Reservation allocation algorithm

Question

I am looking for algorithms for allocating reservations to resources. This could be Hotel reservations matched to available rooms - Meeting reservations matched to available meeting rooms - Restaurant reservations matched to tables.

What they have in common:

Each reservation has a specific unchangeable start and end time.
Each reservation is not bound to a specific resource before the start time.
There can be a variable number of resources.
Every time a new reservation comes, the algorithm should at least be able to check if it is possible to match to a resource or not.

So far I have mostly looked at genetic algorithm approaches to solve the problem, but I'm having trouble encoding the problem to chromosomes.

Any thoughts on algorithms for this is welcome, also algorithms that only finds a "good" solution as opposed to an optimal one.

Is this an on-line problem (where you get requests one at a time), or one where you have all the reservations up front? — EmeryBerger, Jan 14 '11 at 12:54
It would be one request at the time. But a reservations does not have to tied to a resource before its start time. So there will be tied reservations and not tied reservations when a new reservations is added. — Lemmedaskeren, Jan 14 '11 at 12:58
What is the question here? Since you say start/end is unchangeable, isn't this just this question: "Can I accept reservation X"? — Lasse V. Karlsen, Jan 14 '11 at 13:14
Basically, isn't this question just this: For the entire period of time that this reservation is for, is the required number of resources currently available? If this isn't the question, what is it? Why do you need a genetic algorithm for this? — Lasse V. Karlsen, Jan 14 '11 at 13:21
Exactly. If in your situation, a reservation for the period [start, end] must be accepted if the interval has no prior reservations (for any "resource") and rejected if there is overlap in all, then you just need to check those intervals for each resource. — EmeryBerger, Jan 14 '11 at 13:51
Yes, you are correct, the question is "Is there room for the reservation" - but that can depend on moving other reservations, and their new possible placements can in turn depend on moving a third set of reservations and so on. — Lemmedaskeren, Jan 14 '11 at 14:02
Does each reservation require exactly one resource? If so, then the question becomes simple as nothing can be gained by reorganising existing pairings of reservations to resources when a new reservation request comes in as they are all equivalent. — j_random_hacker, Jan 15 '11 at 17:37

score 6 · Answer 1 · answered Apr 06 '11 at 06:37

This article includes various time operation to check for free, overlapping and intersecting time periods. You can easily combine this classes with your business objects:

// ----------------------------------------------------------------------
public void TimeRangeSample()
{
  // --- time range 1 ---
  TimeRange timeRange1 = new TimeRange(
    new DateTime( 2011, 2, 22, 14, 0, 0 ),
    new DateTime( 2011, 2, 22, 18, 0, 0 ) );
  Console.WriteLine( "TimeRange1: " + timeRange1 );
  // > TimeRange1: 22.02.2011 14:00:00 - 18:00:00 | 04:00:00

  // --- time range 2 ---
  TimeRange timeRange2 = new TimeRange(
    new DateTime( 2011, 2, 22, 15, 0, 0 ),
    new TimeSpan( 2, 0, 0 ) );
  Console.WriteLine( "TimeRange2: " + timeRange2 );
  // > TimeRange2: 22.02.2011 15:00:00 - 17:00:00 | 02:00:00

  // --- time range 3 ---
  TimeRange timeRange3 = new TimeRange(
    new DateTime( 2011, 2, 22, 16, 0, 0 ),
    new DateTime( 2011, 2, 22, 21, 0, 0 ) );
  Console.WriteLine( "TimeRange3: " + timeRange3 );
  // > TimeRange3: 22.02.2011 16:00:00 - 21:00:00 | 05:00:00

  // --- relation ---
  Console.WriteLine( "TimeRange1.GetRelation( TimeRange2 ): " +
                     timeRange1.GetRelation( timeRange2 ) );
  // > TimeRange1.GetRelation( TimeRange2 ): Enclosing
  Console.WriteLine( "TimeRange1.GetRelation( TimeRange3 ): " +
                     timeRange1.GetRelation( timeRange3 ) );
  // > TimeRange1.GetRelation( TimeRange3 ): EndInside
  Console.WriteLine( "TimeRange3.GetRelation( TimeRange2 ): " +
                     timeRange3.GetRelation( timeRange2 ) );
  // > TimeRange3.GetRelation( TimeRange2 ): StartInside

  // --- intersection ---
  Console.WriteLine( "TimeRange1.GetIntersection( TimeRange2 ): " +
                     timeRange1.GetIntersection( timeRange2 ) );
  // > TimeRange1.GetIntersection( TimeRange2 ):
  //             22.02.2011 15:00:00 - 17:00:00 | 02:00:00
  Console.WriteLine( "TimeRange1.GetIntersection( TimeRange3 ): " +
                     timeRange1.GetIntersection( timeRange3 ) );
  // > TimeRange1.GetIntersection( TimeRange3 ):
  //             22.02.2011 16:00:00 - 18:00:00 | 02:00:00
  Console.WriteLine( "TimeRange3.GetIntersection( TimeRange2 ): " +
                     timeRange3.GetIntersection( timeRange2 ) );
  // > TimeRange3.GetIntersection( TimeRange2 ):
  //             22.02.2011 16:00:00 - 17:00:00 | 01:00:00
} // TimeRangeSample

score 4 · Answer 2 · answered Mar 09 '11 at 11:53

Take a look at Tabu search and Simulated Annealing as a replacement for genetic algorithms.

This is very similar to the PAS example in Drools Planner (java, open source), which is about scheduling patients into hospital beds with all kinds of constraints. See the slide and the next slide.

score 0 · Answer 3 · answered Jul 15 '21 at 15:16

Use a sparse matrix.

In the case of a hotel rooms reservations

axe x you have the rooms
axe y you have the dates
axe z you have the time intervals, pointing to the reservation data object.

All them (1,2,3) could be represented as a list or for 3 a hash table.

Example:

x = room 10
y = date 2021/4/3
z = time from 10am till 9pm

Then you add all the methods for inserting, deleting, collisions etc. reservations logic.

It can be proved that with this structure you can easily manage any reservation by traveling the matrix.

Reservation allocation algorithm

3 Answers3