evaluating and optimizing the performance of complex multi-stage supply chains under disruptions...
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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
eiLt
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.
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