Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering

We study inventory systems with two demand classes (critical and non-critical), Poisson demand and backordering. We analyze dynamic rationing strategies where the number of items reserved for critical demand depends on the remaining time until the next order arrives. Different from results in the literature, we do not discretize demand but derive a set of formulae that determine the optimal rationing level for any possible value of the remaining time. Moreover, we show that the cost parameters can be captured in a single relevant dimension, which allows us to present the optimal rationing levels in charts and lookup tables that are easy to implement. Numerical examples illustrate that the optimal dynamic rationing strategy outperforms all static strategies with fixed rationing levels.

[1]  Izak Duenyas,et al.  Optimal Policies for Inventory Systems with Priority Demand Classes , 2003, Oper. Res..

[2]  Gilvan C. Souza,et al.  INVENTORY RATIONING AND SHIPMENT FLEXIBILITY ALTERNATIVES FOR DIRECT MARKET FIRMS , 2009 .

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

[4]  Suresh K. Nair,et al.  Inventory rationing via drop-shipping in Internet retailing: A sensitivity analysis , 2006, Eur. J. Oper. Res..

[5]  Sven Axsäter,et al.  Stock Rationing in a Continuous Review Two-Echelon Inventory Model , 2004, Ann. Oper. Res..

[6]  Horst Tempelmeier,et al.  Supply chain inventory optimization with two customer classes in discrete time , 2006, Eur. J. Oper. Res..

[7]  R. Dekker,et al.  On the (S − 1, S) lost sales inventory model with priority demand classes , 2002 .

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

[9]  Herbert Meyr,et al.  A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System , 2009 .

[10]  Yushin Hong,et al.  A stock rationing policy in a (s,S)-controlled stochastic production system with 2-phase Coxian processing times and lost sales , 2003 .

[11]  P. Jackson,et al.  An Exact Optimal Solution to a Threshold Inventory Rationing Model for Multiple Priority Demand Cases , 2006 .

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

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

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

[15]  R. Dekker,et al.  Finding optimal policies in the (S - 1, S ) lost sales inventory model with multiple demand classes , 2009 .

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

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

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

[19]  Jeffrey I. McGill,et al.  Revenue Management: Research Overview and Prospects , 1999, Transp. Sci..

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

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

[22]  Izak Duenyas,et al.  Optimal Admission Control and Sequencing in a Make-to-Stock/Make-to-Order Production System , 2000, Oper. Res..

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

[24]  Barbara A. Price,et al.  A model for use in the rationing of inventory during lead time , 1989 .

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

[26]  K. Talluri,et al.  The Theory and Practice of Revenue Management , 2004 .

[27]  Yves Dallery,et al.  Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System , 2001, Manuf. Serv. Oper. Manag..

[28]  A. F. Veinott.  Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes , 1965 .

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