Page 142 - Data Science Algorithms in a Week

126 Alfonso T. Sarmiento and Edgar Gutierrez

relies on dynamic modeling and control theory. The approach is based on two elements, a
framework to capture the dynamics of the SC, and on the design of methodical
procedures defined by control laws to manage the SC. They test several heuristic control
laws and analyze their impact on the behavior of the SC.
Model structural analysis methods have also been used to eliminate oscillatory
behavior in SC models.
Lertpattarapong (2002) and Gonçalves (2003) used eigenvalue elasticity analysis to
identify the loops that are responsible for the oscillatory behavior of the inventory in the
SC. Then they use the insights about the impact of feedback structures on model behavior
to propose policies for stabilizing the system. These policies are based on inventory
buffers or safety stock. Saleh et al. (2006) used the Behavior Decomposition Weights
(BDW) analysis to identify relevant parameters that stabilize the inventory fluctuations in
a linear inventory-force model. To explore the utility of the method in a SD nonlinear
model they choose a medium-size economic model. In order to perform the BDW
analysis, they linearize the model at a point in time, once the eigenvalues have become
stable. The method provides a partial policy analysis as it studies the effects of changing
individual policy parameters. Currently, the method does not consider the interactions
due to changes in several parameters simultaneously.
Forrester (1982) presented several policies for stabilizing dynamic systems. The first
two approaches, reduction of the frequency of oscillations and increment in the rate decay
of oscillations, represent a measure of behavior of the whole system and are covered by
the linear system control theory. Other methods such as variance reduction and gain
reduction are focused on the stability of a particular variable of the system. Therefore,
they have to be extended to implement stabilizing policies of the entire system.
Policy optimization provides an efficient method for obtaining SC stabilization
policies. O’Donnell et al. (2006) employed GA to reduce the bullwhip effect and cost in
the MIT Beer Distribution Game. The GA is used to determine the optimal ordering
policy for members of the SC. Lakkoju (2005) uses a methodology for minimizing the
oscillations in the SC based on SD and GA. He applies the variance reduction criterion
proposed by Forrester to stabilize the finished goods inventory of an electronics
manufacturing company.
The literature review on stability analysis of the SC shows that several techniques
have been used to generate stabilization policies. Model structural analysis methods can
provide some insights into how to tackle the behaviors that generate instability of supply
chains modeled as dynamic systems through the identification of the loops responsible
for them. However, these methods rely on sensitivity analysis to design the stabilization
policies. Control theory can support the stabilization methodologies by providing
theoretical concepts to stabilize dynamics systems. One problem with the approaches
based on control theory is the mathematics involved to determine the analytical solution.
Moreover, like the model structural analysis methods, they can require certain