© J. Christopher Beck 20051 Lecture 29: Supply Chain Scheduling 3.

© J. Christopher Beck 2005 1

Lecture 29: Supply Chain Scheduling 3


Outline Medium-term Planning

Data is aggregated but still complex! Short-term Scheduling Medium-term/Short-term

Integration


Supply Chain Scheduling


Supply Chain Decomposition

Medium-term plannin

g

Short-term

sched-uling

Stage 1 Stage 2 Stage 3 Stage 4


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


Medium-term Planning Costs

Production cost

Storage cost

Transportation costTardiness cost

Non-delivery cost

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*2

3

Cost of moving one unit of any type from DC to the customer

Tardiness 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

Non-delivery Penalty cost for never delivering one unit of any product


Medium-term Planning Costs

Production cost

Storage cost

Transportation costTardiness cost

Non-delivery cost

cpij

h

Cmi2*

Cmi*3

Cm*23

w’’j

w’’’j


IP Objective:Minimize

2

143

2

142

3

1

2

13

3

1

2

12

4

1

2

1

2

1

23*

4

1

2

1

2

133*

4

1

2

1

2

12*2

4

1

2

12

4

1

2

1

2

1

jj

jj

t jjtj

t jjtj

t j ijt

m

t j ijtii

m

t j ijtii

m

t jjt

t j iijtij

p

vv

vwvw

zcycyc

hqxc

Production Costs

xijt = # units of family j produced at factory i in week t



2

143

2

142

3

1

2

13

3

1

2

12

4

1

2

1

2

1

23*

4

1

2

1

2

133*

4

1

2

1

2

12*2

4

1

2

12

4

1

2

1

2

1

jj

jj

t jjtj

t jjtj

t j ijt

m

t j ijtii

m

t j ijtii

m

t jjt

t j iijtij

p

vv

vwvw

zcycyc

hqxc

Storage Costs

q2jt = # units of family j in storageat DC at end of week t



2

143

2

142

3

1

2

13

3

1

2

12

4

1

2

1

2

1

23*

4

1

2

1

2

133*

4

1

2

1

2

12*2

4

1

2

12

4

1

2

1

2

1

jj

jj

t jjtj

t jjtj

t j ijt

m

t j ijtii

m

t j ijtii

m

t jjt

t j iijtij

p

vv

vwvw

zcycyc

hqxc

Transportation Costs

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


IP Objective: Minimize

2

143

2

142

3

1

2

13

3

1

2

12

4

1

2

1

2

1

23*

4

1

2

1

2

133*

4

1

2

1

2

12*2

4

1

2

12

4

1

2

1

2

1

jj

jj

t jjtj

t jjtj

t j ijt

m

t j ijtii

m

t j ijtii

m

t jjt

t j iijtij

p

vv

vwvw

zcycyc

hqxc

Tardiness Costs

v2jt = # units of family j tardyat DC at end of week t

v3jt = # units of family j tardyat customer at end of week t



2

143

2

142

3

1

2

13

3

1

2

12

4

1

2

1

2

1

23*

4

1

2

1

2

133*

4

1

2

1

2

12*2

4

1

2

12

4

1

2

1

2

1

jj

jj

t jjtj

t jjtj

t j ijt

m

t j ijtii

m

t j ijtii

m

t jjt

t j iijtij

p

vv

vwvw

zcycyc

hqxc

Non-delivery Costs

v2j4 = # units of family j notdelivered to DC at end

of horizonv3j4 = # units of family j not

delivered to customer at end of horizon


Production Constraints

2,1;4,...,1168ˆ2

1

itxpj

ijtij

Estimate processing time for1 unit of family j at factory i

Total weekly hours

# 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)


Medium-term Planning Computes:

Productionamounts

Storage amounts

Transportation amounts


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?


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!


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?


This is Your Factory – How Do You Model It?


Possible Models & Components

Flowshop with 5 tasks and parallel resources?

Single machine?

Sequence dependent setups? Buffer capacity?


FSP with Parallel Machines

Minimize

Hard problem!

ijkijkjj sITw 21

Setup cost if job k followsjob j on machine i

Weighting parameters


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!


The Modeling Problem

It is an open research question of how you take a real factory (or call centre) and create a “model” of it with optimization tools What’s the best level of detail? What can you ignore?

© J. Christopher Beck 20051 Lecture 29: Supply Chain Scheduling 3.

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Transcript of © J. Christopher Beck 20051 Lecture 29: Supply Chain Scheduling 3.