Staffing and Scheduling – Part
II
HCM 540 – Operations
Management
Primary Objectives
1. Staff scheduling is a difficult, time
2.
3.
4.
5.
consuming managerial problem
Many flavors of staff scheduling
problems
Staff scheduling inextricably linked with
determining total amount of staff
Tactical and operational staff scheduling
Computerized staff scheduling systems
High Level Staffing Framework
Budgeting and
Planning
• Annual or as needed
• Planned capacity
• Staffing/scheduling
policies
Tactical Staff
Scheduling
Analysis
Budget, staffing plan, policies
Operational
staffing/scheduling
• Every 2-6 weeks
• Target staffing levels
• Create employee
schedules for core staff
Realized shortages
and surpluses
Staff schedule
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)
The Challenge of Staff Scheduling
1
Postpartum Staffing Needs
45
40
Nurses
35
30
25
20
15
10
5
Sat 06 pm
Sat 12 pm
Sat 06 am
Sat 12 am
Fri 06 pm
Fri 12 pm
Fri 06 am
Fri 12 am
Thu 06 pm
Thu 12 pm
Thu 06 am
Thu 12 am
Wed 06 pm
Wed 12 pm
Wed 06 am
Wed 12 am
Tue 06 pm
Tue 12 pm
Tue 06 am
Tue 12 am
Mon 06 pm
Mon 12 pm
Mon 06 am
Mon 12 am
Sun 06 pm
Sun 12 pm
Sun 06 am
Sun 12 am
0
So…, how much staff is needed and how should they by scheduled?
2
Position
Tour Type
FTE Sun Mon Tue Wed Thu
Fri
Sat
Tour Type Tot FTEs 3
1
2
3
4
5
6
7
(8 hrs, 5 days/wk)
(8,5)
(8,3)
(10,4)
(10,4)
(12,3)
(12,4)
1.0 O
1.0 O
0.6 O
1.0 O
1.0 O
1.0 O
1.0 7a-7p
FTE = Full Time Equivalent (40 hrs/wk = 1.0 FTE)
7a-3p
3p-11p
8a-4p
7a-5p
7a-5p
O
7a-7p
7a-3p
3p-11p
8a-4p
7a-5p
8a-6p
7a-7p
O
7a-3p
3p-11p
8a-4p
O
7a-5p
7a-7p
7a-7p
7a-3p
3p-11p
O
7a-5p
O
O
7a-7p
O
7a-3p
3p-11p O
O
O
7a-5p
O
8a-6p
O
7a-7p
O
O
O
(8,5)
(8,3)
(10,4)
(12,3)
30.0
6.6
4.0
22.0
62.6
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 Environments
Planning 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 Patterns
1=working, 0=off
So, how many different patterns are
there for working 5 out of 7 days?
Su Mo Tu We Th Fr Sa
0 1 1 1 1 1 0
Su
0
1
Mo
1
1
Tu We
1
1
1
0
Th Fr
1
1
1
1
Sa
0
0
Su
0
0
Mo
1
1
Tu We
0
1
1
1
Th Fr
1
1
1
1
Sa
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 Environments
Employee
preferences
for various
schedule
characteristics
A challenge of
scheduling
problems is to
balance
schedule
quality with
coverage
Tactical vs. Operational
Scheduling
Tactical
Not concerned with specific
employees.
Determine minimum staff needed to
meet TOD/DOW staffing targets
subject to various scheduling
policies.
Operational
Specific employees identified.
Schedule current staff to meet
TOD/DOW staffing targets
subject to scheduling policies,
staff preferences and
availability.
Done periodically as part of planning
or a special study.
Done every two to six weeks.
Done by department staff or
operations analyst
Done by department staff.
Performance of Schedules
Overall scheduling efficiency
Total Hours Required
Scheduling Efficiency 
Total 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 planning
Concerned 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 constraints
Quantify cost of scheduling policies
Example - Shift Length Flexibility
All full time
{
8 hr
10 hr
12 hr
Total FTEs
1
42
Scenario
2
28
10
42
38
3
23
10
4
37
Dantzig’s Linear-Integer Programming Based Scheduling Optimization
Model
N
Minimize å c j x j
j1
Subject to:
N
å Aij x j ³ di
j1
(Total staffing cost)
for i  1,2KP
c j  cost of shift j
x j  # of people working shift j
(Staffing coverage in each period (e.g. hourly))
x j ³ 0 and integer, for j  1,2,K N
di  demand for staff in period i
1 if shift j call for work in period i
Aij  
otherwise

• 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
“A Comment on Edie’s Traffic Delays at Toll Booths”, Dantzig, G. (1954)
What is Optimization?
In a business problem context
Loosely – Finding the “best” solution to a
problem
More precise – Finding the answer to a
problem that minimizes (maximizes) some
objective or goal of a decision maker while
taking into account business constraints
Mathematical 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:
LP
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 ³ 0 , i=1..n, (decision variables)
The ci and aij are just numeric coefficients
that are multiplied by the values of the decision
variables (x )
LP=linear program i
Yet Another Observation
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)
MIP
xi ³ 0 , i=1..n, (decision variables)
Some of the xi must be integers
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.xls
Scheduling_AdvancedDaysOff1.xls
Scheduling_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.xls
ShiftSchedulingModel2.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
Sched=Staff scheduled
Target=Min staff requirements
+/- = Over/understaffing
FTE Summary
Sample
summary report
from a tactical
scheduling
analysis
FTE implications of
Constrained vs. Flexible
scheduling policies
Summary of FTEs and #
of positions
These solutions were
derived from user
specified scheduling
policies and a
scheduling optimization
model
Note also the variance
pooling effect that an
LDRP gives
Mil
Mil
Mil
Civ
Civ
Civ
Civ
Civ
Civ
Civ
Civ
Mil
Mil
Mil
Civ
Civ
Civ
Civ
Civ
Civ
Civ
Civ
# of Shifts
Shift
Worked in
Length
Two Weeks
12 hr Full Time
7
10 hr Full Time
8
8 hr Full Time
10
12 hr Full Time 6+one 8 hr
8 hr Full Time
10
8 hr Part Time
8
8 hr Part Time
6
8 hr Part Time
4
4 hr Part Time
10
4 hr Part Time
8
4 hr Part Time
6
Number of scheduled FTEs
FTE
1.05
1.00
1.00
1.00
1.00
0.80
0.60
0.40
0.50
0.40
0.30
LDR
Postpartum LDR+Postpart
LDRP
2,150 Births 2,150 Births 2,150 Births 2,150 Births
Const Flex Const Flex Const Flex Const Flex
16.8
12.6
16.8
14.7
33.6
27.3
27.3
23.1
3.0
3.0
6.0
2.0
6.9
4.9
7.8
2.9
14.7
7.8
12.0
6.9
2.0
3.0
3.0
5.0
3.0
3.0
3.0
0.8
1.6
0.8
1.6
1.6
0.8
3.2
0.6
0.6
0.6
0.6
0.6
0.8
1.2
0.4
0.8
1.2
2.0
1.0
0.5
1.5
0.5
0.4
0.4
0.4
0.6
0.6
1.2
0.6
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 Births
Length
Two Weeks FTE Const Flex Const Flex Const Flex Const Flex
12 hr Full Time
7
1.05
16
12
16
14
32
26
26
22
10 hr Full Time
8
1.00
3
3
6
2
8 hr Full Time
10
1.00
12 hr Full Time 6+one 8 hr 1.00
7
5
8
3
15
8
12
7
8 hr Full Time
10
1.00
2
3
3
5
3
3
3
8 hr Part Time
8
0.80
1
2
1
2
2
1
4
8 hr Part Time
6
0.60
1
1
1
1
1
8 hr Part Time
4
0.40
2
3
1
2
3
5
4 hr Part Time
10
0.50
2
1
3
1
4 hr Part Time
8
0.40
1
1
1
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
Civ Benefit Factor
Full time
Part time
Number of FTEs on Staff
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
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?
?
Sample Applications
Surgical nurses/techs
Communications operators
Appointment scheduling clerks
Short stay unit nurses
Recovery room nurses
Medical transcriptionists
Radiation oncology technicians
Obstetrical 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)
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0
0:
00
2:
00
4:
00
6:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
16
14
0:
00
2:
00
4:
00
6:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
16
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 needed
Workload varies by shift by skill level by unit
Rotation to off-shifts?
Multiple skill levels (RN, LPN, aide, etc.)
Covering weekends
Shortage of personnel
Dealing 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
External Human
Resources
System
Personnel
Module
Workload
Module
HR Data
Staffing Targets
Personnel
External Service
Delivery Support
System
Workload Data
Workload
Identification
Availability
Preferences
Automated
Scheduling
Active Schedules
Schedule
Editor
Schedules and
Management
Reports
Schedules
Supports day to
day scheduling of
current staff.
Stored
Schedules
Schedules
Wide range of system
capabilities and cost.
Healthcare, retail, police,
fire/EMS, telesales, tech
support, fast food,
banking
ANSOS – Per Se Technologies
ANSOS - 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
See “Automated nurse
scheduling” by Warner et al that
was passed out last time
• Shift centric as opposed to time
of day centric
• Extent of use varies widely
among institutions
• glorified typewriter vs.
sophisticated auto-scheduler
A few scheduling packages
ANSOS - http://www.per-se.com/forhospitals/h_onestaff.asp
ActiveStaffer - http://www.api-wi.com/products/activestaffer.asp
AtStaff - http://www.atstaff.com/Products/Products.htm
AcuStaf - 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/vastech247/247modules.htm
ESP eXpert - http://www.total-care.com/
InTime - http://www.intimesoft.com/
VSS Pro - http://www.abs-usa.com/index.epl
Kronos - http://www.kronos.com/
ScheduleSource - http://www.schedulesource.com/content/scheduling/default.asp
ORBIS - http://www.sieda.com/features_e.htm
Various packages - http://www.hr-software.net/pages/217.htm
StaffSchedule.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 support
Strong user base
Hardware and software
requirements
How applicable to multiple
departments within the
same institution?
Flexible Scheduling Ideas
Mix 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