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Enterprise-Wide Optimization Seminar

Integration of Supply Chain Design and Operation with Stochastic Inventory Management

Fengqi You and

Ignacio E. GrossmannCenter for Advanced Process Decision-making

Department of Chemical EngineeringCarnegie Mellon University

October 20, 2009

2Enterprise-Wide Optimization Seminar – Supply Chain Design and Operation with Stochastic Inventory Management

(*U.S. Census Bureau, “Manufacturing and Trade Inventories and Sales in U.S.”, August 2009; Smartops, S. Tayur, 2005)

Motivation•

Inventory is everywhere

•

A fact about U.S. inventories*Total value: $1.4 trillion (≈ 10% U.S. GDP)Estimated inefficiency: 50+ %Economic opportunity:

$700+ billion

•

Optimizing inventories across the entire Supply ChainWhich location and chemical to stock? –

Supply Chain Design & Operation

How much in each location under uncertainty? –

Stochastic Inventory

•

Objective: develop optimization models and methods

for integration of supply chain design and operation with stochastic inventory


•

Modeling the Stochastic Inventory SystemsDealing with uncertain customer demand and

uncertain supply

Uncertain lead time

and service level for multi-echelon systemsPotential saving by risk-pooling

•

Integrating Inventory Model with Supply Chain Design & OperationDifferent time scales: operational vs. strategicModeling the timing relationship

and demand uncertainty quantification

Measure of supply chain responsiveness•

Computational Challenge

Always leads to

Non-convex mixed-integer nonlinear program

(MINLP)−

That is why the integration has not been addressed. But, we like

MINLP !

Solving large-scale industrial size problems

Challenges


•

Review of Stochastic Inventory ModelsInventory control policies and modelsSingle-stage stochastic inventory systemMulti-echelon stochastic inventory system

•

Supply Chain Design with Stochastic InventoryIntegrating facility location with inventory managementSupply chain design with multi-echelon inventoryResponsive supply chain with stochastic inventory

•

Process Planning under Supply and Demand UncertaintyStochastic programming models and algorithmsSimulation framework, risk managementCase study with 12,000 uncertain

parameters

Time

Inve

ntor

y

Review period p

Inventory on hand

Lead time l

Safety Stock

Pipeline Inventory

Place orderPlace order

Inventory position

Receive order

Receive order

Outline

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Maximum Guaranteed Service Time of Markets (days)

Tot

al S

afet

y St

ocks

(Kto

n)

$62

$64

$66

$68

$70

$72

$74

Tot

al C

ost (

10^6

$)

Total Safety StockTotal Cost

38

3

4

1

5

8

12 13

16

17

32

28

H

Supplier

F

I

R

Market

Market

Market

Market

Market

Market

Market

Market

T

Supplier

Supplier

Market

Supplier

B

C

D

Supplier

E

A

M

G

J

O

Q

P

N

S

K

Supplier

Supplier

Supplier

Supplier

14 MarketL

Acetylene

Propylene

Benzene

Nitric Acid

Acetaldehyde

Acrylonitrile

Phenol

Acetone

Cumene

Ethylene

Carbon Monoxide

Methanol

Ethylbenzene

NaphthaChlorobenzene

Styrene

Ethanol

Ethylene Glycol

Acetic Acid

Byproducts


•


•


•

Process Planning under Supply and Demand UncertaintyStochastic programming models and algorithms Simulation framework, risk managementCase study with 12,000 uncertain parameters

Time

Inve

ntor

y

Review period p

Inventory on hand

Lead time l

Safety Stock

Pipeline Inventory

Place orderPlace order

Inventory position

Receive order

Receive order

Outline


Stochastic Inventory System

TimeSafety Stock

Reorder PointOrder placed

Lead Time

ReplenishmentInventory

Review of Stochastic Inventory Models


Inventory Profile with Safety Stocks

Maximum Inventory

Safety Stock

Time

Inventory

Cycle Inventory

Average Inventory

• Inventory System under Demand Uncertainty• Total Average Inventory = Cycle Inventory + Safety Stock



Inventory Control Policy

• What is an Inventory Policy?Determines when to re-order and how much to re-orderDecisions about inventory level and service level

• Periodical Review – Base-Stock PolicyInventory level is checked at regular periodic intervals (e.g. daily)Each time place an order

to bring inventory position

up to S

Inventory position = inventory on-hand + inventory in-transit• Continuous Review – (Q, r) Policy

inventory level is continuously trackedWhen inventory level falls to r, order for quantity of QSame as base-stock policy, when r+Q=S



Time

Inventory on-hand

Review period pReview period p

Inventory position

Base-Stock Level S

Place order

Receive order

Lead time l

Constant Demand Rate = D

Base-stock Inventory PolicyInventory

• Inventory position = inventory on-hand + inventory in-transit• Base-stock level is not a “physical” stock level in the storage facility

Safety Stock



constant demand rate = D

replenishment arrive

Time

Inventory

Place order cycle stock

p p

Place order

Place order

p

Inventory on hand

• Base-stock inventory system under deterministic demandOrder quantity: demand over the review period (p)Expected order quantity = Dp; cycle stock = Dp/2

Deterministic Base-stock Inventory SystemReview of Stochastic Inventory Models


TimeLead Time

Order Quantity

(Q)

Reorder Point

(r)

Order placed

ReplenishmentInventory

Safety Stock

(Q, r) Inventory Policy

Reorder Point = Expected Demand over Lead Time + Safety Stock



Deterministic (Q, r) Inventory System w/ Ordering Cost

Average Inventory

(Q/2)

Order quantity (Q)

h = Unit inventory holding costF = Fixed ordering cost for each replenishment

Constant Demand Rate = D

replenishment arrive

Time

Inventory



Economic Order Quantity Model

Total Cost 2 * 2Qh FDQD

Q hF= + ⇒ =⋅⋅

Holding Cost CurveTotal Cost Curve

Order Cost Curve

Order quantity Q

Annual Cost

Optimal Order Quantity (Q*)

Minimum Total Cost

Economic Order Quantity (EOQ)



Safety Stock

• Single-Stage Inventory

i - 1 i i + 1• Multi-Echelon InventoryGuaranteed service approach

Safety Stocks

(Graves, 1988; Zipkin, et al. 2000; Graves & Willem, 2000, 2005)

D: ton

d: ton/day

Net lead time



Guaranteed Service Approach

Each stage has an order processing time T and a service time SOrder processing time T −

Summation

of all the deterministic

times

unrelated to replenishment

−

Including transportation time, process/production time, review period−

Can be calculated directly or given parameter

Service time S (response time to orders)−

By time S, all the demand from downstream will be satisfied

−

A variable for all stages except the last one−

The last stage’s service time

can be a measure of responsiveness


i - 1 i i + 1


Timing Relationship in Guaranteed Service Approach

Net Lead Time

at stage i:

NLTi = Si-1 + Ti – Si

If

Si = Si-1 + Ti (NLTi =0)−

“Pull”

system, zero inventory, just in time, make-to-order

If Si = 0−

“Push”

system, immediate order fulfillment, make-to-stock


i - 1 i i + 1


Risk-Pooling Effect• Single facility:

• Centralized system:Several facilities share common inventoryIntegrated demand

• Distributed system:Each facility maintains its own inventoryDemand for each facility

is

Inventory Facility

Inventories Facility

Inventory

Facility

(Eppen, 1979)



Example: Risk-Pooling

• Before risk-pooling (distributed system):

• After risk-pooling (centralized system):

• If we have 100 facilities

with i.i.d. random demand

Risk-pooling can save 90% safety stocks



•


•


•

Process Planning under Supply and Demand UncertaintyStochastic programming models and algorithms Simulation framework, risk managementCase study with 12,000 uncertain parameters

Outline

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Maximum Guaranteed Service Time of Markets (days)

Tot

al S

afet

y St

ocks

(Kto

n)

$62

$64

$66

$68

$70

$72

$74

Tot

al C

ost (

10^6

$)

Total Safety StockTotal Cost


SC Design with Single-Stage Stochastic Inventory• Given: A supply chain superstructure

Including fixed suppliers, retailers and potential DC locationsEach retailer has uncertain

demand, using (Q,

r) policy

Assume all DCs have identical lead time L (lumped to one supplier)

Suppliers RetailersDistribution Centers

(Daskin et al., 2002; Shen et al., 2003; You & Grossmann, 2008)

Supply Chain Design with Single-Stage Stochastic Inventory


Problem Statement• Objective: (Minimize Cost)

Total cost

= DC installation cost + transportation cost + fixed order cost + working inventory cost + safety stock cost

• Major Decisions: (Network + Inventory)Network:

number of DCs and their locations, assignments between

retailers and DCs (single sourcing), shipping amountsInventory:

number of replenishments, reorder point, order quantity, neglect inventories in retailers

retailersupplier

DC

Supplier RetailersDistribution Centers



Economic Order Quantity (EOQ) Model

Annual EOQ cost at a DC:

ordering cost transportation cost cycle stock cost

v(x)= g + ax



Working Inventory Cost

The

optimal number of replenishments

is:

The

optimal annual transportation, ordering and cycle stock

cost:

Annual EOQ

cost at a DC:

ordering cost transportation cost cycle stock cost

Convex Function of n



Safety Stock Cost for DCs

•

Demand at retailer i ~ N(μi , σ2i )

• Centralized

system (risk-pooling)

•

Expected annual cost of safety stock at a DC is:

where za is the standard normal deviate for which

Reorder Point(ROP)

Time

Inve

ntor

y Le

vel

Lead Time



INLP Model Formulationretailersupplier

DC

DC – retailer transportation

Safety Stock

EOQ

DC installation cost


Assignm

ents

Nonconvex INLP(Daskin, et al., 2002; Shen, et al., 2003; You & Grossmann, 2008)

YijXj



Illustrative Example• Small Scale Example

A supply chain includes 3 potential DCs and 6 retailers

(pervious slide)Different weights for transportation (β) and inventory (θ)

β = 0.01, θ = 0.01 β = 0.1, θ = 0.01 β = 0.01, θ = 0.1

• Model Size for Large Scale Problem INLP

model for 150 potential DCs and 150 retailers has 22,650 binary variables

and 22,650 constraints – need effective algorithm to solve it …



Model Properties

Non-convex MINLP

Avoid unbounded gradient

• Variables Yij can be relaxed as continuous variables (MINLP)Local or global

optimal solution always have all Yij at integer

If h=0, it reduces to an “uncapacitated facility location” problemNLP relaxation

is very effective (usually return integer solutions)

Z1j Z2j

(You & Grossmann, 2008)



Lagrangean Relaxation


• Lagrangean Relaxation (LR) and DecompositionLR: dualizing the single sourcing constraint:Spatial Decomposition: decompose the problem for each potential DC jImplicit constraint:

at least one DC should be installed,

−

Use a special case of LR subproblem that Xj =1

decompose by DC j

YijXj

(You & Grossmann, 2008; Daskin, et al., 2002)



Computational Results

No. Retailers β θ

Lagrangean Relaxation BARON (global optimum)

Upper Bound

Lower Bound Gap Iter. Time (s) Upper

BoundLower Bound Gap

88 0.001 0.1 867.55 867.54 0.001 % 21 356.1 867.55* 837.68 3.566 %

88 0.001 0.5 1230.99 1223.46 0.615 % 24 322.54 1295.02* 1165.15 11.146 %

88 0.005 0.1 2284.06 2280.74 0.146 % 55 840.28 2297.80* 2075.51 10.710 %

88 0.005 0.5 2918.3 2903.38 0.514 % 51 934.85 3022.67* 2417.06 25.056 %

150 0.001 0.5 1847.93 1847.25 0.037 % 13 659.1 1847.93* 1674.08 10.385 %

150 0.005 0.1 3689.71 3648.4 1.132 % 53 3061.2 3689.71* 3290.18 12.143 %

• Case 2: 88 ~150 retailers and potential DCsFor the maximum problem with 150 retailers and 150 potential DCs−

The INLP has 22,650 bin. var., 22,650 constraints

−

The MINLP has 150 bin. var., 22,800 cont. var., 22,800 constraints

* Suboptimal solution obtained with BARON for 10 hour limit.



Tank Sizing – Vehicle Routing under Uncertainty

• No ordering cost

for replenishments, the optimal interval T comes from the tradeoff between inventory and

routing

• Required tank size ≥ max. inv. = Safety Stock + demand rate× T

Max. Inv.

Safety Stock

Time

Inven

tory

Replenishment Interval T

working inventory

Constant demand

rate

(You et al., 2009)


• Given: A supply chain superstructurePlants, potential DC locations and markets (with uncertain demand)Both DCs and markets hold inventories (three-echelon stochastic inventory)Use guaranteed service approach to model the multi-echelon inventory system

Plants MarketsDistribution Centers


Supply Chain Design with Multi-Echelon Stochastic InventorySupply Chain Design with Multi-Echelon Stochastic Inventory


Non-Convex Mixed-Integer Nonlinear ProgramLinearization

Network Structure

kPlants

i DCs

j Market

k(You & Grossmann, 2009)

min: Total Cost = Investment cost + transportation cost + pipeline & cycle stock cost + safety stock cost

(P)

YjXij

Zjk

Guaranteed Service Time

(GST)

Supply Chain Design with Multi-Echelon Stochastic Inventory


Example 1•

Small Size Liquid Oxygen Supply Chain Example

Including 2 plants, 3 potential DCs and 6 markets (97.5% service level)Vendor-managed inventory, both DCs and customers hold inventory

•

Remark : It is important to integrate inventory in the SC designSignificant change of SC structure after integrating inventoryRisk-pooling effect leads to reduction in the optimal DC number

Plants CustomersDistribution centers

SuperstructurePlants CustomersDistribution centers

257 L/day

86 L/day

194 L/day

75 L/day

292 L/day

95 L/day

387 L/day

343 L/day

269 L/day

Optimal network w/o

inventory costPlants CustomersDistribution centers

257 L/day

86 L/day

194 L/day

75 L/day

292 L/day

95 L/day

462 L/day

537 L/day

Optimal network w/

inventory cost



Optimal Solution of Example 1

3 days

Service time of DC1 = 5 days(Net lead time of DC1 = 0)

Net lead time of Customer1 & 2 = 7 days

Guaranteed service time of Plant2

2 days

2 days

3 days Customer 3

Customer 2

Customer 1

2 days

Net lead time of Customer3 = 8 days

Order processing time from Plant2 to DC1

Order processing time from DC1 to customers

2 days

Service time of DC3 = 4 days(Net lead time of DC3 = 0)

Net lead time of Customer5 & 6 = 6 days

Guaranteed service time of Plant1

2 days

2 days

3 days

Customer 6

Customer 5

Customer 4

2 days

Net lead time of Customer4 = 7 days

Order processing time from Plant1 to DC3

Order processing time from DC3 to customers

Plants CustomersDistribution centers

257 L/day

86 L/day

194 L/day

75 L/day

292 L/day

95 L/day

462 L/day

537 L/day

1

2

3

4

5

6


2 days

3 days

5 days

4 days

2 days

2 days

2 days

2 days

3 days

3 days

1

3

1

2


Problem SizesPlant i DC j Market k # of Disc. Var. # of Cont. Var. # of Constraints

2 3 6 27 124 2563 3 4 24 185 2102 20 20 460 2,480 5,3005 30 50 1,680 13,640 33,19010 50 100 5,550 70,250 185,35020 50 100 6,050 120,250 335,3503 50 150 7,700 52,800 120,45015 100 200 21,600 380,500 1,040,700

•

Non-convex Mixed-Integer Nonlinear Program (MINLP)Large scale instances cannot

be globally optimized

directly

Need an efficient algorithm for solution



No

Initialization

Convergence ? Yes Stop

Solve the | j | MILP relaxation of LR subproblems of (AP) under Yj =1,

set Vj as the optimal objective

Update subgradients

Solve reduced (P) for UB

Update LB

NoYes

Fixed 0-1 variables


Plants i Markets kDCs j


LR Algorithm


Computational Results

Plant i

DC j

Market k

Proposed Algorithm Global OptimizerSolution ($) CPU (s) Gap Solution ($) CPU (s) Gap

2 3 6 152,107 10 0% 152,107 12 0%2 20 20 1,776,969 175 0% 2,490,148 360,000 62.9%5 30 50 4,417,353 3,279 0.3% --- 360,000 ---10 50 100 7,512,609 14,197 0.1% --- 360,000 ---20 50 100 5,620,045 27,748 0.4% --- 360,000 ---3 50 150 12,291,296 16,112 0.1% --- 360,000 ---15 100 200 23,565,443 35,612 0.0% --- 360,000 ---

•

The proposed algorithm is very efficientMuch faster than BARON (currently best

general global optimization software)

Can solve very large scale problems with small global optimality

gap

With BARON for 100 hours No solution was returned



•


•


•

Process Planning under Supply and Demand UncertaintyStochastic programming models and algorithmsSimulation framework, risk managementCase study with 12,000 uncertain

parameters

Outline

38

3

4

1

5

8

12 13

16

17

32

28

H

Supplier

F

I

R

Market

Market

Market

Market

Market

Market

Market

Market

T

Supplier

Supplier

Market

Supplier

B

C

D

Supplier

E

A

M

G

J

O

Q

P

N

S

K

Supplier

Supplier

Supplier

Supplier

14 MarketL

Acetylene

Propylene

Benzene

Nitric Acid

Acetaldehyde

Acrylonitrile

Phenol

Acetone

Cumene

Ethylene

Carbon Monoxide

Methanol

Ethylbenzene


Styrene

Ethanol

Ethylene Glycol

Acetic Acid

Byproducts


•

Given:A chemical complex−

A set of dedicated

processes and chemicals

Production capacity and production delayA number of suppliers and markets Service level, mass balance coefficients Unit production, inventory and purchase costDemand uncertainty

(normal distribution)

Supply uncertainty

(maximum service time)•

Determine: (min: total cost)

Production, purchase and sale levelsInventory level of each chemicalSupplier selection, lead time quotation

A Chemical Complex

Stochastic Inventory for Planning under Uncertainty


Stochastic Inventory for Process Planning under Supply and Demand Uncertainty


Modeling Challenge•

Challenges

Shall we stock all

the feedstocks, intermediates and products?Deal with

demand and supply uncertainty

Handle recycles and by-products•

Approach

Guaranteed service approach + planningQuantifying the uncertain Internal demand−

Modeling the information flow

−

Cramér's

theory & perfect splitting property−

Worst case:

variance-to-mean ratio increases

from downstream to upstream (for processes)−

Ideal case:

variance is averaged when

information transfers to upstream (for chemicals)

Process i

A

j’

A

j…

…

……

1

j

Market l

i’

1

i

……

……

Market 1……



450000

455000

460000

465000

470000

475000

480000

0 1 2 3 4 5 6 7

Iteration

Obj

ectiv

e Fu

nctio

n

Upper BoundLower Bound

•

Solving the Nonconvex MINLPModel Property: Any optimal net lead time must be a multiple

of

the greatest common divisor of all the timing parametersThe reformulated MINLP includes only square root terms

•

Branch & Refine AlgorithmGlobal optimizationPiece-wise linear approximationTakes at most 5 minutesBARON takes 1 hour with suboptimum ( >20% gap)

Branch-and-Refine Algorithm

Computational Challenge

xx

secant

LB1

UB1xx

secant

LB1

UB1

LB2

UB2

xx

secant

LB1

UB1

LB2

UB2

1

2

3

u1u0 u2 u3

β3

α1β2

β1

α2

α3



3 days

GST of chemical A = 3 days(Net lead time of DC3 = 0)

GST of Supplier 1

2 days

Net lead time of Chemical B to Process 3 = 7 days

Production delay of Process 1

8 days

Net lead time of Chemical B to Process 2 = 8 days(GST of Chemical B to Process 2 = 0)

GST of Supplier 2

1 day

GST of Chemical B to Process 3

3 days

Process 3

Process 2

2 days

Production delay of Process 2 & 3

Net lead time of Chemical c to market = 3 days

Example 1 – Timing Relationship & Mass Balance

100

0

30

50

70

0

0

20

40

60

80

100

Cap

acity

Util

izat

ion

(ton

/day

)

1 2 3

Process

Unused CapacityProduction Level

0

200

400

600

800

1000

1200

1400

A B CChemical

Inve

ntor

y L

evel

(ton

)

Cycle StocksSafety Stocks

A complex with 3 processes (1, 2 & 3), 3 chemicals (A, B & C), 2 suppliers and 1 market

Optimal timing relationship

1

2

3

A B C Market

Supplier 2

Supplier 1

Optimal inventory levels

Optimal production levels



Example 2 – Centralized vs. Decentralized Inventory

1

2

3

4 5

6

A

B

C

D

E

F

G

Market

Market

I

H

J

Market

Supplier 1

Market

Market

Market

Supplier 2

Supplier 1

Supplier 2

Supplier 1

Supplier 2

Supplier 1

Supplier 2

Acetylene

Propylene

Benzene

Nitric Acid

Acetaldehyde

Acrylonitrile

Isopropanol

Phenol

AcetoneCumene

1

2

3

4 5

6

A1

B1

C

D

E

F1

G

Market

Market

I

H

J1

Market

Supplier 1

Market

Market

Market

Supplier 2

Supplier 1

Supplier 2

Supplier 1Supplier 2

Supplier 1

Supplier 2

A2Supplier 1Supplier 2

B2

B3

Supplier 1Supplier 2

Supplier 1

Supplier 2

J2

F2 Market

Acetylene

Propylene

Benzene

Nitric Acid

Acetaldehyde

Acrylonitrile

Isopropanol

Phenol

AcetoneCumene

Acrylonitrile

Propylene

•

A Complex with 6 processes, 10 chemicals, 2 suppliers and 1 market

Centralization

–

pooling

all

the inventory

of the same chemical in a central stocking locationDecentralization

–

each process hold its own

inventories for feedstocks and products

“Centralized” System

“Decentralized” System

0

100

200

300

400

500

600

700

Acetyle

nePro

pylene

Benzen

eNitr

ic Acid

Acetald

ehyd

eAcry

lonitr

ileIso

propan

olPhen

olAcet

one

Cumene

Centralized Inventory Management

Decentralized Inventory Management



Example 3 – 20 Chemicals & 13 Processes

38

3

4

1

5

8

12 13

16

17

32

28

H

Supplier

F

I

R

Market

Market

Market

Market

Market

Market

Market

Market

T

Supplier

Supplier

Market

Supplier

B

C

D

Supplier

E

A

M

G

J

O

Q

P

N

S

K

Supplier

Supplier

Supplier

Supplier

14 MarketL

Acetylene

Propylene

Benzene

Nitric Acid

Acetaldehyde

Acrylonitrile

Phenol

Acetone

Cumene

Ethylene

Carbon Monoxide

Methanol

Ethylbenzene


Styrene

Ethanol

Ethylene Glycol

Acetic Acid

Byproducts



Optimal Inventory Levels of Example 3

0

500

1000

1500

2000

2500

3000

3500

4000

Nitric

AcidPro

pylene

Benzen

eEthyle

neAcet

ylene

Carbon

Mon

oxide

Ethylben

zene

Naphtha

Meth

anol

Acrylon

itrile

Acetald

ehyd

eAcet

one

Cumene

Chlorob

enzen

ePhen

olStyr

ene

Ethanol

Acetic

Acid

Ethylene G

lycol

Bypro

ductsIn

vent

ory

Lev

el (t

on)

Cycle StocksSafety Stocks



Optimal Production Levels of Example 3

0

50

100

150

200

250

Cap

acity

Util

izat

ion

(ton

/day

)

1 3 4 5 8 12 13 14 16 17 28 32 38Process

Unused CapacityProduction Level



Example 4 – 28 Chemicals & 38 Processes

38

D

ASupplier

BSupplier

Supplier

FSupplier

JSupplier

ISupplier

CSupplier

ESupplier

HSupplier

GSupplier

MarketK

MarketL

MarketM

MarketO

MarketQMarketR

MarketS

MarketT

MarketU

MarketV

MarketW

MarketX

MarketY

MarketP

MarketN

MarketZ1

2

3

45

6

7

89

10

AA

AB

29

27

11

12

13

14

15

16

1718

19

20

2122

23

24 25

26

28

30

31

32

33

3435

37

36



0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50Maximum guaranteed service time to the market (day)

Tot

al in

vent

ory

(10^

3 to

n)

330

340

350

360

370

380

390

400

Tot

al d

aily

cos

t (10

^3 $

/day

)

Total InventoryTotal Daily Cost

Pareto Optimal Curve of Example 4

Good Choice


MGSTM


Optimal Inventory Levels when MGSTM = 0 day

0

500

1000

1500

2000

2500

3000

3500

4000

Nitr

ic Ac

idPr

opyl

ene

Benz

ene

Ethy

lene

Acet

ylen

e

Carb

on M

onox

ide

Ethy

lben

zene

Naph

tha

Met

hano

lAc

rylo

nitr

ileAc

etal

dehy

deAc

eton

eCu

men

eCh

loro

benz

ene

Phen

olSt

yren

eEt

hano

lAc

etic

Acid

Ethy

lene G

lyco

lBy

prod

ucts

Viny

l Ace

tate

Acet

ic An

hydr

ide

Ethy

lene D

ichlo

ride

Ethy

lene G

lyco

lFo

rmal

dehy

deBy

prod

ucts

Ket

ene

Ethy

lene C

hlor

ohyd

rin

Inve

ntor

y L

evel

(ton

) Cycle StocksSafety Stocks



Optimal Inventory Levels when MGSTM = 10 days

0

500

1000

1500

2000

2500

3000

3500

4000

Nitr

ic Ac

idPr

opyl

ene

Benz

ene

Ethy

lene

Acet

ylen

e

Carb

on M

onox

ide

Ethy

lben

zene

Naph

tha

Met

hano

lAc

rylo

nitr

ileAc

etal

dehy

deAc

eton

eCu

men

eCh

loro

benz

ene

Phen

olSt

yren

eEt

hano

lAc

etic

Acid

Ethy

lene G

lyco

lBy

prod

ucts

Viny

l Ace

tate

Acet

ic An

hydr

ide

Ethy

lene D

ichlo

ride

Ethy

lene G

lyco

lFo

rmal

dehy

deBy

prod

ucts

Ket

ene

Ethy

lene C

hlor

ohyd

rin

Inve

ntor

y L

evel

(ton





0

500

1000

1500

2000

2500

3000

3500

4000

Nitr

ic Ac

idPr

opyl

ene

Benz

ene

Ethy

lene

Acet

ylen

e

Carb

on M

onox

ide

Ethy

lben

zene

Naph

tha

Met

hano

lAc

rylo

nitr

ileAc

etal

dehy

deAc

eton

eCu

men

eCh

loro

benz

ene

Phen

olSt

yren

eEt

hano

lAc

etic

Acid

Ethy

lene G

lyco

lBy

prod

ucts

Viny

l Ace

tate

Acet

ic An

hydr

ide

Ethy

lene D

ichlo

ride

Ethy

lene G

lyco

lFo

rmal

dehy

deBy

prod

ucts

Ket

ene

Ethy

lene C

hlor

ohyd

rin

Inve

ntor

y L

evel

(ton




Conclusions

•

Concluding RemarksIntegrated models

for supply chain design and operation with stochastic

inventory management under demand and supply uncertainty

Effective algorithm

based on Lagrangean relaxation and/or piecewise linear approximation and for global optimization

•

Future ExtensionsIntegration with planning & scheduling

under uncertainty

Integration with (production & storage) capacity

planning

Integration with multi-site planning

under uncertainty

??? (– your comments & suggestions here)


Acknowledgement

The Enterprise-Wide Optimization Group−

Thank you for your support, help and suggestions!

Special Thanks to:−

Dr. John Wassick

& Dr. Jeff Ferrio

(Dow Chemical)

−

Dr. Jose Pinto & Dr. Larry Megan (Praxair, Inc.)

I owe a big THANKS to Professor Ignacio Grossmann for his care for my well-being in the past 1,433 days …

global supply chain - carnegie mellon universityegon.cheme.cmu.edu/ewo/docs/ewo_you.pdf · dp;...

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