Mikio Kubo Tokyo University of Marine Science and Technology 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 Recently, we Japanese had a large disruption caused by an earthquake, and then Tsunami, and finally an explosion of nuclear plants in Fukushima. Many supply chains are stopped; so we recognized supply chains should be not only efficient but also robust with respect to such disruptions. Supply Chain Risk Management (SCRM) is a new area of SCM to copy with the supply chain disruptions. This figure represents the change of the performance of a supply chain before and after a disruption event. The action before the disruption is called “proactive” , while the action after the disruption is called “response”. Our aim is to use the supply chain optimization models so that the supply chain becomes robust w.r.t the disruption and recovers quickly after the disruption. Recovery Proactive Response Time

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) Humanitarian Logistics can be defied as a branch of logistics which specializes in organizing the delivery and warehousing of supplies during natural disasters to the affected area and people. It is different from the usual (commercial) logistics with respect to the following points. It is decentralized and there are many players (government, self defense force, NGOs). And No SCM unit nor trained staffs Everything is ad hoc No performance measure (fairness, speed, …) No information & communication technology

Mathematical Optimization Approach to SCRM and HL Stochastic Optimization a classical mathematical programming approach to cope with uncertainty Disruption (Recovery) Management an approach to recover from disruption quickly (mainly used in airline and rail industries) Risk Optimization a new framework =Stochastic Optimization + Disruption Management

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

Stochastic Optimization (2) Scenario approach (# of typical scenarios is not so large) S : set of scenarios x : here & now variable vector Xs: recourse variable vector for scenario s

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

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

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

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

Supply Chain Risk Optimization Models モデル名 準備フェイズ 応答フェイズ 途絶要因 確率的在庫 複数調達/在庫 適応発注/緊急発注 供給途絶 安全在庫配置 調達先・リード時間変更 生産時間変動 ロットサイズ決定 多モード/複数調達/在庫 モード選択/生産量調整 資源途絶/ スケジューリング 多モード/ 余裕時間 ・資源 モード選択 リスケジューリング 作業時間変動 配送計画 緊急配車/ リスケジューリング 移動時間変更/資源途絶 ネットワーク設計 多モード/余裕資源/在庫 モード選択/リルーティング 資源途絶/生産・輸送時間変動 収益管理 安全在庫 価格変更 需要・供給途絶

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

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

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

Resource Constrained Scheduling Problem (1)

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

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) We can also use optimization techniques to the SCRM. Basically we can apply all the SC optimization models using what if analysis. For proactive decisions, strategic and tactical models are useful. For response decisions, we use operational models such as scheduling, transportation and vehicle routing models. If you want to model both decisions simultaneously, we need to use the framework of stochastic programming in which decisions before the disruption is modeled as here and now variables, while decisions after the disruption is modeled as recourse variables. 予防 応答 時間

支援物資備蓄・配置モデル 動機 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） 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）

多期間輸送計画モデル 動機 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 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

多期間在庫配送計画モデル 動機 多期間の在庫+配送の同時求解モデル 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