Safety stock placement for serial systems under supply process uncertainty

In this study, we address safety stock positioning when demand per period is a known constant but supply is uncertain. The supply is either available or not available, while the setting is that of a periodically reviewed, serial system following a base stock policy. Each stage is allowed to operate according to the guaranteed or stochastic service model. We use a Discrete Time Markov Chain model for expressing the expected on-hand inventories for each stage, along with other terms of interest, as a function of policy parameters determined by a given service level requirement for the end product. Exact models are constructed for single-stage and two-stage systems. As the number of states for a two-stage system grows exponentially, we propose an approximation for expressing the effect of the input stage using a single parameter. A generalization for the approximation is provided for a multi-stage problem. Computational evaluations of the approximation, as well as numerical comparisons of different cases, are presented.

[1]  Sean P. Willems,et al.  Supply Chain Design: Safety Stock Placement and Supply Chain Configuration , 2003, Supply Chain Management.

[2]  Refik Güllü,et al.  Analysis of an inventory system under supply uncertainty , 1999 .

[3]  Raik Stolletz,et al.  The buffer allocation problem in production lines: Formulations, solution methods, and instances , 2018, IISE Trans..

[4]  Jingshan Li,et al.  Analysis, design, and control of Bernoulli production lines with waiting time constraints , 2018 .

[5]  Kan Wu,et al.  Analysis of tandem queues with finite buffer capacity , 2017 .

[6]  Yigal Gerchak,et al.  The Structure of Periodic Review Policies in the Presence of Random Yield , 1990, Oper. Res..

[7]  Sean P. Willems,et al.  Optimally configuring a two-stage serial line supply chain under the guaranteed service model , 2016 .

[8]  Jun Zhang,et al.  Managing two-stage serial inventory systems under demand and supply uncertainty and customer service level requirements , 2004 .

[9]  Ag Ton de Kok,et al.  Analysis of assembly systems with service level constraints , 1999 .

[10]  Ivo J. B. F. Adan,et al.  Assemble-to-order systems: A review , 2017, Eur. J. Oper. Res..

[11]  Sean P. Willems,et al.  Optimizing the Supply Chain Configuration for New Products , 2005, Manag. Sci..

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

[13]  Stefan Minner,et al.  Safety stocks in multi-stage inventory systems under different service measures , 1998, Eur. J. Oper. Res..

[14]  Larry R. Taube,et al.  An inventory model with random replenishment quantities. , 2010 .

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

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

[17]  W. Shih.  Optimal inventory policies when stockouts result from defective products , 1980 .

[18]  George Liberopoulos,et al.  Performance evaluation of a production line operated under an echelon buffer policy , 2018, ArXiv.

[19]  Sean P. Willems,et al.  Analytical insights into two-stage serial line supply chain safety stock , 2016 .

[20]  Chrissoleon T. Papadopoulos,et al.  A dynamic programming algorithm for the buffer allocation problem in homogeneous asymptotically reliable serial production lines , 2004 .

[21]  David D. Yao,et al.  A Supply Network Model with Base-Stock Control and Service Requirements , 2000, Oper. Res..

[22]  Amanda J. Schmitt,et al.  OR/MS models for supply chain disruptions: a review , 2014 .

[23]  Stanley B. Gershwin,et al.  An Efficient Decomposition Method for the Approximate Evaluation of Tandem Queues with Finite Storage Space and Blocking , 1987, Oper. Res..

[24]  Jörg Rambau,et al.  The stochastic guaranteed service model with recourse for multi-echelon warehouse management , 2014, Math. Methods Oper. Res..

[25]  Stanley B. Gershwin,et al.  Efficient algorithms for buffer space allocation , 2000, Ann. Oper. Res..

[26]  Jun-Ho Lee,et al.  Serial Production Lines With Waiting Time Limits: Bernoulli Reliability Model , 2018, IEEE Transactions on Engineering Management.

[27]  Jun Zhang,et al.  Managing Inventory and Supply Performance in Assembly Systems with Random Supply Capacity and Demand , 2004, Manag. Sci..

[28]  Liang Zhang,et al.  Bernoulli serial lines with deteriorating product quality: performance evaluation and system-theoretic properties , 2014 .

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

[30]  Sven Axsäter,et al.  Supply Chain Operations: Serial and Distribution Inventory Systems , 2003, Supply Chain Management.

[31]  Srinagesh Gavirneni,et al.  Supply Chain Management at a Chip Tester Manufacturer , 2004 .

[32]  Jing-Sheng Song,et al.  Supply Chain Operations: Assemble-to-Order Systems , 2003, Supply Chain Management.