Page 141 - Data Science Algorithms in a Week

Simulation Optimization Using a Hybrid Scheme … 125

quantify five desirable characteristics of a production distribution system by drawing in
classical control techniques for use in a modern optimization procedure based on GA.
They demonstrate that their procedure can improve the performance of a production or
distribution control system by fully understanding the trade-off between inventory levels
and factory orders. Riddalls and Bennett (2002) study the stability properties of a
continuous time version of the Beer Distribution Game.
They demonstrate the importance of robust stability, i.e., stability for a range a
production/distribution delays, and how stock outs in lower echelons can create vicious
circle of unstable influences in the supply chain. Nagatani and Helbing (2004) studied
several production strategies to stabilize supply chains, which is expressed by different
specifications of the management function controlling the production speed in
dependence of the stock levels. They derive linear stability conditions and carry out
simulations for different control strategies. Ortega and Lin (2004) showed that control
theory can be applied to the production-inventory problem to address issues such as
reduction of inventory variation, demand amplification, and ordering rules optimization.
Linearization is frequently the quickest and easiest way to determine stability of an
equilibrium point (EP) for a nonlinear system. The linearization approach of nonlinear
systems can be used to extend the stability concepts for linear systems (eigenvalue
2
analysis ) to equilibrium points of nonlinear systems in which deviation from linear
behavior can be presumed small. Mohapatra and Sharma (1985) applied modal control to
analyze and improve a SD model of a manufacturing company that has two departments:
manufacturing and distribution. The eigenvalues of the motion equations are used to
synthesize new policy options. The main strength of using modal control theory is that
new policy structures can be generated mathematically. Drawbacks of modal control
theory include the amount of computation, and the design of realistic policies from the
synthetically generated policies.
Control theory has been combined with other approaches to determine stability
conditions. Daganzo (2004) examined the stability of decentralized, multistage supply
chains under arbitrary demand conditions. He uses numerical analysis for conservation
laws to design stable policies. His research looks for intrinsic properties of the inventory
replenishment policies that hold for all customer demand processes and for policies with
desirable properties.
He discovers that a simple necessary condition for the bullwhip avoidance is
identified in terms of a policy’s gain. Gain is defined as the marginal change in average
inventory induced by a policy where there is a small but sustained change in demand rate.
It is shown that all policies with positive gain produce the bullwhip effect if they do not
use future order commitments. Perea et al. (2000) proposed an approach for SCM that

2 Eigenvalues in the right half of the complex plane cause instability, whereas eigenvalues in the left half of the
complex plane determine stable systems.