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

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 ( Method...

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Bibliographic Details
Published in:Annals of operations research Vol. 181; no. 1; pp. 1 - 19
Main Authors: Melamed, Benjamin, Fan, Yihong, Zhao, Yao, Wardi, Yorai
Format: Journal Article
Language:English
Published: Boston Springer US 01.12.2010
Springer Science + Business Media
Springer
Springer Nature B.V
Subjects:
Backorders
Business and Management
Combinatorics
Computation
Control algorithms
Derivatives
Health maintenance organizations
Inventories
Inventory
Inventory management
Marketing
Mathematical models
Operations research
Operations Research/Decision Theory
Random variables
Replenishment
Stockpiling
Stocks
Studies
Supply chain management
Theory of Computation
Infinitesimal perturbation analysis (IPA)
IPA derivatives
Discrete model
Make-To-Stock production-inventory system (MTS system)
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-009-0662-9