Inventory Systems with Stochastic Demand and Supply: Properties and Approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.

[1]  David Perry,et al.  Inventory models of future supply uncertainty with single and multiple suppliers , 1996 .

[2]  Stephan M. Wagner,et al.  Supplier default dependencies: Empirical evidence from the automotive industry , 2009, Eur. J. Oper. Res..

[3]  Yanfeng Ouyang,et al.  Joint Inventory-Location Problem Under Risk of Probabilistic Facility Disruptions , 2011 .

[4]  Volodymyr Babich,et al.  Supply Disruptions, Asymmetric Information, and a Backup Production Option , 2009, Manag. Sci..

[5]  Hau L. Lee,et al.  Lot Sizing with Random Yields: A Review , 1995, Oper. Res..

[6]  M. Parlar,et al.  Future supply uncertainty in EOQ models , 1991 .

[7]  William T. Scherer,et al.  The triangular density to approximate the normal density: decision rules-of-thumb , 2003, Reliab. Eng. Syst. Saf..

[8]  Amanda J. Schmitt,et al.  A Quantitative Analysis of Disruption Risk in a Multi-Echelon Supply Chain , 2011 .

[9]  E. Silver.  Establishing The Order Quantity When The Amount Received Is Uncertain , 1976 .

[10]  Volodymyr Babich,et al.  Independence of Capacity Ordering and Financial Subsidies to Risky Suppliers , 2008, Manuf. Serv. Oper. Manag..

[11]  Lawrence V. Snyder,et al.  Infinite-Horizon Models for Inventory Control under Yield Uncertainty and Disruptions , 2010 .

[12]  David Perry,et al.  Analysis of a (Q, r, T) inventory policy with deterministic and random yields when future supply is uncertain , 1995 .

[13]  Manoj Kumar Tiwari,et al.  Fuzzy goal programming for inventory management: A bacterial foraging approach , 2011, Eur. J. Oper. Res..

[14]  Uriel G. Rothblum,et al.  Nature plays with dice - terrorists do not: Allocating resources to counter strategic versus probabilistic risks , 2009, Eur. J. Oper. Res..

[15]  Brian Tomlin,et al.  On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks , 2006, Manag. Sci..

[16]  Amanda J. Schmitt.  Strategies for customer service level protection under multi-echelon supply chain disruption risk , 2011 .

[17]  Antonio Arreola-Risa,et al.  Production , Manufacturing and Logistics Optimizing stochastic production-inventory systems : A heuristic based on simulation and regression analysis , 2011 .

[18]  Paul H. Zipkin,et al.  Inventory Control with Information About Supply Conditions , 1996 .

[19]  Lian Qi,et al.  A Continuous-Review Inventory Model with Disruptions at Both Supplier and Retailer , 2009 .

[20]  Paul H. Zipkin,et al.  Foundations of Inventory Management , 2000 .

[21]  Diwakar Gupta,et al.  The {Q,r) Inventory System With An Unreliable Supplier , 1996 .

[22]  Maqbool Dada,et al.  A Newsvendor's Procurement Problem when Suppliers Are Unreliable , 2007, Manuf. Serv. Oper. Manag..

[23]  Volodymyr Babich,et al.  Competition and Diversification Effects in Supply Chains with Supplier Default Risk , 2006, Manuf. Serv. Oper. Manag..

[24]  Z. Shen,et al.  Product substitution and dual sourcing under random supply failures , 2011 .

[25]  Emre Berk,et al.  Note on future supply uncertainty in EOQ models , 1994 .

[26]  Mahmut Parlar,et al.  Continuous-review inventory problem with random supply interruptions , 1997 .

[27]  Soundar Kumara,et al.  A Single-Period Analysis of a Two-Echelon Inventory System with Dependent Supply Uncertainty , 2011 .

[28]  S. Chopra,et al.  The importance of decoupling recurrent and disruption risks in a supply chain , 2007 .

[29]  Lawrence V. Snyder,et al.  Inventory Management with Advanced Warning of Disruptions , 2005 .

[30]  Refik Güllü,et al.  Analysis of a deterministic demand production/inventory system under nonstationary supply uncertainty , 1997 .