Chapter 19
Business Dynamics by John D. Sterman
Labor Supply Chains and the
Origin of Business Cycles
Chapter outline
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The Labor Supply Chain
Interactions of Labor and Inventory
Management
Inventory-Workforce Interactions and
the Business Cycle
Summary
§ Labor supply chain (LSC)
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The human resource supply chain
Omission of labor and capital in
production model- not realistic
We now apply the stock management
structure to represent labor
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Hiring rate- delay
Quit rate (Attrition rate)-delay
Structure of Labor and Hiring
Referring to figure 19-1 on page 758
 Labor=INTEGRAL (Hiring rate- Attrition rate, Laborto)
..19-1
 Attrition Rate= Labor/Avg Duration of Employment
..19-2
 Hiring Rate=Vacancies/Time to fill vacancies
..19-3
 Vacancies=INTEGRAL (Vacancy Creation RateVacancy Closure Rate, vacanciesto).. 19-4
 Vacancy Closure Rate =Hiring Rate
..19-5
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Why isn’t there a direct flow from vacancies to labor?
What can you say about the source of hiring?
-
Vacancy
Cancellation
Time
+
+
-
Maximum
Vacancy
Cancellation
Rate
+
Average
Layoff Time
+
+
Vacancy
Cancellation
Rate
Layoff Rate
Desired
Vacancy
Cancellation
Rate
Expected
Time to Fill
Vacancies
B
+
+
Adjustment for
Vacancies
-
+
-
+
-
Average
Duration of
Employment
Average
Time to Fill
Vacancies
+
+
Quit Rate
Hiring Rate
+
+
Desired
+
Vacancy
Creation Rate
Desired
Labor
Labor
Vacancy
Closure Rate
Vacancy
Creation
+
+
Vacancies
Vacancy
Creation
Rate
<Initial Desired
Labor>
<Input>
Maximum
Layoff Rate
-
Labor
Adjustment
Time
Adjustment
for Labor
+
Desired
Vacancies
+
+
Expected
Attrition
Rate
B
Labor
Adj ustment
Vacancy
Adjustment
Time
Desired
Lay Off
Rate
+
+
Desired
Hiring Rate
+
Willingness
to Lay Off
+
More equations of key rates
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Vacancy Creation Rate= MAX(0, Desired Vacancy Creation rate)
..19-6
Desired Vacancy Creation Rate =Desired Hiring Rate+
adjustment for Vacancies
..19-7
Adjustment for Vacancies = (Desired Vacancies-Vacancies)/Time
to Adjust Vacancies
.. 19-8
Desired Vacancies = MAX(0, Exp Time to fill vacancies*Desired
Hiring Rate)
.. 19-9
Exp time to fill Vacancies = average time to fill Vacancies
.. 19-10
Desired Hiring rate= Expected Attrition rate +Adjustment for
Labor
..19-11
Expected Attrition rate=Attrition rate
..19-12
Adjustment for Labor=(Desired Labor-Labor)/Time to Adjust
Labor
..19-13
Behavior of LSC (Labor Supply
chain)
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Desired labor is ‘exogenous’
Hire time depends on several factors
Model parameters
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Avg employment time =100 weeks(2 yrs)
Time to fill vacancies= 8 weeks
Initial=1000 workers; Quit rate= 10/week
80 vacancies (in supply line)
Vacancies adj time= 4 weeks
Labor adj time = 13 weeks
Test run with 50% step at week 5
Behavior of LSC cont’d…
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Behavior is similar to stock management structure –on simulation
50% step sends desired vacancy creation rate from 10/week to
125/week
Think about need to down size?
We need ‘lay off rate’ and ‘vacancy cancellation rate’
Both these processes have time delays
Vacancy Cancellation rate=MIN (Desired vacancy cancellation rate,
Maximum vacancy cancellation rate)
..19-14
Maximum Vacancy cancellation rate= vacancies/Vacancy cancellation
time
..19-15
Desired Vacancy Cancellation rate= MAX(0, -Desired Vacancy
Creation Rate)
..19-16
Similar logic is applied for formulation of 19-17, 19-18 and 19-19
(refer page 764) in respect of Layoff Rate
Willingness to lay off=0 =no layoff policy; =1 layoff ok
Interactions of Labor and
Inventory Management
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Extending the model to include production structure
from Chapter 18
Give a 20% step increase in Customer orders
Production starts adjust to desired starts with delaylabor hiring etc- so Inventory takes longer to adjust
System oscillates vigorously
Production Start rate= Labor * workweek* Labor
productivity
..19-20
Desired Labor= Desired Production Starts/(Standard
workweek*Expected Productivity)
..19-21
Source of Oscillation
Refer the phase plot on page 772
 Orders jump production same inventory falls.
Firm’s demand goes up desired production rises
but now labor needs to rise before WIP can rise
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With delays labor finally rises desired start rate
=customer orders. However, Inventory keeps falling
due to delay in Production process
Corrective forces acting on the system to adjust it to
the shock produce the oscillation, before the system
finally reaches new equilibrium at 20% above the
initial start point (10,000 widgets/week)
Adding Over time
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Work week= Standard Work week * Effect of
Schedule Pressure on workweek
Effect of Schedule pressure on work week=
ƒ(Schedule Pressure)
Schedule Pressure= Desired Production
Starts/Standard Production Starts
Standard Production Starts= labor* Standard
Workweek*Expected Productivity
Schedule Pressure<1 => Surplus labor
Schedule Pressure>1 => Shortage of labor
Schedule Pressure-Workweek
Refer to the plot on page 775
 Reference line workweek=1
 45% line workweek adjusted per schedule pressure
(overtime policy that adjusts to work pressure)
 Workweek typically lies between the two reference
lines- not reasonable to adjust workweek to expect
workweek to be 80 hours under pressure- or to let
workweek fall below 30 hours under no pressure
 Management would like to continue production for
stocking purpose when pressure <1 (to keep workers
busy, skills intact etc)
Flexible workweek
Refer the new phase plot on page 778
 Flexible workweek makes it possible to reach new
equilibrium with less oscillation than under fixed work
week scenario
 System recovers from shock without generating
cycles seen under constant workweek case
 Obviously the workweek can not increase indefinitely
and stretching the work week for sustained periods
of time may lead to undesirable results- Since labor is
simultaneously adjusting to the desired level defined
by current demand- Schedule Pressure will ease
Cost of instability
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There is no account by name ‘cost of
instability’
However, its well known that instability and
oscillation are costly
To properly assess the impact of policies one
needs to identify costs of instability and
include them in the model
Conversely, define the profit function in short
and long run and try to optimize such profit
function variable in the model
More improvements/variations
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Training and Experience
Separation of rookies and experts
policy of lay offs- quit rates etc
On the job training delays and costs
Think of industries where trained staff
are not readily available/training time is
too long (aerospace, machine tools)
Business Cycles
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Business Cycles are caused by the
fundamental structure of the industrial
economy rather than other factors
IT has helped in several ways to reduce the
instability by providing instantaneous
information (delay reduction)
Lean manufacturing, JIT etc also help reduce
the instability