
Description:
Online algorithms aim to
adaptively control supply chains over time with the objective of minimizing
the inventory onhand but without compromising customer service
metrics. Infinitesimal Perturbation Analysis (IPA)
is a research area that develops sensitivity estimators in terms of
gradients of system performance metrics with respect to parameters of
interest. IPA can be used in the optimal design and online control of
various systems, including productioninventory systems, via
gradientdriven methods.
My research in this area
focuses on developing unbiased IPA gradients for various production inventory systems (under either
stochastic fluid model or discrete model).

Zhao, Y., B. Melamed (2007). IPA Gradients for MaketoStock
ProductionInventory Systems with Lost Sales. IEEE Transactions
on Automatic Control 52: 14911495.
Abstract: This note applies the
stochastic fluid model (SFM) paradigm to a class of singlestage,
singleproduct maketostock (MTS) productioninventory systems with
stochastic demand and random production capacity, where the finishedgoods
inventory is controlled by a continuoustime basestock policy and
unsatisfied demand is lost. This note derives formulas for infinitesimal
perturbation analysis (IPA) derivatives of the samplepath time averages of
the inventory level and lost sales with respect to the basestock level and
a parameter of the production rate process. These formulas are
comprehensive in that they are exhibited for any initial inventory state,
and include right and left derivatives (when they differ). The formulas are
obtained via sample path analysis under very mild regularity assumptions,
and are inherently nonparametric in the sense that no specific probability
law need be postulated. It is further shown that all IPA derivatives under
study are unbiased and fast to compute, thereby providing the theoretical
basis for online adaptive control of MTS productioninventory systems.

Zhao, Y., B. Melamed (2006). IPA Gradients for
MaketoStock ProductionInventory Systems with Backorders. Methodology
and Computing in Applied Probability 8: 191222.
Abstract: These two papers model a MaketoStock (MTS)
productioninventory system as a stochastic fluid model (SFM), and derive
formulas for IPA derivatives of the samplepath time averages of the
inventory level, backorder level and lost sales with respect to control
parameters (basestock level and production rate). The IPA
derivatives are comprehensive because they are exhibited for any initial
inventory state, and include right and left derivatives (when they differ).
The IPA derivatives obtained can be applied to online control, since they
are fast to compute and unbiased. Furthermore, these derivatives are
nonparametric in the sense that they do not assume any underlying
probability law, but only require sample path information. This generality
renders them suitable for simulation as well as reallife systems.

Fan, Y.,
B. Melamed, Y. Zhao, Y. Wardi (2009). IPA Derivatives for MaketoStock
ProductionInventory Systems with Backorders under the (R,r) Policy. Methodology and Computing in
Applied Probability 11: 159179.
Abstract: This paper
addresses Infinitesimal Perturbation Analysis (IPA)
in the class of Maketo Stock (MTS)productioninventory systems with backorders under the
continuousreview (R,r) policy, where
R is the stockupto level and r is the reorder point. We
map an underlying discrete MTS system to a Stochastic Fluid Model(SFM)
counterpart and derives closedform IPA derivative formulas of the
timeaveraged inventory level and timeaveraged backorder level with
respect to the policy parameters, R and r, and shows them
to be unbiased. The obtained formulas are comprehensive in the sense
that they are computed for any initial inventory state and any time
horizon, and are simple and fast to compute. These properties hold
the promise of utilizing IPA derivatives as an ingredient of offline design
algorithms and online management and control of the class of systems under
study.

