Staffing and Scheduling – Part II

HCM 540 – Operations Management

Primary Objectives

1. Staff scheduling is a difficult, time consuming managerial problem

2. Many flavors of staff scheduling problems

3. Staff scheduling inextricably linked with determining total amount of staff

4. Tactical and operational staff scheduling

5. Computerized staff scheduling systems

High Level Staffing Framework

Budgeting and Planning

•Annual or as needed

•Planned capacity

•Staffing/scheduling policies

Operational staffing/scheduling

•Every 2-6 weeks

•Target staffing levels

•Create employee schedules for core staff

Daily allocation•Ongoing

•Reacting to staffing variances

•Floating staff, overtime, contract staff, agencies

Adapted from Abernathy et. al. (1973), Hershey et. al. (1981), Warner et. al. (1991)

Budget, staffing plan, policies

Staff schedule

Realized shortagesand surpluses

Tactical Staff Scheduling

Analysis

The Challenge of Staff Scheduling

So…, how much staff is needed and how should they by scheduled?

Postpartum Staffing Needs

0

5

10

15

20

25

30

35

40

45

Su

n 1

2 am

Su

n 0

6 am

Su

n 1

2 p

m

Su

n 0

6 p

m

Mo

n 1

2 am

Mo

n 0

6 am

Mo

n 1

2 p

m

Mo

n 0

6 p

m

Tu

e 12

am

Tu

e 06

am

Tu

e 12

pm

Tu

e 06

pm

Wed

12

am

Wed

06

am

Wed

12

pm

Wed

06

pm

Th

u 1

2 am

Th

u 0

6 am

Th

u 1

2 p

m

Th

u 0

6 p

m

Fri

12

am

Fri

06

am

Fri

12

pm

Fri

06

pm

Sat

12

am

Sat

06

am

Sat

12

pm

Sat

06

pm

Nu

rses

Position Tour Type FTE Sun Mon Tue Wed Thu Fri Sat

1 (8 hrs, 5 days/wk) 1.0 O 7a-3p 7a-3p 7a-3p 7a-3p O 7a-3p2 (8,5) 1.0 O 3p-11p 3p-11p 3p-11p 3p-11p 3p-11p O3 (8,3) 0.6 O 8a-4p 8a-4p 8a-4p O O O4 (10,4) 1.0 O 7a-5p 7a-5p O 7a-5p 7a-5p O

5 (10,4) 1.0 O 7a-5p 8a-6p 7a-5p O 8a-6p O

6 (12,3) 1.0 O O 7a-7p 7a-7p O 7a-7p O7 (12,4) 1.0 7a-7p 7a-7p O 7a-7p 7a-7p O O

FTE = Full Time Equivalent (40 hrs/wk = 1.0 FTE)

Tour Type Tot FTEs

(8,5) 30.0 (8,3) 6.6 (10,4) 4.0 (12,3) 22.0

62.6

1

32

Staff Scheduling - It’s a Problem

Policies and practices affect total labor cost. little “tactical” scheduling analysis done

Overstaffing increases labor costs while understaffing may impact quality of care or service

Presents difficult combinatorial problems.

Consumes costly managerial time and effort; ad-hoc methods are the rule.

Bias often to favor employee over institutional needs.

Large impact on employee dissatisfaction and turnover

Not only in healthcare - police, fast food, call centers, airlines

Computerized systems under-utilized and often require inputs which themselves are the solution to a difficult scheduling analysis problem.

Elements of Scheduling EnvironmentsPlanning cycle is the number of weeks in the scheduling horizon

1, 2, 4, 6, 8, etc.

Each day is composed of planning periods 15 minutes, half-hours, hours, 8-hr shifts staffing or “coverage” requirements by planning period

where did they come from? hard constraints vs. soft constraints (e.g. understaffing costs)

A shift has a start time, a day of week, and a length (8hr shift, starting Mon @ 7:30am)

allowable start times

Tour Types: (periods/shift-shifts/week) (8-5) is someone who works 5 8-hr shifts per week (12-3, 12-3, 12-4) works three 12-hr shifts for two out of

three weeks and four 12-hr shifts for one of three weeks (12-3, 12-3 + 8-1) works three 12-hr shifts every week +

one 8-hr shift every other week

Elements of Scheduling Environments

Days-off PatternsSu Mo Tu We Th Fr Sa

0 1 1 1 1 1 0

1=working, 0=offSo, how many different patterns are there for working 5 out of 7

days?

Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa0 1 1 1 1 1 0 0 1 0 1 1 1 11 1 1 0 1 1 0 0 1 1 1 1 1 0

2-weeks

A tour is a combination of days worked and shifts worked workstretch - # days worked consecutively time between consecutive worked shifts – e.g. 16 hours

The “standard 3-shift nurse scheduling problem” day, afternoon, midnight shift each shift for each day of the week can have

unique staffing requirement multiple week issues

covering “off-shifts” (permanent, rotation) weekend rotation issues (A out of B weekends off) some tour types, e.g. (12-3,12-3,12-4)

Elements of Scheduling EnvironmentsEmployee preferences for various schedule characteristics

A challenge of scheduling problems is to balance schedule quality with coverage

Tactical vs. Operational Scheduling

Specific employees identified.

Schedule current staff to meet TOD/DOW staffing targets subject to scheduling policies, staff preferences and availability.

Done every two to six weeks.

Done by department staff.

Not concerned with specific employees.

Determine minimum staff needed to meet TOD/DOW staffing targets subject to various scheduling policies.

Done periodically as part of planning or a special study.

Done by department staff or operations analyst

OperationalTactical

Performance of Schedules

Overall scheduling efficiencyTotal Hours Required

Scheduling EfficiencyTotal Hours Scheduled

Distribution of under and overstaffing usually more desirable to “spread out”

under and overstaffing than concentrate it costs of understaffing

Schedule quality / implementability Fairness Ongoing manageability

Approaches to Solving Scheduling Problems

Trial and error + basic scheduling principles self-scheduling within management set parameters Get a “master cyclic schedule” built and try to follow it

making modifications as needed Various specialized heuristics or algorithms have been developed for different versions of scheduling problems

lower bounds on staff size then build a schedule Website devoted to Excel based templates for scheduling

http://www.shiftschedules.com/ Mathematical optimization models Artificial intelligence based techniques

suited for finding good solutions for problems with many complicated constraints

Many different commercial scheduling systems exist with widely varying capabilities and incorporating one or more of the above approaches

Classes of Scheduling Problems

Days-off scheduling staffing specified at daily level (1 or more “standard

shifts” per day) by DOW find min staff size to meet coverage and other

constraints on weekends worked, workstretch, allowable patterns

traditional nurse scheduling

Shift scheduling usually posed as a 1-day problem with staffing

requirements specified by time of day (e.g. hourly)

Tour scheduling basically a combination of days-off and shift scheduling

over some planning cycle (1 or more weeks)

Countless industry specific variations on all of these problems

Tactical Staff Scheduling Analysis

Used periodically as part of planningConcerned with capturing the essence of staff scheduling problems

TOD/DOW specific staffing targets allowable mix of tour types (shift lengths and # days worked per week) allowable shift start times and flexibility budget constraints days worked constraints (e.g. no 3 consecutive 12hr shifts)

Determine minimum staff size needed to meet coverage requirements subject to scheduling related constraintsQuantify cost of scheduling policies

Scenario1 2 3

8 hr 42 28 2310 hr 10 1012 hr 4

Total FTEs 42 38 37

Example - Shift Length Flexibility

All full time {

Dantzig’s Linear-Integer Programming Based Scheduling Optimization Model

“A Comment on Edie’s Traffic Delays at Toll Booths”, Dantzig, G. (1954)

Minimize

N

j jxjc1

Subject to:

N

j idjxijA1

for Pi 2,1

Njjx ,2,1for integer, and 0

(Total staffing cost)

(Staffing coverage in each period (e.g. hourly))

• Provided basis for 35 years of scheduling research and practice.• Many extensions:

– understaffing costs– varying skill levels and productivity– breaks and lunches– industry specific side constraints

cost of shift

# of people working shift

j

j

c j

x j

demand for staff in period

1 if shift call for work in period

otherwise

i

ij

d i

j iA

What is Optimization?In a business problem context

Loosely – Finding the “best” solution to a problemMore precise – Finding the answer to a problem that minimizes (maximizes) some objective or goal of a decision maker while taking into account business constraintsMathematical version – Finding the values of a set of decision variables that minimizes (maximizes) some objective function subject to constraints (equations or inequalities) on the decision variables

Some Optimization Concepts

A potential solution is feasible if it satisfies all the constraints we build in the model

a model is infeasible if no solution satisfies all the constraints

A potential solution is optimal if it is feasible AND it is better than all other feasible solutions in minimizing (or maximizing) our objective

a model is unbounded if we can make the objective as big as we want (assume we’re maximizing) and still satisfy the constraints

So, how do we search among the (potentially huge number of) feasible solutions to find the optimal solution?

that’s what optimization algorithms such as those built into the Excel Solver do

Linear Programming

Many useful, important problems can be formulated as:

Maximize c1x1 + c2x2 + … + cnxn (objective function)

Subject to a11x1 + a12x2 + … + a1nxn b1 (1st constraint)

a21x1 + a22x2 + … + a2nxn b2 (2nd constraint)… am1x1 + am2x2 + … + amnxn bm (mth constraint)

xi 0 , i=1..n, (decision variables)

The ci and aij are just numeric coefficients that are multiplied by the values of the decision variables (xi)

LP

LP=linear program

Yet Another ObservationMany useful, important problems can be formulated as:

Maximize c1x1 + c2x2 + … + cnxn (objective function)

Subject to a11x1 + a12x2 + … + a1nxn b1 (1st constraint)

a21x1 + a22x2 + … + a2nxn b2 (2nd constraint)…

am1x1 + am2x2 + … + amnxn bm (mth constraint)

xi 0 , i=1..n, (decision variables)

Some of the xi must be integers

MIP

MIP=mixed integer-linear program

So, what is different?

Some of the toughest mathematical problems solved routinely in business today are optimization problems

Example 1: Simple 1 week, days-off problem

• Formulated model in Excel and we will solve it using Solver• Goal 1: give flavor of optimization applied to scheduling• Goal 2: illustrate fact that scheduling policies affect staffing needs• Goal 3: real scheduling problems can lead to huge optimization problems

SchedulingDSS_Northpark.xlsScheduling_AdvancedDaysOff1.xlsScheduling_AdvancedDaysOff2.xls

Example 2: Simple 1 day, shift scheduling problems

• Formulated model in Excel and we will solve it using Solver• Goal 1: see difference between shift and days-off scheduling• Goal 2: treat staffing requirements as both hard and soft constraints• Goal 3: real scheduling problems can lead to huge optimization problems

ShiftSchedulingModel1.xlsShiftSchedulingModel2.xls

Example 2-Week Schedule• Creating a sample schedule is good “test” of whether you’ve come up with

an implementable solution• Schedule can be reviewed by staff for undesirable characteristics, errors,

other ideas for improvement• Sample schedule helps sell scheduling policy changes because people can

visualize the end product

Cyclic Schedules Idea is to create a set of schedules that employees cycle through. Various mathematical methods, computerized and trial and error approaches to creating cyclic schedules

Pros – schedules can be specified well in advance, fair, once created relatively easy to manage for stable workforce

Cons – very rigid, difficult for mix of full/part time staff, difficult when varying shift lengths, difficult for 24/7 operations

http://www.shiftschedules.com/

Coverage Report – Comparison of Targeted to Scheduled Staff Levels

Target=Min staff requirements

Sched=Staff scheduled

+/- = Over/understaffing

FTE Summary# of Shifts LDR Postpartum LDR+Postpart LDRP

Shift Worked in 2,150 Births 2,150 Births 2,150 Births 2,150 BirthsLength Two Weeks FTE Const Flex Const Flex Const Flex Const Flex

Mil 12 hr Full Time 7 1.05 16.8 12.6 16.8 14.7 33.6 27.3 27.3 23.1 Mil 10 hr Full Time 8 1.00 - 3.0 - 3.0 - 6.0 - 2.0 Mil 8 hr Full Time 10 1.00 - - - - - - - - Civ 12 hr Full Time 6+one 8 hr 1.00 6.9 4.9 7.8 2.9 14.7 7.8 12.0 6.9 Civ 8 hr Full Time 10 1.00 2.0 - 3.0 3.0 5.0 3.0 3.0 3.0 Civ 8 hr Part Time 8 0.80 - 0.8 1.6 0.8 1.6 1.6 0.8 3.2 Civ 8 hr Part Time 6 0.60 0.6 - - 0.6 0.6 0.6 0.6 - Civ 8 hr Part Time 4 0.40 0.8 1.2 0.4 0.8 1.2 2.0 - - Civ 4 hr Part Time 10 0.50 - 1.0 - 0.5 - 1.5 - 0.5 Civ 4 hr Part Time 8 0.40 - - - 0.4 - 0.4 - 0.4 Civ 4 hr Part Time 6 0.30 - 0.6 - 0.6 - 1.2 - 0.6

Number of scheduled FTEs 27.1 24.1 29.6 27.3 56.7 51.4 43.7 39.7

Position Summary# of Shifts LDR Postpartum LDR+Postpart LDRP

Shift Worked in 2,150 Births 2,150 Births 2,150 Births 2,150 BirthsLength Two Weeks FTE Const Flex Const Flex Const Flex Const Flex

Mil 12 hr Full Time 7 1.05 16 12 16 14 32 26 26 22 Mil 10 hr Full Time 8 1.00 - 3 - 3 - 6 - 2 Mil 8 hr Full Time 10 1.00 - - - - - - - - Civ 12 hr Full Time 6+one 8 hr 1.00 7 5 8 3 15 8 12 7 Civ 8 hr Full Time 10 1.00 2 - 3 3 5 3 3 3 Civ 8 hr Part Time 8 0.80 - 1 2 1 2 2 1 4 Civ 8 hr Part Time 6 0.60 1 - - 1 1 1 1 - Civ 8 hr Part Time 4 0.40 2 3 1 2 3 5 - - Civ 4 hr Part Time 10 0.50 - 2 - 1 - 3 - 1 Civ 4 hr Part Time 8 0.40 - - - 1 - 1 - 1 Civ 4 hr Part Time 6 0.30 - 2 - 2 - 4 - 2

Number of scheduled employees 28 28 30 31 58 59 43 42

Mil Benefit Factor ? ? ? ? ? ? ? ?Civ Benefit Factor Full time ? ? ? ? ? ? ? ?Civ Benefit Factor Part time ? ? ? ? ? ? ? ?

Number of FTEs on Staff ? ? ? ? ? ? ? ?

Sample summary

report from a tactical

scheduling analysis

FTE implications of Constrained vs. Flexible scheduling policiesSummary of FTEs and # of positionsThese solutions were derived from user specified scheduling policies and a scheduling optimization modelNote also the variance pooling effect that an LDRP gives

Sample ApplicationsSurgical nurses/techsCommunications operatorsAppointment scheduling clerksShort stay unit nursesRecovery room nursesMedical transcriptionistsRadiation oncology techniciansObstetrical nurses

How much staff needed?Can current staff absorb increased demand through rescheduling?What are the potential savings from increased flexibility in shift lengths and start times? By how much can we improve customer service through scheduling changes?

Isken, M.W. and W.M. Hancock, 1998, “Tactical Staff Scheduling Analysis for Hospital Ancillary Units”, Journal of the Society for Health Systems, Vol. 5, No. 4, pp. 11-23.

Comments on Tactical Scheduling

How do shift start times and shift lengths match the work flow of the department?

can’t make general statements that certain shift lengths or scheduling practices are “good” or “bad”

look for opportunities to smooth workload to ease the scheduling burden

Pay attention to policies and procedures regarding the definition of OT

>40 hrs/week vs. >80 hrs/pay period

Schedule desirability can vary widely by employee don’t assume what people will and will not like

Important to involve staff in analysis of scheduling policies easy for them to undermine intangibles not captured by scheduling models

Another Link between staffing and scheduling

Time of day staffing targets are really decision variables,

Simultaneous solution of staffing targets and schedules may lead to better solutions from cost, service, and schedule quality perspectives. Preliminary experimental results are promising.

Considers workload smoothing, buffering, and scheduling schemes.

Operational setting drives the model building process (Lab and Transcription).

Challenge is resulting problems more difficult to solve (research ongoing)

0

2

4

6

8

10

12

14

16

0:00

2:00

4:00

6:00

8:00

10:00

12:00

14:00

16:00

18:00

20:00

22:00

0

2

4

6

8

10

12

14

16

0:00

2:00

4:00

6:00

8:00

10:00

12:00

14:00

16:00

18:00

20:00

22:00

Operational Personnel Scheduling

The ongoing process of creating and managing staff schedules Balancing system needs with staff availability and preferences Several methods: computerized scheduling systems self-scheduling manual scheduling done by committee or

manager

A difficult, time consuming process it’s like doing a really hard jigsaw puzzle

Nurse Scheduling Challenges

24/7 coverage neededWorkload varies by shift by skill level by unitRotation to off-shifts?Multiple skill levels (RN, LPN, aide, etc.)Covering weekendsShortage of personnelDealing with daily fluctuations in supply & demand OT, agency, part-time, float on/off unit,

contingent, send home, call-in

ANSOS

Typical architecture of Computerized Personnel Scheduling Systems

Personnel

Autom atedScheduling

W orkload

StoredSchedules

ScheduleEditor

Schedules andManagem ent

Reports

Identif icationAvailabilityPreferences

Staffing Targets

Schedules

Active Schedules

Schedules

PersonnelModule External Serv ice

Delivery SupportSystem

W orkload Data

External Hum anResources

System

HR Data

W orkloadModule

Supports day to day scheduling ofcurrent staff.

Wide range of systemcapabilities and cost.

Healthcare, retail, police, fire/EMS, telesales, tech support, fast food, banking

ANSOS – Per Se TechnologiesANSOS - One Staff

• Created in 1970s by Warner, tested at UMMC• The standard for nurse scheduling software• Staffing requirements, scheduling policies, and nurse preferences

• optimization model based• Integrates with 3rd party PCS• Numerous add-on modules

• Shift centric as opposed to time of day centric

• Extent of use varies widely among institutions

• glorified typewriter vs. sophisticated auto-scheduler

See “Automated nurse scheduling” by Warner et al that

was passed out last time

A few scheduling packagesANSOS - http://www.per-se.com/forhospitals/h_onestaff.aspActiveStaffer - http://www.api-wi.com/products/activestaffer.aspAtStaff - http://www.atstaff.com/Products/Products.htmAcuStaf - http://www.acustaf.com/Pathways Staff Scheduling - http://www.hboc.com/Shiftwork Solutions - http://www.shift-schedules.com/ShiftMaker - http://www.vastech.com/24-7/solutions/vastech24-7/247modules.htmESP eXpert - http://www.total-care.com/InTime - http://www.intimesoft.com/VSS Pro - http://www.abs-usa.com/index.eplKronos - http://www.kronos.com/ScheduleSource - http://www.schedulesource.com/content/scheduling/default.aspORBIS - http://www.sieda.com/features_e.htmVarious packages - http://www.hr-software.net/pages/217.htmStaffSchedule.com - http://www.staffscheduling.com/schedule.htm

web based scheduling

Evaluating Computerized Scheduling Systems

How are staffing requirements specified (TOD or Shift)?

Auto-scheduling or just a schedule manager?

Schedule editing

Support for self scheduling?

Single vs. multiple weeks

Easy access to emp. data

Employee requests and preferences

Skeleton rotation patterns

Archive past schedules

Reporting – built in and ad-hoc capabilities

Does it handle YOUR scheduling environment?

Can be integrated with 3rd party workload systems?Can be integrated with 3rd party timekeeping, payroll, and/or HR systems?Cost and licensing

consulting, installation, training, sofware, hardware, maintenance, add-on modules

Tech supportStrong user baseHardware and software requirementsHow applicable to multiple departments within the same institution?

Flexible Scheduling IdeasMix of different shift lengths >8 hr shift gives more days off per week easier to match fluctuating workload

Increase number of allowable start times easier to match fluctuating workload more complex to manage; rotation issues

Mix of full and part-time tour types part-timers can provide invaluable flexibility

in dealing with vacations, odd shifts, absences, workload variation by day of week and time of day

Flexible Scheduling Ideas Float pools (internal agency) cross training sufficient voluntary “floaters”? How big should the pool be? How should the

“core” staffing levels be set?

Temp agencies pay a premium for staff on demand issues with integration with permanent staff

Contingent usually from the employees perspective

On-call Forced TO (time-of) and Forced OT not a super staff satisfier

Miscellaneous issues Circadian rhythms researchers study effect of shift work

Shift overlap communication improvements

12hr tour types 334, 3334, 33-1, 2-12 2-8 cost and scheduling implications

Self scheduling need to have a good staffing plan and

set of scheduling policies

Learning More

Professional association trade journals and academic journals Nursing Management, Medical Laboratory

Observer, Nursing Times, and numerous other Interfaces Search Medline for “staff scheduling”

Google it – “healthcare staff scheduling”Introduction to Employee Scheduling: Issues, Problems, Methods – Nanda and Browne