Multi-class dynamic inventory rationing with stochastic demands and backordering

Dynamic inventory rationing is considered for systems with multiple demand classes, stationary stochastic demands, and backordering. In the literature, dynamic programming has been often applied to address this type of problems. However, due to the curse of dimensionality, computation is a critical challenge for dynamic programming. In this paper, an innovative two-step approach is proposed based on an idea similar to the certainty equivalence principle. First the deterministic inventory rationing problem is studied, where the future demands are set to be the expectation of the stochastic demand processes. The important properties obtained from solving the problem with the KKT conditions are then used to develop effective dynamic rationing policies for stochastic demands, which gives closed-form expressions for dynamic rationing thresholds. These expressions are easy to calculate and are applicable to any number of demand classes. Numerical results show that the expressions are close to and provide a lower bound for the optimal dynamic thresholds. They also shed light on important managerial insights, for example, the relation between different parameters and the rationing thresholds.

[1]  H. Simon,et al.  Dynamic Programming Under Uncertainty with a Quadratic Criterion Function , 1956 .

[2]  L. Lee,et al.  Dynamic inventory rationing for systems with multiple demand classes and general demand processes , 2012 .

[3]  R. Dekker,et al.  A spare parts stocking policy based on equipment criticality , 1998 .

[4]  Jean-Philippe Gayon,et al.  Stock rationing in an M/E r /1 multi-class make-to-stock queue with backorders , 2009 .

[5]  Albert Y. Ha.  Stock-rationing policy for a make-to-stock production system with two priority classes and backordering , 1997 .

[6]  Rommert Dekker,et al.  Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes , 1998, J. Oper. Res. Soc..

[7]  Yu-Sheng Zheng.  On properties of stochastic inventory systems , 1992 .

[8]  David Simchi-Levi,et al.  A Produce-to-Stock System with Advance Demand Information and Secondary Customers , 2007 .

[9]  Steven Nahmias,et al.  Operating Characteristics of an Inventory System with Rationing , 1981 .

[10]  Rajesh Piplani,et al.  Comparison of capacity rationing policies for a make-to-order production system with two customer classes , 2014 .

[11]  Stephen C. Graves,et al.  A Single-Product Inventory Model for Multiple Demand Classes , 2005, Manag. Sci..

[12]  Loo Hay Lee,et al.  Dynamic rationing and ordering policies for multiple demand classes , 2013, OR Spectr..

[13]  Philipp Melchiors,et al.  Restricted time-remembering policies for the inventory rationing problem , 2003 .

[14]  Richard V. Evans.  Sales and Restocking Policies in a Single Item Inventory System , 1968 .

[15]  Önder Bulut,et al.  An embedded Markov chain approach to stock rationing , 2010, Oper. Res. Lett..

[16]  Önder Bulut,et al.  A dynamic rationing policy for continuous-review inventory systems , 2010, Eur. J. Oper. Res..

[17]  Ruud H. Teunter,et al.  Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering , 2008, Eur. J. Oper. Res..

[18]  H. Theil.  A Note on Certainty Equivalence in Dynamic Planning , 1957 .

[19]  Suk-Ho Kang,et al.  Rationing policies for some inventory systems , 1998, J. Oper. Res. Soc..

[20]  Paul R. Kleindorfer,et al.  Service Constrained s, S Inventory Systems with Priority Demand Classes and Lost Sales , 1988 .

[21]  Albert Y. Ha.  Stock Rationing in an M/Ek/1 Make-to-Stock Queue , 2000 .

[22]  Yves Dallery,et al.  Optimal Stock Allocation for a Capacitated Supply System , 2002, Manag. Sci..

[23]  Önder Bulut,et al.  Production control and stock rationing for a make-to-stock system with parallel production channels , 2011 .

[24]  Ulrich W. Thonemann,et al.  An optimal critical level policy for inventory systems with two demand classes , 2008 .

[25]  D. M. Topkis.  OPTIMAL ORDERING AND RATIONING POLICIES IN A NONSTATIONARY DYNAMIC INVENTORY MODEL WITH n DEMAND CLASSES , 1968 .

[26]  Albert Y. Ha.  Inventory rationing in a make-to-stock production system with several demand classes and lost sales , 1997 .

[27]  Karen Donohue,et al.  A Threshold Inventory Rationing Policy for Service - Differentiated Demand Classes , 2003, Manag. Sci..