(508a) Surrogate Based Derivative Free Optimization Methodology for Supply Chain Management

Surrogate
based Derivative Free Optimization Methodology for Supply Chain Management

Nihar Sahay and Marianthi
Ierapetritou

Department
of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ

Simulation
models are one of the most effective tools to study supply chains. Compared to
analytical and mathematical programming techniques, they offer the capability
to include a greater deal of fidelity. Different kinds of simulation models
have been widely used to study various aspects of supply chain management. These
models provide a very convenient approach to generate various ?what-if?
scenarios and find the optimal values of the discrete variables. However
stand-alone simulation models cannot be used to optimize the continuous
variables. It is necessary to couple the simulation model with an optimization approach
in order to find the optimal values of the continuous variables. During the
recent years, supply chains have evolved into global, highly complex networks
and the overall supply chain operations are a result of numerous autonomous,
adaptive and intelligent entities. A high fidelity simulation model is not only
difficult to develop but also difficult to use in an optimization framework due
to computational complexity involved in each function evaluation. In order to
optimize the variables in these simulation models, deterministic optimization
solvers cannot be used as the derivatives are unavailable. Also, since the
simulations take long times to run, it is not possible to perform a large
number of simulation runs in order to approximate the derivatives. Taking these
factors into consideration, we propose a surrogate based derivative free
optimization methodology to solve a supply chain planning problem.

Simulation
based optimization approaches have been extensively studied in the literature.
These approaches have been used to solve diverse problems. Jung et al.¹
propose a simulation based optimization framework to determine the safety level
of each product at each production site in order to meet the required customer
satisfaction. The objective is the minimization of the expected value of the
cost of the supply chain. The optimization framework consists of an outer and
an inner loop. The outer loop consists of a stochastic simulation coupled with
a stochastic gradient based search module for finding the optimal safety level.
The inner loop consists of the discrete event simulation model coupled with a
deterministic planning and scheduling optimization model.  Wan et al.² propose
a simulation based optimization framework that includes domain reduction, use
of least square support vector machine to construct the surrogate model, and
incremental sampling by maximizing Bayesian information and expected
improvement. The framework is used to optimize the inventory levels in a three
stage supply chain. Mele et al.³
propose a simulation based optimization framework for parameter optimization of
supply chain networks. The logical rules defined for the agents in the
simulation model are parametrized and then a genetic algorithm is used to
optimize the parameter values. The framework is used to determine the optimal
values of the parameters associated with the inventory control policy. Derivative
free optimization methods have been comprehensively reviewed by Rios and
Sahinidis.⁴
Development of surrogate models for solving derivative free optimization
problems has also received a great deal of attention in the literature.^5-8

In
this work, a surrogate based derivative-free optimization approach is proposed
to optimize a supply chain planning problem. An initial global sampling is
performed to construct an initial surrogate model using the expensive
simulation model, which is improved by adaptive sampling. A kriging model⁹
is used to develop the surrogate approximation whereas, a trust region based
framework is used to optimize the surrogate model. The proposed optimization
framework addresses issues related to the number of function calls required and
also the limitations related to high dimensionality. A high dimensional supply
chain planning problem is used to demonstrate the effectiveness of the proposed
framework. The detailed agent based simulation model that is used as the black
box function is able to provide a realistic representation of the supply chain
operations.  

References:

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GV, Eversdyk D. A simulation based optimization approach to supply chain
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Guillén G, Espuña A, Puigjaner L. A Simulation-Based Optimization Framework for
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