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Mathematical Programming Approach to Supply Chain Optimization and Humanitarian Logistics

Mathematical Programming Approach to Supply Chain Optimization and Humanitarian Logistics. Mikio Kubo Tokyo University of  Marine Science and Technology. Supply Chain “Risk” Management (SCRM). Proactive and response approaches to cope with supply chain disruptions. Performance. Disruption.

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Mathematical Programming Approach to Supply Chain Optimization and Humanitarian Logistics

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  1. Mathematical Programming Approach to Supply Chain Optimization and Humanitarian Logistics Mikio Kubo Tokyo University of  Marine Science and Technology

  2. Supply Chain “Risk” Management (SCRM) Proactive and response approaches to cope with supply chain disruptions. Performance Disruption Recovery Proactive Response Time

  3. 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)

  4. 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

  5. Stochastic Optimization (1) Here & Now Variables Recourse Variables =>flexibility scenarios Performance Disruption Proactive Response Time

  6. 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

  7. Stochastic Optimization (3) +CVaR approach (disruption is a rare event; decision maker is risk averse) (1- λ ) Expectation + λ [ β-CVaR]

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

  9. Disruption Management (2) = Recovery OptimizationAfter a disruption (scenario), find a recovery solution that is close to the “base” solution x*

  10. Risk Optimization A new framework to copy with disruptions = Stochastic + Recovery Optimization

  11. Supply Chain Risk Optimization Models

  12. 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 δ: =0 disruption occurs =1 otherwise

  13. Probabilistic Inventory Model (2) Multi period, Single stage, Static policy, CVaR

  14. Probabilistic Inventory Model (3) Multi period, Multi stage, Adaptive policy, Nominal

  15. Resource Constrained Scheduling Problem (1)

  16. Resource Constrained Scheduling Problem (2) Resource constraints Precedence constraints Processing time (p), resource upper bound (RUB), and resource usage (a) depend on scenarios

  17. 人道支援サプライ・チェイン最適化 即時決定変数 (備蓄場所， 備蓄量決定） リコース変数 (備蓄品輸送量， 輸送経路決定） 操業度（性能） 途絶 支援物資備蓄・配置 (ストラテジック，タクティカル ) 多期間輸送計画 多期間在庫配送計画 (タクティカル，オペレーショナル) 予防 応答 時間

  18. 支援物資備蓄・配置モデル • 動機 • 避難所に保管されていた備蓄品(支援物資）が流された（土砂で埋まった） • 備蓄予算で水と乾パンだけを購入（保管しやすいから） • 適切な箇所に適切な備蓄を行う（即時決定変数） • 災害発生後の輸送経路（リコース変数）

  19. 多期間輸送計画モデル • 動機 • 行政単位で支援物資を直接長距離輸送で受け入れ • 緊急に必要な物資とそうでない物資が混在(需要と供給のミスマッチ） • 大量の不要在庫 • 日別の需要を適切に選択された中継地点を経由して輸送（在庫）するモデル

  20. 多期間在庫配送計画モデル • 動機 • 最終需要地点（避難所）への配送の遅れ • 初期に必要な支援物資（毛布）と，その後に必要になる支援物資（清潔用品，食品）の切り替え • （非効率な）高頻度補充 • 多期間の在庫+配送の同時求解モデル

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