Dynamic Pricing and Inventory Control in a Make-to-Stock Queue With Information on the Production Status

This paper addresses the dynamic pricing problem of a single-item, make-to-stock production system. Demand arrives according to Poisson processes with changeable arrival rate dependent on the selling price. Item processing times follow an Erlang distribution, which allows to use the information on the production status in a tractable way. The objective is to identify a dynamic control policy that decides production and adjusts the price to maximize the long-run total discounted profit. An optimal policy is based on the so-called work-storage level that captures the information of the inventory level and the status of ongoing production process. Specifically, we show that: 1) the finished goods inventory is optimally managed by a critical stage level policy: when the inventory is below a certain work-storage level, production is started if the system is currently idle and 2) the price is optimally set by threshold levels: a certain price is posted when the work-storage level is at or below a threshold corresponding to that level of price. Moreover, we develop an efficient algorithm to compute the optimal policy.

[1]  Albert Y. Ha.  Optimal Dynamic Scheduling Policy for a Make-To-Stock Production System , 1997, Oper. Res..

[2]  Alper Sen,et al.  Spare parts inventory management with demand lead times and rationing , 2007 .

[3]  F. Karaesmen,et al.  OPTIMAL PRICING AND PRODUCTION POLICIES OF A MAKE-TO-STOCK SYSTEM WITH FLUCTUATING DEMAND , 2009, Probability in the Engineering and Informational Sciences.

[4]  Franco Blanchini,et al.  Effective Information for Offline Stochastic Feedback and Optimal Control of Dynamic Systems , 2003 .

[5]  P. Brémaud.  Point Processes and Queues , 1981 .

[6]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

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

[8]  Evan L. Porteus.  Conditions for characterizing the structure of optimal strategies in infinite-horizon dynamic programs , 1982 .

[9]  Saif Benjaafar,et al.  Optimal Control of an Assembly System with Multiple Stages and Multiple Demand Classes , 2010 .

[10]  Etienne Craye,et al.  Optimal control of a nested-multiple-product assemble-to-order system , 2008 .

[11]  Fikri Karaesmen,et al.  STOCK RATIONING IN A MULTI-CLASS MAKE-TO-STOCK QUEUE WITH INFORMATION ON THE PRODUCTION STATUS August 2006 , 2004 .

[12]  Jihong Ou,et al.  Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach , 2006, IEEE Transactions on Automatic Control.

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

[14]  Saif Benjaafar,et al.  Production and Inventory Control of a Single Product Assemble-to-Order Systems with Multiple Customer Classes , 2006, Manag. Sci..

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

[16]  Stephen C. Graves,et al.  Technical Note - A One-Product Production/Inventory Problem under Continuous Review Policy , 1980, 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]  Lode Li,et al.  A Stochastic Theory of the Firm , 2015, Math. Oper. Res..

[19]  Matthew J. Sobel,et al.  The Optimality of Full Service Policies , 1982, Oper. Res..

[20]  Konstantin Kogan,et al.  Production control under uncertainty: Closed-loop versus open-loop approach , 2009 .