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If X = (x
1
,x
2
,...,x
n
) represents a point in the n-
dimensional design space, and multiple runs of the the
stochastic simulation model estimate some average
performance metric f (X), then the meta-model g(X )
is an (ideally smooth and significantly faster to eval-
uate) function which approximates f . It can be con-
structed by measuring f at only a few points in the de-
sign space and performing some form of interpolation
or regression between them. As the number of mea-
surement points increases, the meta-model typically
becomes more and more accurate unless it suffers
from over-fitting (leading to drastic overshoots or os-
cillations in the meta-model surface in-between mea-
sured points). Continuous gradient-based optimiz-
ers can then be applied over the meta-model surface
g to quickly identify promising areas in the design
space for further exploration. Although meta-models
can assist in the optimization process, the process of
choosing the right meta-model type, the number of
data points to build the meta-model and the right op-
timizer can be non-trivial and can significantly affect
the results. Response Surface Models (RSM), Ra-
dial Basis Functions, Kriging (Gaussian Process Re-
gression), and Neural Networks (NN) are some meta-
models types that are used in various application do-
mains. Kriging, also known as Gaussian Process Re-
gression (GPR) is a spatial correlation meta-model
(Kleijnen, 2009; Ankenman et al., 2008). It uses a
kernel function to represent the correlation between
different input parameter values. Gaussian kernel,
Radial Basis Function (RBF), and periodic RBF are
some examples of kernel functions used in Kriging).
A Neural Network meta-model is built using a neu-
ral network architecture (for example, a multi-layer
feed-forward network) with the measured points as
training data to learn and mimic the input-output re-
lation. It is then used to approximate the performance
measures of the system at a given point. The pro-
cess of selecting the meta-model type, tuning it and
selecting the right optimizer for optimizing over for it
are nuanced and problem-dependent choices. While
there exist several commercial tools (such as Any-
Logic, FLEXSIM, Arena, IBM Supply Chain solu-
tions), there is a dearth of open libraries in popular
programming languages for supply chain design and
optimization. General-purpose discrete-event simula-
tion frameworks such as Python’s SimPy library (Sim,
2020) can be used for building simulation models of
supply chains. However, validation constitutes a sig-
nificant fraction of model development time. Having
an open library of validated parameterized component
models can be very useful in rapid modeling and de-
sign space exploration. In a similar vein, while there
exist open, general-purpose optimization packages,
an open tool-set specifically designed for design ex-
ploration and optimization of supply chains can have
wide utility.
This paper presents the design overview and
work-in-progress status of InventOpt - a Python-
based open library and tool-set for supply chain and
inventory systems simulation and meta-model based
optimization. InventOpt primarily consists of a li-
brary of component models for simulating supply
chains. These component models are built using
Python’s SimPy library, and can be instantiated, con-
figured and connected together to model complex
supply chains. In addition, InventOpt includes a GUI-
based tool for guided design-space exploration, meta-
model tuning and optimization. To make suitable de-
sign choices for InventOpt (such as the meta-model
type, number of measurement points relative to the
size of the design space, and the choice of the op-
timization algorithm) that are specifically suited for
simulation-based optimization of supply chains, we
present a detailed case study. The case study focuses
on modeling and simulation-based optimization of in-
ventory threshold levels in a particular supply chain
system. The case study illustrates some of the com-
ponents in InventOpt that are already built and those
that can be generalized further, and serves as a val-
idation for the meta-model based approach. Most
importantly, in this case study we perform optimiza-
tions using a wide set of meta-models and optimiz-
ers and compare the solutions to those generated us-
ing a more exhaustive search, as a means of arriv-
ing at design choices for InventOpt. The observations
from the case study lead us to design choices such as
the best meta-model type and parameters, the choice
of optimizer and the number of simulation runs for
a accuracy-versus-computational cost trade-off. The
rest of the paper is organized as follows: in Section 2,
we present a summary of related work and existing
tools for supply chain simulation and optimization.
We then present an overview of InventOpt and dis-
cuss its proposed features and implementation plan in
Section 3. Lastly, Section 4 presents the detailed case
study and a summary of the observations, insights and
conclusions gained from the case study towards the
implementation of InventOpt.
2 RELATED WORK
Anylogic (AnyLogic, 2022), FlexSim (Flexsim,
2022), and Arena (Arena, 2022) are some examples
of popular commercial tools that support supply chain
simulation. AnyLogic and FlexSim also support op-
timization, which is built on top of the OptQuest
An Open Tool-Set for Simulation, Design-Space Exploration and Optimization of Supply Chains and Inventory Problems
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