Mathematical Programming Approach to Supply Chain Optimization and Humanitarian Logistics

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Mathematical Programming Approach to Supply Chain
Optimization and Humanitarian Logistics 

• Mikio Kubo
• Tokyo University of  Marine Science and Technology

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Supply Chain Risk Management (SCRM)

• Proactive and response approaches to cope with
  supply chain disruptions.

Disruption
Performance
Recovery
Proactive
Response
Time
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Humanitarian Logistics (HL)

• is a branch of logistics which specializes in
  organizing the delivery and warehousing of
  supplies during natural disasters to the affected
  area and people.
• Decentralized
• No SCM unit nor trained staffs
• Everything is ad hoc
• No performance measure (fairness, speed, )
• No information communication technology
• Many players (government, NGOs)

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Mathematical Optimization Approach to SCRM and HL

• Stochastic Optimization a classical mathematical
  programming approach to cope with uncertainty
• Disruption (Recovery) Managementan approach to
  recover from disruption quickly (mainly used in
  airline and rail industries)
• Risk Optimization a new framework Stochastic
  Optimization Disruption Management

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Stochastic Optimization (1)
Here Now Variables
Recourse Variables
gtflexibility
scenarios
Disruption
Performance
Proactive
Response
Time
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Stochastic Optimization (2)

• Scenario approach ( of typical scenarios is
  not so large)
• S set of scenariosx here now variable
  vectorXs recourse variable vector for scenario
  s

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Stochastic Optimization (3)

• CVaR approach (disruption is a rare event
  decision maker is risk averse)
• (1- ? ) Expectation ? ß-CVaR

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Disruption Management (1)
Response Action X
Base Solution x
Disruption
Performance
Deviation from x
Proactive
Response
Time
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Disruption Management (2)

• Recovery OptimizationAfter a disruption
  (scenario), find a recovery solution that is
  close to the base solution x

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Risk Optimization

• A new framework to copy with disruptions
• Stochastic Recovery Optimization

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Supply Chain Risk Optimization Models
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Probabilistic Inventory Model (1)
Multi period, Single stage, Static policy, Nominal
Variables I inventory B backorder x ordering
amount
Parameters h inventory cost b backorder
cost p probability d 0 disruption occurs
1 otherwise
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Probabilistic Inventory Model (2)
Multi period, Single stage, Static policy, CVaR
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Probabilistic Inventory Model (3)
Multi period, Multi stage, Adaptive policy,
Nominal
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Resource Constrained Scheduling Problem (1)
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Resource Constrained Scheduling Problem (2)
Resource constraints
Precedence constraints
Processing time (p), resource upper bound (RUB),
and resource usage (a) depend on scenarios
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