shi$%scheduling%in%apediatric% emergency%departmentand ... ·...

Shi$ Scheduling in a Pediatric Emergency Department and Implica7ons for Beyond

Amy Cohn University of Michigan

Seminar at Mayo Clinic

October 2014

OVERVIEW

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•  My background •  What is CHEPS? •  Scheduling Medical Residents: The Problem •  Mathema7cal Challenges •  Mathema7cal Solu7ons •  Non-‐Mathema7cal Challenges •  Mathema7cal Solu7ons •  Non-‐Mathema7cal Solu7ons

Overview

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A LiSle Background

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A LiSle Background

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CHEPS: THE CENTER FOR HEALTHCARE ENGINEERING AND PATIENT SAFETY

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CHEPS: Center for Healthcare Engineering and Pa7ent Safety

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The mission of CHEPS is to improve the safety and quality of healthcare delivery through a mul<-‐disciplinary, systems engineering-‐based approach. We do so through: Collabora<on, Implementa<on, Innova<on, Educa<on, and Dissemina<on.

CHEPS: Center for Healthcare Engineering and Pa7ent Safety

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Three-‐year old collabora7ve center between medicine, engineering, nursing, public health and more

•  Formal: –  Development of masters concentra7on –  Cross-‐disciplinary seminar series

•  Students: –  Mul7-‐disciplinary, mul7-‐genera7onal group –  Roughly 35 students from engineering (IOE, CSE), nursing, pre-‐med, public

health, medicine –  Undergrad, masters, PhD, post-‐doc, resident, fellow

•  Collaborators: –  Emergency medicine –  Pediatrics –  Thoracic surgery –  General surgery –  Endocrinology –  Oncology –  …

My Current Ac7vi7es Within CHEPS

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SCHEDULING MEDICAL RESIDENTS: THE PROBLEM

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Collaborators

•  PhD student Young-‐Chae Hong •  Current and former Chief Residents in Pediatrics – Brian Jordan, Micah Long, Jenny Zank, Ed O’Brien

•  Current CHEPS students – Billy Pozehl, Ji Wang, Zak VerSchure, Peter Mayoros

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Acknowledgments

•  The Bonder Founda7on •  The Doctors Company Founda7on •  UMHS Pediatrics •  College of Engineering •  CRLT •  SURE

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•  A key issue: Dual role of residency –  Learning experience: Residency (and Fellowship) are parts of the medical educa7on training process

–  Pa7ent care: Residents/Fellows provide a significant amount of the pa7ent care in teaching hospitals and the associated clinical system

•  A typical resident might engage in all of the following ac7vi7es: –  “Con7nuity clinics” –  Shi$s on service –  Seminars, formal educa7onal ac7vi7es –  Research

A Key Logis7cal Challenge of Medical Residency

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•  Staffing issues for residents can have all the complexity as for aSendings, plus a whole second level due to this duality – Impact on pa7ent care in the short term – Impact on pa7ent care in the long term – Impact on the pipeline of future physicians

A Key Logis7cal Challenge of Medical Residency

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•  How to schedule residents’ 7me – Need adequate pa7ent coverage with a limited pool of residents

– Need adequate training opportuni7es – Need adequate rest – fa7gue increases risk of error – Need to address resident sa7sfac7on, personal life

•  Not just quan7ty of hours but paSern –  Con7nuity of care –  Sleep issues (especially associated with overnight shi$s)

– Opportuni7es for different medical experiences

Inherent Time Conflicts

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Given a set of residents to be trained and a set of shiEs to be covered, build a schedule that saJsfies all paJent care, educaJonal, and other requirements

What is the general problem?

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•  Pediatric residency program at UM’s MoS Children’s Hospital •  Residents from 2 – 5 different programs on any given month •  7 overlapping shi$s every day of the month •  Every shi$ has to have exactly one resident assigned •  Excep7ons: 10a – 7p and 12p – 9p shi$ coverage is op7onal

–  Not all of these shi$s can be le$ uncovered for the en7re month –  Ideally one of the two “flex shi$s” should be covered each day

•  Certain shi$s cannot be assigned to an intern •  Certain overlapping pairs of shi$s require a Peds resident on at

least one of the two shi$s –  …

Some More Specifics

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•  Resident availability –  Senior residents switch on the first of the month –  Interns switch on the 27th of the preceding month –  Pre-‐assigned vaca7on 7me must be respected –  Con7nuity clinics/post CC –  Some shi$s are pre-‐assigned to certain residents/programs

–  10-‐hour rule –  First and last shi$s must recognize boundaries of other rota7ons

– …

And Even More Specifics

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•  Manually, by Chief Resident •  Limited decision support tools •  Best-‐case is some fundamental tracking and error-‐checking

•  When we began working with MoS, the Chiefs o$en spent 20+ hours/month on the schedule and all were unsa7sfied with results – Chiefs, Residents, ASendings

How are schedules typically built?

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MATHEMATICAL CHALLENGES

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Why is it hard to schedule manually?

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•  The more squares you fill in, the fewer choices you have le$ for what is valid

•  Once you make a mistake, you might not know it for a long 7me •  Once you realize something is wrong, it can be very hard to back track and

correct •  If a requirement changes, you have to start from scratch

•  Tremendous computa7onal complexity •  Enormously 7me consuming •  Difficult to achieve feasibility – Par7cularly for mul7-‐event issues, such as rest rules

•  Difficult to achieve high quality – Par7cularly for mul7-‐event issues, such as sleep paSerns

•  Issues of percep7on of equity (or lack thereof)

Manual Scheduling Issues

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MATHEMATICAL SOLUTIONS

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•  Mixed integer programming approach –  xrsd = 1 if resident r is assigned to shi$ s on day d, else 0

•  Can model virtually all “laws of physics” by linear equa7ons –  E.g. Σr∈R xrsd = 1 ∀s∈S, d∈D

•  Run 7me of at most a few few second using C++ and CPLEX on a standard PC to get a feasible solu7on

•  But not all feasible schedules are equally good

How do we solve it?

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NON-‐MATHEMATICAL CHALLENGES

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•  No one clear objec7ve func7on, but many important metrics –  Equity across residents

•  Number of shi$s •  Number of night shi$s •  General quality of schedule

–  “Bad sleep paSerns” –  Personal requests –  Post-‐con7nuity clinic calls –  Flex shi$ coverage –  Transi7on shi$ coverage

How to “op7mize”?

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•  We could treat this as a mul7-‐criteria objec7ve func7on, assign weights to normalize, and solve – Weights are hard to find – Convergence can slow drama7cally


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•  Our approach thus far: – Set boundaries on the metrics – Define as hard constraints – Search for a feasible solu7on

•  If found, review and decide what to 7ghten next •  If not found, loosen the boundaries

– Repeat un7l sa7sfied


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•  Results thus far: – Drama7c decrease in 7me required to find solu7ons –  Elimina7on of all errors and rule viola7ons –  Significant improvement in resident sa7sfac7on (e.g. more day-‐off requests granted)

–  Significant decrease in number of cancelled con7nuity clinics

–  Significant decrease in number of post-‐CC shi$s –  Significant decrease in number of “bad sleep paSerns”


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•  But this s7ll limits the search space and is driven by the pa7ence of the Chief Resident!

•  Can we do even beSer?


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MATHEMATICAL SOLUTIONS

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•  Challenge in mul7-‐criteria op7miza7on: only the user knows what trade-‐offs between criteria s/he is willing to make –  This is o$en qualita7ve, intui7ve, and hard to ar7culate accurately

•  Pareto dominance: –  One schedule dominates another if it is as good or beSer in all categories

–  Pareto dominant solu7ons cannot be made beSer under one metric without being made strictly worse in another

•  Only need to propose Pareto-‐dominant solu7ons

Goal: Generate a Pareto-‐Dominant Set of Solu7ons

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•  Suppose we have a linear integer program with feasible region of the form:

Ax = b x ∈{0,1}n

•  Suppose that we have objec7ve func7ons f1(x), f2(x), … fm(x)

•  For the sake of exposi7on, assume objec7ve func7ons all have integer coefficients

Genera7ng a Pareto-‐Dominant Solu7on: The “Squeeze Method”

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•  First, we find any feasible solu7on x1 •  Next, we solve the following feasibility problem to find a

solu7on x2 that Pareto-‐dominates x1 : Ax = b f1(x) < f1(x1) f2(x) < f2(x1) … fm(x) < fm(x1) f1(x) + f2(x) + … + fm(x) < f1(x1) + f2(x1) + … + fm(x1) -‐ 1 x ∈{0,1}n


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•  We can repeat this process un7l, for a given solu7on x*, the associated problem is infeasible – this means x* is a Pareto dominant solu7on

•  Phase I: Randomly generate “seed” solu7ons and, for each, find an equivalent Pareto-‐dominant solu7on – only need to provide these to the user (“random” might be based on sezng boundaries based on the user’s dissa7sfac7on with the current solu7on)

•  Phase 2: Algorithm to generate the exhaus7ve Pareto fron7er of solu7ons


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Genera7ng Exhaus7ve Set with Two Metrics

•  Find the best value for each metric by op7mizing exclusively over that metric

•  Check the feasibility of achieving all op7mal values across all metrics – if yes, stop!

•  If not, find the best value for each metric given the op7mal value of the other metric

•  The Pareto fron7er is contained within this box (why?)

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Genera7ng Exhaus7ve Set with Two Metrics

•  Start with the PDS (Pareto-‐Dominant Solu7on) defined by metric 2 at its op7mal value and metric 1 at its associated op7mal value

•  Require metric 1 to decrease by at least 1 unit and re-‐solve, op7mizing over metric 2 (which must strictly increase over its current op7mal value)

•  “Squeeze” this solu7on – no PDS can be found in between

•  Repeat

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•  What happens when we move to three metrics, i.e. three dimensions?

•  Idea: Fix Metric 1 to its op7mal value and solve the resul7ng two-‐dimensional problem; repeat for increasing values of Metric 1

•  Key: Can no longer use op7mal values of Metric 2 and 3; must condi7on them on the op7mal value of Metric 1 to ensure feasibility

•  What is the stopping criteria for Metric 1?

Genera7ng Exhaus7ve Set with Three Metrics

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Genera7ng Exhaus7ve Set with Three Metrics

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NON-‐MATHEMATICAL SOLUTIONS

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•  Engagement with Chief Resident has been cri7cal every step of the way

•  We have learned an enormous amount from him

•  He has learned an enormous amount from us •  Our approach to solving the problem – collabora7vely – depends completely on this

•  How do we as a community facilitate and establish the value of such collabora7ons?

It’s Not Just About Algorithms

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QUESTIONS AND DISCUSSION

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