IPA derivatives for a discrete model of make-to-stock production-inventory systems with backorders

Benjamin Melamed (), Yihong Fan (), Yao Zhao () and Yorai Wardi ()

Annals of Operations Research, 2010, vol. 181, issue 1, 19 pages

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 Probability 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 disadvantages 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 are rarely known, and consequently, need to be estimated. In this paper, we remedy both disadvantages by using a discrete setting, where transaction identity is maintained, and order fulfillment from inventory following demand arrivals and inventory restocking following replenishment arrivals are modeled as discrete jumps in the inventory level. We then compute the aforementioned IPA derivatives with respect to the base-stock level and a parameter of the lead-time process in the discrete setting under any initial system state. The formulas derived are shown to be unbiased and directly computable from sample path observables, and their computation is both simple and computationally robust. Copyright Springer Science+Business Media, LLC 2010

Keywords: Infinitesimal perturbation analysis (IPA); IPA derivatives; Make-To-Stock production-inventory system (MTS system); Discrete model (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-009-0662-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:181:y:2010:i:1:p:1-19:10.1007/s10479-009-0662-9

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-009-0662-9

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().