Evaluating and Optimizing the Performance of Complex Multi-stage Supply Chains Under Disruptions

Sanjay KumarUniversity of Texas at Dallas

Kathryn E Stecke University of Texas at Dallas

Thomas G SchmittUniversity of Washington Seattle

Fred GloverUniversity of Colorado at Boulder

A Simple Multi-Stage Supply Chain

SuppliersSuppliers ManufacturersManufacturers DistributorsDistributors RetailersRetailers CustomersCustomers

TransportersTransporters

Demand

Supply Chain Management

Certain events can disturb the balance of demand and supply.

Supply

A Simple Multi-Stage Supply Chain

SuppliersSuppliers ManufacturersManufacturers DistributorsDistributors RetailersRetailers CustomersCustomers

TransportersTransporters

Natural catastrophes

Accidents

Terrorist attacks

Modern supply chain design

Scope of this Research

Develop optimization tools for making cost-effective decisions under disruptions.

Study the effectiveness and rationale of popular disruptions response methods used in supply chains.

Explore the vulnerabilities and understand the (long-term) effects of disruptions at various stages of a supply chain.

Supply Chain Risk Management

Ordering decisions under disruptions

Outline of the Presentation

Problem background and motivations

The model

Literature

Solution methodologies

Results

Conclusions and contributions

Background and Motivations

Recent Supply Chain Disruptions

9/11– Economic losses to New York city in the month following the

attacks: $1.5 billion

– Jobs lost in NY: 200,000

– Estimated total jobs lost in the country: 1.5 million

Hurricane Katrina– Economic losses to insurance industry far exceeded the

losses because of hurricane Andrew, 9/11, and Northridge California earthquake combined together.

The 2000 fuel crisis in UK – Resulted in disruptions far more severe than 9/11.

Various types of disruptions affect supply chains. For many industries 9/11 was not the most disruptive event.

Disruptions Response

Decisions made during disruptions are often based on short-term goals, or lack of foresight.

In many cases losses occur because of “poor” or “wrong” response– 9/11 and Homeland Security Advisory System

– Kobe earthquake

Does company level decisions made during disruptions also negatively affect the supply chain performance?– Ordering and transportation

Disruptions Response

Homeland Security Department:

– Sandia National Labs started developing models to understand the economic consequences of disruptions in critical infrastructure.

– The aim was to predict and mitigate the economic effects of disruptions in• Manufacturing facilities

• Transportation

• Electric power

• Telecommunications

Manufacturing/Transportation: Questions to Address

What kind of disruptions affect manufacturing/ transportation?– Length– How often

How does present supply chains cope with them?

Can we help companies make better ordering decisions during disruptions and even otherwise?

Does company level decisions made during disruptions also negatively affect the supply chain performance?– Ordering and transportation

Answers to these questions could vary between industries.

Our focusElectronics companies

Why Electronics Manufacturing Supply Chains?

Electronics are widespread in the functioning of our society.– Since WWII, electronics products have accounted for over 30% of

US GDP.

Electronics assembly is very susceptible to disruptions.– Typical electronics products can have 70-700 components

Electronics supply chains involve global, multinational interests that broaden the exposure to disruptions.– Over 80% of electronics components are internationally sourced.

Modern electronics products have very short life cycles.– Less than 4 months for DVD players and Digital Camcorders

Key Characteristics of an Electronics Supply Chain: Three Case Studies (from a sample of 14,000 electronics firms)

Design of supply chain– Assembly is an integral part.– Often global.

Response– Each company expedite orders to overcome shortages.

The final customer demand follows AR(1) process.– The demand across periods are correlated.

Supply chain well coordinated– Shortages become lost sales only at the retailer.

Level 1

Supply Chain

Level 4 Level 3

Level 2LT: 10

ELT: 6

LT: 30

ELT: 15

LT: 25 days

ELT: 10 days

LT: 35

ELT: 30

LT: 42

ELT: 40Assembly

(Finished Product)

Stage 4A

LT: 45

ELT: 40

Stage 3A

LT: 30

ELT: 28

Assembly is an integral part of electronics supply chain.

Both facility and transportation disruptions are critical.Each stage expedites orders to overcome shortages.The final customer demand is AR(1).The supply chain is well coordinated. Demand is lost only at the retailer.

Stage 3BStage 4B

SuppliersSuppliers ManufacturersManufacturers DistributorsDistributors RetailerRetailerAssemblerAssembler

Problem Statement

In a multi-stage model supply chain, determine the cost effective order-up-to levels for each stage considering the costs of– Backorders

– Lost sales

– Inventory carrying

– Expediting

Literature

Supply chain security: CSI, increased tracking and visibility, product and process standardization (Sheffi, 2003).

Inventory policies– Single stage

– Stationary assumptions

– Nonstationarity is induced by expediting and disruptions

Little research to find policies for multi stage and non-stationary supply chains considering bullwhip.– Chen et al. (2001), Lee et al. (1997), and Kahn (1987) deal with the

existence and quantification of bullwhip.

Almost all research articles consider an i.i.d demand.– The “best” demand function is correlated across periods.

Objective Function

i

iti

YYY

wSCMinii

(11 ,...,

itii

tii

tii lcbgIh

1)1( tii SCw

A weighted function of the costs of expediting, backorder, lost sales, and inventory holding is minimized.

s.t. Inventory flow constraints are satisfied (next slide)

Decision variables: Order quantities at each of the six stages of the supply chain.

)0

ei

eiLt

i

Lti

Ii Se

Holding costBackorder costLost sales costExpediting cost

Flow Constraints (for Stage i) Inventory and quantity on order

ei

eiLt

i

iiLt

i

Lti

Ii

LtiIi

ti

ti SeSeII

00

1 )1(

1ti

ti QQ

ei

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i

iiLt

i

Lti

Ii

LtiIi SeSe

00)1(

Previous Period Inventory

Regular Shipment

Expedited Shipment

InventorytiI

iiLt

i

LtiIi Se

)1(0

ei

eiLt

i

Lti

Ii Se

0

0,:::

0

inventorytheif1IndicatorexpeditedordersofFractione

ttimeiStageatInventoryI

iLtiI

i

ti

timeleadExpeditedLtimeLeadL

ShipmentS

ei

i

Lti

i

:::

Flow Constraints (for Stage i)

Shipment to Stage i-1

BABAiqbIS ti

ti

ti

ti 4,4,3,3,1),,min( 11

2),,,,min( 133133332 iqbqbIIS tB

tB

tA

tA

tB

tA

t

Shipments are minimum of available inventory and the order quantity

+backlogAdditional constraint for assembly stage

BackordersbttimeiStageatInventoryI

ti

ti

::

ShipmentSquantityOrderq

iLti

ti

::1

stagesAssemblyBA :,

Flow Constraints (for Stage i)

Regular Shipment to stage i-1:

Expedited Shipment to stage i-1:

tiIi Se t

i101 )1(

1

tiIi Se t

i101

1

If inventory is positive, regular orders are placed

Negative inventory (shortages) results in expedited orders

0,::

0

inventorytheif1IndicatorexpeditedordersofFractione

iLtiI

i ShipmentS iLti :

Flow Constraints (for Stage i)

Shortages:

),0max( 11 t

iti

ti

ti Iqbs

Backorders and lost sales:

)(11 retailersb tt

)()1( 11 retailersl tt

)4,3,2(, isb ti

ti

Effective order- inventory

All shortages backordered

A fraction is backordered, rest is lost

backloggedshortagesofFractionShortagess

ttimeiStageatInventoryIti

ti

:::

salesLostlquantityOrderq

ti

ti

::

Nature of the Cost Function

Sensitivity of Cost

0

5000

10000

15000

20000

25000

30000

35000

1001 1101 1201 1301 1401

Order-up-to Values at Level 1

Cos

t

Order-up-toLevel 2= 2900

Order-up-toLevel 2= 3000

Order-up-toLevel 2= 3100

Order-up-toLevel 2= 3500

Solution Strategies

The objective function is non-convex in the order quantities.

Certain deterministic cases are NP complete.

Solution methods– Fibonacci

• Results in local optimal solutions

– Genetic algorithms

• Significantly longer run time

– Tabu search

0

20000

40000

60000

80000

100000

GA

(139.7 min)

Fibonacci

(2.8 min) Tabu

(28.5 min)

Co

st

0

50

100

150

200

250

Stage 1 Stage 2 Stage 3A Stage 4AMea

n O

rder

Var

iabi

lity

Comparison of the Solution Methods

0

10000

20000

30000

40000

50000

60000

70000

No

-exp

edit

ing

4.7%

No

ExpeditingExpediting

0

20

40

60

80

100

120

Stage 1 Stage 2 Stage 3A Stage 4A

Me

an

Ord

er

Va

ria

bili

tyC

ost

Expediting vs. no Expediting

Effect of Assembly

Assembly stage reduces the order amplification effect– The reduction is prominent in the higher stages.

– The bullwhip-reducing effect of assembly increases with increase in number of components assembled.

This provides an explanation for counter-intuitive results of Cachon et al. (2006).

0

20

40

60

80

100

120

Stage 1 Stage 2 Stage 3A Stage 4A

Me

an

Ord

er

Va

ria

bili

ty

2 components assembly

No assembly

Effects of Disruption

15 days disruption at retailer

Magnitude of losses

15 days disruption at manufacturer

Magnitude of losses

Disruption

Disruption

Conclusions and Summary

– We developed and implemented a search-based optimization methodology and effectively used it to find order-up-to quantities in a multi stage supply chain.

• First such method with the potential to help supply chains make ordering decisions considering

- Nonstationarity

- Expediting

– Tabu Search

• First such application for Tabu search.

• Developed and adapted Tabu search to be effectively used for this problem.

• Genetic search is shown to be inferior.

Conclusions and Summary

– Bullwhip

• Assembly stage filters the demand thus reducing bullwhip.

• We provided a possible explanation to Cachon et al.’s findings.

– Expediting

• Widely prevalent expediting practice may hurt supply chain performance.

• Expediting may also result in longer recovery times.