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Problem Statement Solution Approach Results

𝐦𝐢𝐧 𝒇𝟏 𝒙 ,𝒇𝟐 𝒙 ,𝒇𝟑(𝒙) 𝒔. 𝒕.𝒙 ∈ ℋ

Solving a sequence of constrained bi-objective problems:

Acknowledgements

This research is generously supported by the Center for Healthcare Engineering and Patient Safety, The Seth Bonder Foundation, and The Doctors Company Foundation.

Recursive Method for Finding Pareto-Dominant Shift Schedules for a Pediatric ER Department Jonathan Mogannam, Young-Chae Hong M.S.E., Amy Cohn Ph.D., Marina Epelman Ph.D., Stephen Gorga M.D.

2016 Healthcare Systems Process Improvement Conference

Building resident shift schedules for the U-M Pediatric Emergency Department is a multi-objective combinatorial problem. It is difficult to satisfy the 25+ governing rules and requirements in addition to individual preferences. Additionally, there is no single objective function or clear weights to trade off governing metrics.

Time consuming process

- 20 – 25 hours/month

Difficult to satisfy all requirements:

- 25 Governing rules & Preferences

Educational Training Requirements

Patient Safety

Regulations

Resident Satisfaction

Shift equity / Vacation requests

Bad sleep patterns

Post continuity clinic shifts

We are developing an algorithm for generating Pareto-dominant schedules to reduce the solution space for Chief Residents to review and to help elicit their preferences.

Monday

Continuity Clinics7AM – 2PM

4PM – 1AM

NIG

HIT

Day

NIG

HIT

Tuesday Wednesday

Monday

1AM – 10AM

1PM – 10PM

NIG

HIT

Wake-up

Sleepy

Day

NIG

HIT

Tuesday Sleep Pattern

Resident Name

Smith Jones Chen Joe

Night Shifts / Total Shifts

0 / 7 1 / 7 1 / 7 5 / 7

Fairness

Resident Name

Smith Jones Chen Joe

Night Shifts / Total Shifts 0 / 7 1 / 7 1 / 7 5 / 7

Fairness

𝓗 (Solution Space) : the set of feasible solutions

𝓘 (Objective Space) : the set of objective values, 𝓘 = 𝒇 𝒙 :𝒙 ∈ 𝓗

⋠ (Dominance) : 𝒙 ⋠ 𝒙′ if and only if 𝒇𝒊 𝒙 ≤ 𝒇𝒊 𝒙′ for all 𝒊 with at least one strict inequality.

𝒛 (Pareto solutions) : there is no other feasible solution 𝒙′ such that 𝒙′ ⋠ 𝒙

ℇ (Efficient Set) : set of all Pareto solutions in the solution space 𝓗

𝓕 (Pareto Front) : the set of solutions in objective space 𝓘, 𝓕 = {𝒇 𝒙 :𝒙 ∈ ℇ}

𝒛𝒊∗ (Ideal Value) : the best value of 𝒛𝒊 over the efficient Set, 𝒛𝒊

∗ = 𝒎𝒊𝒏 𝒇𝒊 𝒙 :𝒙 ∈ ℇ

𝒛 𝒊 (Nadir Value) : the worst value of 𝒛𝒊 over the efficient Set, 𝒛 𝒊 = 𝒎𝒂𝒙 𝒇𝒊 𝒙 :𝒙 ∈ ℇ

𝐦𝐢𝐧 𝒇𝟏 𝒙 ,𝒇𝟐 𝒙 𝒔. 𝒕.𝒙 ∈ ℋ

Solving a sequence of two constrained single-objective problems:

P3:(3,3)

P4:(7,2)

P2:(1,4)

P1:(0,5)

P5:(11,0)A:(0,0)

B:(7,2)

D:(1,4) C:(8,4)

(squeezing)

(squeezing)

0123456789

0 1 2 3 4 5 6 7 8 9 10 11 12 13

nu

mD

VR

numPostCC

Total shift equity (TSE) / Night shift equity (NSE) Bad sleep patterns (BSPs)

Denied vacation requests (DVRs) Post continuity clinic shifts (PCCs)

Preferences, tradeoff Pareto Optimality

Ongoing & Future Research

INPUT : ,

WHILE

STEP 1 : Solve

STEP 2 : Get

STEP 3 : Set

END WHILE

OUTPUT :

Candidate shift schedules created for a data set containing 18 residents with pre-determined continuity clinic shifts and vacation requests. Bi-objective problem minimizing PostCC, DVR Pareto-dominance shown between and