Hospital placements allocation
Download
1 / 24

Hospital placements allocation - PowerPoint PPT Presentation


  • 87 Views
  • Uploaded on

Hospital placements allocation. Stephen Cresswell and Lee McCluskey. Introduction. Problem belongs to Human & Health Department, who run on course on Operating Department Practi{c|s}e (ODP). 2-year course, in which students are sent on 7 hospital placements per year.

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 ' Hospital placements allocation' - jerom


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
Hospital placements allocation

Hospital placements allocation

Stephen Cresswell

and

Lee McCluskey


Introduction
Introduction

  • Problem belongs to Human & Health Department, who run on course on Operating Department Practi{c|s}e (ODP).

  • 2-year course, in which students are sent on 7 hospital placements per year.

  • Up to now, each student has been allocated to a single hospital for the year – so hospitals have taken the responsibility for organising a suitable programme.


Introduction 2
Introduction (2)

  • ODP would like to organise placements centrally.

    • Work around bottlenecks to increase the capacity of the course

    • Give students experience of more than one hospital

  • A side-effect of this change will be that allocating students to placements has become a combinatorial problem seemingly too difficult to do by hand.

  • In the rest of the talk, we describe the problem and our approaches to solving it.


Constraints
Constraints

  • Reachability of hospitals: Placements must be within reasonable commuting distance from home location of student. Participating hospitals:

    • Leeds(3), Bradford, Huddersfield, Halifax, Dewsbury, Wakefield, Pontefract, Keighley, Harrogate.

  • Non-repetition: Each of 6 placements is in either anaesthetics or surgery in one of 4 specialities:

    • General Surgery, Gynaecology, Urology, Orthopaedics.


More constraints
More constraints

  • Capacity: Each hospital has a limited capacity (usually 0-2) for the number of placement students that can be accepted in each speciality.

  • Alternation: A student should not have

    • 2 consecutive placements of anaesthetic, or

    • 2 consecutive placements of surgery.


Goals
Goals

  • Can we produce an allocation of students to placements which meets all the constraints?

  • How many more students can be accommodated under the central placements system?

    • The availability of placements is the main factor limiting the expansion of the course.


Simplifying assumptions
Simplifying assumptions

  • Pair timeslots so that students take

    • Surgery then Anaesthetic, or

    • Anaesthetic then Surgery

      in the same speciality.

      Student has same phase for all placements.

  • We then have 3 timeslots, and we must allocate 3 from 4 specialities.



Model
Model

  • Symbols:

    h - hospital, st - student,

    sp - speciality, t - timeslot, ph - phase

  • cap(h,sp)

    • Integer capacity of hospital h in speciality sp

  • reachable(st)

    • Set of hospitals reachable by student st

  • alloc(st,t)

    • Allocation of student st at time t,

    • Allocation is tuple <h,sp,ph>


Model capacity
Model: Capacity

  • Number of students allocated to a particular hospital, speciality and phase is within available capacity.


Model reachability of hospitals
Model: Reachability of hospitals

  • Student can only be allocated to reachable hospitals


Model non repetition
Model: Non-repetition

  • Don’t repeat same speciality – i.e. set of student’s allocated specialiaties has unique element for each time slot.


Model alternation
Model: Alternation

  • Phase for student matches alloctation for student in all timeslots:


Prolog solution
Prolog solution

  • For each alloc(st,t) we have a Prolog term t(H,Sp), where H and Sp are initially uninstantiated variables.

  • Use Prolog built-in depth-first-search with heuristic ordering determining solution order for students.

  • Constraints checked as allocations made:

    • Capacity: total for of each <h,sp,ph,t> tracked.

    • Reachability

    • Non-repetition

    • Alternation: checked via phase variable for each student.


Constraint programming
Constraint Programming

  • A finite domain variable for each alloc(st,t).

  • Each tuple <h,sp,ph> represented by an integer value.

  • Constraint types:

    • Capacity - ‘atmost’ constraint

    • Reachability - a priori pruning of domain

    • Non-repetition - ‘alldifferent’ constraint

    • Alternation - element constraint linking a phase variable for student with indexes of compatible tuples.


Constraint programming1
Constraint Programming

  • Post constraints first, then impose search strategy.

  • Finds schedule with (almost) no backtracking.

  • Default search strategy was “fail first” heuristic.

    • Select variable with smallest domain

    • Not so different from Lee’s heuristic

  • There are some symmetries - e.g. between timeslots and between some sets of students. We didn’t try breaking those symmetries.

  • (Implemented in Oz).



Ilp summary
ILP summary

  • Some of the constraints are not naturally encoded as linear inequations, and this defeats the solver.

  • Solving a relaxed version of the problem is good for detecting infeasibility. Relaxations:

    Integer/continuous

    Collapse time

    Ignore phase (A-S or S-A)

  • Appropriate for optimising an objective function rather than finding any feasible solution.


Results
Results

Table shows #students in largest solved prob.


Results 2
Results(2)

  • Pure Prolog solution is faster.

  • CLP approach found solutions for more students.

  • Prolog and CLP programs, used very similar heuristics

    • Prolog a priori ordering of students according to number reachable hospitals

    • CLP program used ‘fail first’ heuristic – dynamically ordering variables to select var with smallest domain – i.e. the smallest choice of <hosp,sp,ph> tuples.


Goals1
Goals

  • Can we produce an allocation of students to placements which meets all the constraints?

    • Yes!

  • How many more students can be accommodated under the central placements system?

    • Current capacity of the course is 56 students.

    • We can produce schedules for up to 69 students, assuming additional students can travel anywhere.

    • There could be solutions up to 73 students.



Conclusions
Conclusions

  • Problem is easy to solve for the number of students currently involved.

  • Maximising number of students is more challenging.

  • Software can be used for Huddersfield ODP problem, and hopefully also elsewhere.



ad