Page 140 - Data Science Algorithms in a Week

124 Alfonso T. Sarmiento and Edgar Gutierrez

fundamental goal is to reduce the difference between the desired trajectories (obtained by
solving the reference model) and the observed trajectories (obtained by simulation of the
system dynamic model).

Stability Analysis of the Supply Chain

The main objective in stability analysis is to determine whether a system that is
pushed slightly from an equilibrium state (system variables do not change over time) will
return to that state. If for small perturbations or disturbances from the equilibrium state
the system always remains within a finite region surrounding that state, then this
equilibrium state is stable. However, if a system tends to continue to move away from its
original equilibrium state when perturbed from it, the system is unstable.
Sterman (2006) stated that “supply chain instability is a persistent and enduring
characteristic of market economies.” As a result, company indicators such as demand
forecast, inventory level, and employment rate show an irregular and constant fluctuation.
Supply chain instability is costly because it creates “excessive inventories, poor customer
service, and unnecessary capital investment” (Sterman, 2006).
In dynamic complex systems like supply chains, a small deviation from the
equilibrium state can cause disproportionately large changes in the system behavior, such
as oscillatory behavior of increasing magnitude over time. The four main contribution
factors to instability in SC have been identified by Lee et al. (1997), which are:

 Demand forecast updating: when companies throughout the SC do not share
information about demand, this have to be forecasted with the possible cause of
information distortion.
 Order batching: this means a company ordering a large quantity of a product in
one week and not ordering any for many weeks, which will cause distortion on
the demand forecast of other members of the SC, because it is based on orders
rather than actual sales.
 Shortage gaming: when a product demand exceeds supply, a manufacturer often
rations its product to customers, which will cause that customers exaggerate their
orders to ensure that they receive enough amount of the required product.
 Price fluctuations: when the price of a product changes significantly, customers
will purchase the product when it is cheapest, causing them to buy in bulk (order
batching problem).

The stability of supply chains models can be analyzed using the vast theory of linear
and nonlinear dynamic systems control. Disney et al. (2000) described a procedure for
optimizing the performance of an industrially design inventory control system. They