Managing Inventory in Global Supply Chains Facing Port-of-Entry Disruption Risks Co-authors: Brian M. Lewis, Alan L. Erera Chelsea C. White III Schneider National Chair of Transportation & Logistics Georgia Institute of Technology 13 October 2008 DIMACS/DyDAn/LPS Workshop, 17 November 2008 1
Initial comments Prevention, identification, response, recovery from major disruptions � Security � Ancillary benefits � – More generally, major disruptions – Productivity (economic strength, private sector perspective) – Pilferage � Use of information technology – real-time supply chain control, based on real-time data for the next level of productivity, resilience (downside risk mitigation), and stability DIMACS/DyDAn/LPS Workshop, 17 November 2008 2
Importance of trade for economic strength Growth in Trade as a Percentage of US GDP 40% 2020, 35% 35% 30% 2000, 26% 25% 20% 15% 1990, 13% 10% 5% 0% Percent of GDP DIMACS/DyDAn/LPS Workshop, 17 November 2008 3
4 Supply chain resiliency Supply chain resiliency DIMACS/DyDAn/LPS Workshop, 17 November 2008
Uncertainty & major disruption � Uncertainty – dealing explicitly with stochastic effects, e.g., variability in demand, supply, congestion, driver availability � Major disruption – a loss of nodes &/or links in the global freight transportation network � Resiliency in supply chains – preventing, gracefully reacting to, and quickly recovering from major disruptions � Comment: lean supply chains are notoriously fragile � Policy implication – the balance in investment between prevention & quick recovery � R&D challenge – for models of sequential decision making (e.g., route finding, MDP), a weighted sum of a multiplicative criterion and an additive criterion produces violations of the Principle of Optimality (dynamic programming); games DIMACS/DyDAn/LPS Workshop, 17 November 2008 5
Supply Chain Disruptions NASA Terrorist Attacks & Columbia U.S.-Canada Disaster Border Closures Nokia - Ericsson Toyota Brake Supplier Fire GM Labor Iraq Plant Fire Sarbanes-Oxley Strike Ford-Firestone War Act Tire Recall 1997 1998 1999 2000 2001 2002 2003 UPS Taiwan Longshoreman SARS Labor Earthquake Strike & West Outbreak Strike Coast Ports Business Failures: Enron, Arthur Lockout Andersen, Worldcom, Global Crossing, K-Mart, etc. DIMACS/DyDAn/LPS Workshop, 17 November 2008 6
Industry Portfolio of Risks Shareholder New or Foreign Public Boycott Financial Strategic Credit Default Activism Competitors & Condemnation Adverse Offensive Changes in Timing of Business Negative Media Risks Risks Fuel Prices Advertising Industry Decisions & Moves Coverage Interest Rate Corporate Regulations Fluctuations Market Share Battles Culture Pricing & Incentive Wars Currency & Loss of Intel. Equip., Facilities, Business Attacks on Brand Loyalty Foreign Market Foreign Exchange Property Acquisitions & Divestitures Protectionism Product-Market Alignment Rate Fluctuations Customer Relations Asset Valuation “Gotta Have Products” Financial Supplier Relations Mergers & Industry Accounting / Tax Liquidity / Cash Program Launch Markets Consolidation Dealer Relations Uncompetitive Law Changes Customer Demand Ineffective Instability Cost Structure Inadequate Mgmt. Seasonality & Variability Inadequate / Planning Oversight Adverse Inaccurate Financial Revenue Ethics Technology Decisions Budget Overruns or Changes in Controls & Reporting Management Violations Economic Unplanned Expenses Joint Venture / Alliance Relations Environmental Recession Perceived Quality Regulations Union Relations, Labor Debt & Credit Product Development Process Disagreements & Rating Currency Health Care & Contract Frustrations Product Design & Engineering Inconvertibility Pension Costs Enterprise HR Risks – Key Skill Shortage, Personnel Turnovers 3 rd Party Risks Asbestos Exposure General Product Warranty / Product Restriction of Harassment & Liability Liability Liability Recall Campaigns Access / Egress Mold Exposure Discrimination Directors & Officers Property Damage Theft Liability Cargo Losses Loss of Key Equipment Vandalism Dealer Distribution Bldg. or Equip. Fire Loss of Key Embezzlement Network Failures Geopolitical Risks Arson Facility Workers Info. Mgmt. Problems Severe Hot / Kidnapping Logistics Provider Compensation Accounting or Internal Cold Weather Failures Boiler or Machinery Explosion Extortion Controls Failures Logistics Route Earthquake Building Collapse Loss of Key Personnel Deductible Health & or Mode Flooding Building IT System Failures Limits Safety Disruptions Subsidence & (Hardware, Software, LAN, WAN) Terrorism / Sabotage Violations Service Provider Sinkholes Op. Risks Wildfire Computer Virus / Denial of Hazard Failures Land, Water, Gov’t Service Attacks Disease / Epidemic Lightning Atmospheric Inquiries Supplier Bus. Strikes Tornados Tier 1, 2, 3, …n Pollution Interruption Workplace Violence Risks Supplier Problems: Animal / Insect Infestation Wind Damage Operator Financial Trouble, Blizzard / Ice Storms Loss of Errors / Quality “Spills”, Hail Damage Tsunami Key Accidental Failure to Deliver Hurricane Supplier Damage Volcano Eruption Materials, etc. / Typhoon Utilities Failures Heavy Rain / DIMACS/DyDAn/LPS Workshop, 17 November 2008 Communications, Electricity, Thunderstorms 7 Water, Power, etc.
Inventory Control with Risk of Major Supply Chain Disruptions Brian M. Lewis, Alan Erera, Chelsea C. White III DIMACS/DyDAn/LPS Workshop, 17 November 2008 8
Outline Motivation and Introduction � Part 1: An Inventory Control Model with Border Closures � Part 2: An Inventory Control Model with Border Closures � and Congestion DIMACS/DyDAn/LPS Workshop, 17 November 2008 9
Motivation and introduction Supply chain security has evolved: from cargo theft to WMD and � border closures Increased focus on supply chain security post-9/11: C-TPAT, CSI, � 24-hour rule Research motivated by possibility of port of entry closures � – September 11 terrorist attacks • US-Canadian border delays: minutes to 12 hours • US air traffic grounded – 2003 BAH Port Security Wargame • Simulated terrorist attack with “dirty bomb” in containers • All US ports closed for 8 days, Backlog takes 92 days to clear – 2002 10-day labor lockout at 29 Western US seaports • Congestion and delays lasted for months DIMACS/DyDAn/LPS Workshop, 17 November 2008 10
Motivation and introduction Questions: � – How can we model major supply chain disruptions (e.g. border closures and congestion) within an inventory control framework? – What does an optimal inventory policy look like? – How are an optimal policy and the long-run average cost affected by the system parameters? – What managerial and policy insights does the model provide? DIMACS/DyDAn/LPS Workshop, 17 November 2008 11
Part 1: An Inventory Control Model with Border Closures Placed Orders Demand International Border Filled Orders Open Border Foreign Domestic Supplier Manufacturer (L>0 days) (0 days) Closed Observe State: Border Border Status, Border Opens Inventory Position (0 days) Orders Waiting at Border DIMACS/DyDAn/LPS Workshop, 17 November 2008 12
Problem statement Border system � – Modeled by a DTMC – State space, S ={“ O”= Open, “ C”= Closed} – Exogenous system p OC >0 O C p OO >0 p CC >0 p CO >0 DIMACS/DyDAn/LPS Workshop, 17 November 2008 13
Problem statement Outstanding order vector, z = { z kt } � – k e{0,1,2,…, L -1}: orders that have been outstanding for exactly k days – L : orders that have been outstanding for at least L days – g: orders that have arrived Order movement function � – Order crossover is prevented DIMACS/DyDAn/LPS Workshop, 17 November 2008 14
Problem statement Long-run average cost criterion - no discounting future costs � Costs – purchase, holding, penalty � Demand - bounded, non-negative, integer-valued, iid � Specialize Song and Zipkin (1996) model � – Stationary state-dependent, basestock policies optimal (denoted, y ) • Reduced sufficient state information: ( i t , x t ) – Ordering decision rule at time t is DIMACS/DyDAn/LPS Workshop, 17 November 2008 15
Theoretical results For the border closure model without congestion, � The optimal state-invariant order-up-to level ( ) is non-decreasing � in the cost ratio The optimal state-invariant order-up-to level ( ) is non-decreasing � in the penalty cost (p) and non-increasing in holding cost (h). The optimal state-invariant order-up-to level ( ) is non-decreasing � in the minimum leadtime (L). DIMACS/DyDAn/LPS Workshop, 17 November 2008 16
Numerical Study Daily review � Parameter Values Purchase Cost, c $150,000 Holding Cost, h $100, $500 Penalty Cost, p $1,000, $2,000 Minimum Leadtime, L 1, 7, 15 Transition Probability, p OC 0.001, 0.003, 0.01, 0.02, 0.05, 0.1, 0.2,...,0.8, 0.9, 0.95 Transition Probability, p CO 0.05, 0.1, 0.2,...,0.8, 0.9, 0.95 Demand Distribution Poisson(Mean=0.5), Poisson(Mean=1) DIMACS/DyDAn/LPS Workshop, 17 November 2008 17
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