RESERVATION QUOTA ALLOCATION PROBLEM

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RESERVATION QUOTA ALLOCATION PROBLEM

• R.Gopalakrishnan
• Western Railway

2
Genesis of the Problem

• Waitlist at the time of booking, but train is
  vacant when boarded
• Wastage of seats at en-route stations whereas
  waitlisted passengers at previous stations were
  denied a seat on the train
• Can partially vacant seats be offered for booking
  passengers without compromising the
  sub-optimality because of cancellation by the
  original passenger?
• Can more passengers be carried in the same
  capacity and can earnings be increased?

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Objective

• Providing confirmed berths to maximum number of
  passengers at the time of booking
• To allocate the given capacity of the train to
  different remote-remote quotas so that all the
  demands for seats on the train are met with the
  minimum number of seats
• Any surplus seats left can be added to the
  general pool
• Determine the minimum capacity required if all
  the demands are to be carried by the train

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The problem defined

• Perceivable demand for different origin-
  destinations on a single train
• Defined capacity in a given class on a train(?)
• Where to create remote locations where quota is
  to be allocated
• How much quota to allocate to different roadside
  stations
• How much quota within the above quota should be
  allocated for different stations We are now
  talking of remote-remote quotas

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The model - basic principles

• Uses past data to project future behaviour data
  warehouse
• Splits seats into multi-leg - upto seven times
  against the conventionally two earlier
• Number of types of splits possible 2(number of
  remotes defined)
• Maximum number of remotes supported by current
  PRS software 6

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Understanding seat splits

• Let us consider a train between BCT and NDLS
• IF there are no (zero) remotes, all seats are
  defined as BCT-NDLS i.e, 201 type of seat
  definition is possible
• When a (one) remote is added, say Surat (ST), the
  number of seat definitions possible are BCT-NDLS
  and BCT-ST-NDLS
• Adding another remote (two remotes), say Vadodara
  (BRC), the number of seat definitions possible
  are BCT-NDLS, BCT-ST-NDLS, BCT-ST-BRC-NDLS,
  BCT-BRC-NDLS. For carrying passengers between BCT
  and ST, both BCT-ST-NDLS and BCT-ST-BRC-NDLS
  seats can be used.

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The model

• Minimizes the seat required to carry all the
  passengers
• Allocates the capacity to the different seat
  definitions possible (related to the number of
  remotes defined on the train)
• Quota allocated between any two pairs of remotes
  stations should be greater than demand (how to
  calculate remote-remote demand?). Only then can
  confirmed seats be given. How many pairs of
  combinations N(N-1)/2 , where N is the number
  of remotes

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Summarizing the model

• Takes past ticket sale data
• Converts them into a matrix form which gives the
  average sales between any two halts of the train
• Select remote stations
• Not all halts can be remotes as PRS has a
  restriction of six
• Best remote stations are those which have
  substantial boarding and detraining traffic.
• Choice of wrong remote can lead to wastage of
  seats (why?)

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Summarizing the model

• Calculate remote-remote demand by compressing the
  original matrix.
• Once the remotes are fixed, run the Operations
  Research (OR) model to find the minimum seats
  required required to fulfill all the demands.
• This also suggests how the distribution is to be
  made

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Pitfalls

• Past ticket sales behaviour is determined by the
  past quota distribution.
• The model assumes unlimited capacity addition is
  possible on a train
• If capacity is limited, then use judgment to deny
  seats to certain pairs of station (where other
  trains exist) so that the seat requirement is
  brought down
• There will always be variation in demand. Keep
  sufficient Pooled Quota to cater to the variations