Lecture 29:
Supply Chain Scheduling 3
© J. Christopher Beck 2008
1
Outline

Medium-term Planning



Data is aggregated but still complex!
Short-term Scheduling
Medium-term/Short-term Integration
© J. Christopher Beck 2008
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Readings

P Ch 8.4,
8.5
© J. Christopher Beck 2008
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Supply Chain Scheduling
© J. Christopher Beck 2008
4
Supply Chain Decomposition
Mediumterm
planning
Shortterm
scheduling
Stage 1
© J. Christopher Beck 2008
Stage 2
Stage 3
Stage 4
5
Medium-term Planning

Assumptions:




4 week horizon
2 product families
3 stages: 2 factories, 1 DC, 1 customer
Factories work 24/7 = 168 hours/week
© J. Christopher Beck 2008
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Medium-term Planning Costs
Storage cost
Non-delivery cost
Production cost
Tardiness cost
Transportation cost
© J. Christopher Beck 2008
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Production
cpij
Cost to produce one unit of family j at factory i
Storage
h
Weekly holding cost for one unit of any type at DC
Transportation
Cmi2* Cost of moving one unit of any type from factory i
to DC
Cmi*3 Cost of moving one unit of any type from factory i
to the customer
Cm*23 Cost of moving one unit of any type from DC to
the customer
Tardiness
Non-delivery
w’’j
Cost per unit per week for an order of family i
delivered late to DC
w’’’j
Cost per unit per week for an order of family i
delivered late to customer

Penalty cost for never delivering one unit of any
product
Medium-term Planning Costs
Storage cost
h
Non-delivery cost

Production cost
cpij
Tardiness cost
Transportation cost
Cmi2*
Cmi*3
Cm*23
© J. Christopher Beck 2008
w’’j
w’’’j
9
IP Objective:
x
Minimize
ijt
4
2
2
4
= # units of family j produced
at factory i in week t
2
p
c
 ij xijt   hq2 jt 
t 1 j 1 i 1
4
2
t 1 j 1
2
4
2
2
4
2
2
m
m
m
c
y

c
y

c
i
2
*
i
*
3


 *23 z jt 
i 2 jt
i 3 jt
t 1 j 1 i 1
3
t 1 j 1 i 1
2
3
 wv
t 1 j 1
j 2 jt
2
v
j 1
2
  wjv 3 jt 
t 1 j 1
2
2 j4
t 1 j 1 i 1
 v3 j 4
Production Costs
j 1
© J. Christopher Beck 2008
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IP Objective:
q
Minimize
4
2
2
4
2jt
= # units of family j in storage
at DC at end of week t
2
p
c
 ij xijt   hq2 jt 
t 1 j 1 i 1
4
2
t 1 j 1
2
4
2
2
4
2
2
m
m
m
c
y

c
y

c
i
2
*
i
*
3


 *23 z jt 
i 2 jt
i 3 jt
t 1 j 1 i 1
3
t 1 j 1 i 1
2
3
 wv
t 1 j 1
j 2 jt
2
v
j 1
2
  wjv 3 jt 
t 1 j 1
2
2 j4
t 1 j 1 i 1
 v3 j 4
Storage Costs
j 1
© J. Christopher Beck 2008
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IP Objective:
Minimize
4
2
2
 c
t 1 j 1 i 1
4
2
4
p
2
yi2jt
# of units of family j
transported from factory i to
DC in week t
yi3jt
# of units of family j
transported from factory i to
customer in week t
zjt
# of units of family j
transported from DC to
customer in week t
x   hq2 jt 
ij ijt
t 1 j 1
2
4
2
2
4
2
2
m
m
m
c
y

c
y

c
i
2
*
i
*
3


 *23 z jt 
i 2 jt
i 3 jt
t 1 j 1 i 1
3
t 1 j 1 i 1
2
3
 wv
t 1 j 1
j 2 jt
2
v
j 1
2
  wjv 3 jt 
t 1 j 1
2
2 j4
t 1 j 1 i 1
 v3 j 4
Transportation Costs
j 1
© J. Christopher Beck 2008
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IP Objective:
Minimize
4
2
2
4
v2jt = # units of family j tardy
at DC at end of week t
2
p
c
 ij xijt   hq2 jt 
t 1 j 1 i 1
4
2
v3jt = # units of family j tardy
at customer at end of week t
t 1 j 1
2
4
2
2
4
2
2
m
m
m
c
y

c
y

c
i
2
*
i
*
3


 *23 z jt 
i 2 jt
i 3 jt
t 1 j 1 i 1
3
t 1 j 1 i 1
2
3
 wv
t 1 j 1
j 2 jt
2
v
j 1
2
  wjv 3 jt 
t 1 j 1
2
2 j4
t 1 j 1 i 1
 v3 j 4
Tardiness Costs
j 1
© J. Christopher Beck 2008
13
IP Objective:
Minimize
4
2
2
4
2
p
c
 ij xijt   hq2 jt
t 1 j 1 i 1
4
2
v2j4 = # units of family j not
delivered to DC at end
of horizon
v3j4 = # units of family j not
delivered to customer at end
of horizon

t 1 j 1
2
4
2
2
4
2
2
m
m
m
c
y

c
y

c
i
2
*
i
*
3


 *23 z jt 
i 2 jt
i 3 jt
t 1 j 1 i 1
3
t 1 j 1 i 1
2
3
 wv
t 1 j 1
j 2 jt
2
v
j 1
2
  wjv 3 jt 
t 1 j 1
2
2 j4
t 1 j 1 i 1
 v3 j 4
Non-delivery Costs
j 1
© J. Christopher Beck 2008
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Production Constraints
2
 pˆ x
j 1
ij ijt
 168 t  1,...,4; i  1,2
Total weekly hours
Estimate processing time for
1 unit of family j at factory i
# units of family j produced
at factory i in week t
Plus storage constraints, transportation constraints,
tardiness constraints, and non-delivery constraints
(see P p. 189-190)
© J. Christopher Beck 2008
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Medium-term Planning
Computes:
Storage amounts
Production
amounts
Transportation amounts
© J. Christopher Beck 2008
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Short Term Scheduling

Production schedule at factories


what products on what machines and
when?
Transportation schedule between
factories, DC, and customers

what products on what trucks and when?
© J. Christopher Beck 2008
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Short Term Scheduling


For each week we know the number of
items of each family that need to be
produced (from xijt)
However, that number was based on an
estimate of the processing time
required!

In reality each product has a process plan
including release date, due date, quantity,
and set-ups!
© J. Christopher Beck 2008
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Looks Like a “Normal”
Scheduling Problem


(like we’ve been studying all along)
But … you are faced with the modeling
problem

How much of the “real world” do you
represent?
© J. Christopher Beck 2008
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This is Your Factory –
How Do You Model It?
© J. Christopher Beck 2008
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Possible Models &
Components



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Flowshop (FSP) with 5 tasks and
parallel resources?
Single machine?
Sequence dependent setups?
Buffer capacity?
© J. Christopher Beck 2008
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FSP with Parallel Machines

Minimize 1  w jT j   2  I ijk sijk
Weighting parameters

Setup cost if job k follows
job j on machine i
Hard problem!
© J. Christopher Beck 2008
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Single Machine

Schedule really depends on a single
bottleneck machine


if the bottleneck schedule is fixed,
everything else is easy
May be a much easier problem in
practice!
© J. Christopher Beck 2008
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The Modeling Problem

It is an open research question of how
you take a real factory (or call centre or
hospital or …) and create a “model” of
it with optimization tools


What’s the best level of detail?
What can you ignore?
© J. Christopher Beck 2008
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