
• At least 3 yachts rented 44 of the time
• All 4 yachts rented 18 of the time

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Yacht rentals

• Each yacht is worth 50,000 and costs 2,000 per
  season to maintain. Rental revenue is 200/day
  per yacht.
• Suppose the rental firm requires 10 ROI. Should
  they sell one of the yachts? Why or why not?
• (Ignore net present value etc.)

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Behavioural queueing

• Waiting as a part of life
• Expectations vs perceptions
• Diversionary tactics
• Anxiety decreases if feel service has started
• Information about length of queue and likely time
  until finished

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Behavioural queueing

• Appointments - advantages and disadvantages
• Equity

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Summary

• Queueing models are used wherever there is
  congestion
• Some basic principles can aid in designing
  processes
• high utilisation is not always a good thing. Plan
  for extra (or flexible) capacity.
• variation causes delays. Try to make arrivals and
  service times more predictable.

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Summary

• pooling servers reduces waiting times. Try to
  combine queues and servers to make most effective
  use of resources.
• queueing systems are complex especially networks
  of queues. You cant predict in advance what a
  small change to one part of the system may do to
  the rest. Try simulating the system to test
  changes in advance.

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Next lecture

• Read texts
• Bring Service Model output for Fatigue Management