Ann Oper Res (2010) 181: 1–19 DOI 10.1007/s10479-009-0662-9 IPA derivatives for a discrete model of make-to-stock production-inventory systems with backorders Benjamin Melamed · Yihong Fan · Yao Zhao · Yorai Wardi Published online: 20 November 2009 © Springer Science+Business Media, LLC 2009 Abstract We consider a class of single-stage, single-product Make-to-Stock production- inventory system (MTS system) with backorders. The system employs a continuous-review base-stock policy which strives to maintain a prescribed base-stock level of inventory. In a previous paper of Zhao and Melamed (Methodology and Computing in Applied Probabil- ity 8:191–222, 2006), the Infinitesimal Perturbation Analysis (IPA) derivatives of inventory and backorders time averages with respect to the base-stock level and a parameter of the production-rate process were computed in Stochastic Fluid Model (SFM) setting, where the demand stream at the inventory facility and its replenishment stream from the production facility are modeled by stochastic rate processes. The advantage of the SFM abstraction is that the aforementioned IPA derivatives can be shown to be unbiased. However, its disad- vantages are twofold: (1) on the modeling side, the highly abstracted SFM formulation does not maintain the identity of transactions (individual demands, orders and replenishments) and has no notion of lead times, and (2) on the applications side, the aforementioned IPA derivatives are brittle in that they contain instantaneous rates at certain hitting times which B. Melamed ( ) Rutgers Business School—Newark and New Brunswick, Department of Supply Chain Management and Marketing Sciences, Rutgers University, 94 Rockafeller Rd., Piscataway, NJ 08854, USA e-mail: melamed@rbs.rutgers.edu Y. Fan Rutgers Business School—Newark and New Brunswick, Department of Management Science and Information Systems, Rutgers University, 1 Washington Park, Newark, NJ 07102, USA e-mail: fanyihon@andromeda.rutgers.edu Y. Zhao Rutgers Business School—Newark and New Brunswick, Department of Supply Chain Management and Marketing Sciences, Rutgers University, 1 Washington Park, Newark, NJ 07102, USA e-mail: yaozhao@andromeda.rutgers.edu Y. Wardi School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA e-mail: wardi@ee.gatech.edu