185
10
Using Probabilistic Models
to Understand Risk
AMR research, now part of Gartner, has been speaking about the com-
plexion of the 21st century supply chain for some time, and during that
dialogue the topic of probabilistic planning continuously arises. is
planning process is supported by stochastic demand management and
dynamic inventory planning.
In this chapter, we will discuss models that have been around for some
time, such as stochastic/ probabilistic models, deterministic methods,
discrete- event simulation, and digital modeling. We’ll also explore how
these methods are being leveraged to map out complex supply chains and
how leaders are appending risk assessments to scenarios supported by
these techniques. Next, we’ll introduce risk response planning, the logical
outcome of stress testing complex supply chains and modeling “what- if”
scenarios in an eort to develop a plan to manage risk scenarios. We con-
clude with several examples that demonstrate how leading companies are
leveraging these powerful and dynamic techniques to identify, assess, mit-
igate, and manage supply chain risks.
DEFINING THE MODELS
Stochastic/ probabilistic models are models where uncertainty is explicitly
considered in the analysis. Furthermore, stochastic/ probabilistic models
are procedures that represent the uncertainty of demand by a set of pos-
sible outcomes (i.e., a probability distribution) and that suggest inven-
tory management strategies under probabilistic demands.
1
Stochastic
186 • Supply Chain Risk Management: An Emerging Discipline
optimization (SO) methods are optimization algorithms that incorporate
probabilistic (random) elements, either in the problem data (the objective
function, the constraints, etc.) or in the algorithm itself (through random
parameter values, random choices, etc.), or in both. is concept contrasts
dramatically with the deterministic optimization methods, such as time
series analysis, linear programming, integer programming, the simplex
method, and regression models where the values of the objective function
are assumed to be exact and the computation is completely determined by
the values developed in the equations. (Table10.1 provides basic deni-
tions of some of the key terms used in this chapter.)
e most critical dierence between probabilistic and deterministic
models is that there is not an ounce of uncertainty explained or handled
in deterministic tools. erefore, the responsibility of handling any uncer-
tainty, complexity, and risk has been the responsibility of supply chain
TABLE10.1
Dening Key Terms
Technique Description
Time series
analysis
Deterministic approaches that use historical data to forecast future
requirements.
Regression
analysis
Deterministic models that represent the relationship between a
dependent variable [y] and independent variables [x].
Discrete-event
simulation
DES models the operation of a system as a discrete sequence of events
in time. Each event occurs at a particular instant in time and marks a
change of state in the system. While simulations allow
experimentation without exposure to risk, they are only as good as
their underlying assumptions.
Forecast error Represents the dierence between an actual value and a forecasted
value. e objective is to minimize forecast error and maximize
forecast reliability.
Stochastic/
probabilistic
models
Models where uncertainty is explicitly considered in the analysis.
Involves statistical procedures that represent the uncertainty of
demand by a set of possible outcomes and that suggest inventory
management strategies under probabilistic demands.
Design of
experiments
e process of setting up a series of tests or experiments to determine
what outputs result from dierent combinations of inputs.
Sensitivity
analysis
Involves systematically changing quantitative inputs or assumptions to
assess their eect on a nal outcome.
Linear
programming
A mathematical technique used in computer modeling (simulation) to
nd the optimal solution that maximizes prot or minimizes cost
considering a set of limited resources, such as personnel, funds,
materials, etc.
Using Probabilistic Models to Understand Risk • 187
professionals. At this point in the growth of supply chain management as a
discipline and because of the expanded nature of uncertainty, complexity,
and risk, it is important to use these “new” techniques to manage global
risk. ese methodologies are not new. Academia, pharmaceuticals, medi-
cal, nance, insurance, and the banking industry have been using these
methods to evaluate and mitigate risk for more than 50years. ey are,
however, new to the supply chain world.
With the framework established for stochastic/ probabilistic methods,
let’s spend a brief moment describing our supply chain comfort zone in
terms of tools.
2
Supply chain professionals have been leveraging determin-
istic methods to solve supply chain problems for more than 35years. We
utilize time series tools to forecast sales, basically using the least squares
method to t a line through a set of sales or order observations and project
anywhere from 1 to 18 or more months of future sales. We regularly track
forecast error by comparing actual demand versus projected demand and
handle that demand variability (i.e., risk) with inventory safety stock, buf-
fer stock, and simple brute force. We also utilize linear programming and
the simplex method to optimize supply chain network designs by model-
ing existing and future network congurations and then optimizing an
objective function to either maximize sales, prots or service levels, or
minimize costs, subject to a series of constraints.
We also utilize, albeit sparingly, regression analyses to build models of
our markets and attempt to predict sales for new product introductions,
which are the dependent Y variables subject to independent X variables.
And we’ve leveraged these tools to optimize revenues or minimize the
costs associated with logistics, truck and rail scheduling, and airline oper-
ations management. While these approaches have merit, none handles
uncertainty and risk. And in today’s volatile world, that in itself is a com-
pelling reason to act.
PROBABILISTIC VERSUS DETERMINISTIC
MODELING TOOLS
is is a good point in our discussion to illustrate the dierences between
the two statistical methodologies and then follow up with some actual
cases showing how probabilistic methods support the eort to man-
age risk within complex global supply chains. ink of this in terms of
188 • Supply Chain Risk Management: An Emerging Discipline
weather forecasters on TV. When hurricane forecasters talk about a new
storm, they present something they call the “cone of uncertainty,” which
Figure10. 1 depicts.
is cone represents a set of outcomes from probabilistic models that
attempt to predict where a storm will travel based on probabilities of
occurrences. Compare this approach to the traditional deterministic
methods where there is no uncertainty within the model. e bottom of
Figure10.1 depicts the extremely V- shaped solution that deterministic
methods attempt to achieve, without uncertainty, in order to present an
is is the Face of New Forecasting ...
“e Cone of Uncertainty”
Deterministic Planning vs Probabilistic Planning
Uncertainty & Solution Range
“Best” value
“Optimal” value
Supply Chain
Cost
Parameter value
Deterministic
Probabilistic Planning
FIGURE 10.1
Stochastic/ probabilistic planning.
Using Probabilistic Models to Understand Risk • 189
optimal solution. e probabilistic method, used by weather forecasters,
provides an approach to gain an optimal solution across a much broader set
of solution variables within the model, explicitly addressing uncertainty.
We are beginning to witness this probabilistic methodology support-
ing scenario planning in the context of supply chain risk management
(SCRM). What does this process look like? First, it starts by digitizing
the entire supply chain and building a ow model of the enterprise, as
illustrated in Figure10.2. Supply chains are nothing more than a network
with speeds and feeds, inputs, outputs, and processing times that can be
digitized as dynamic ow models. Next, companies populate the model
of the enterprise with base case data from their enterprise resource plan-
ning (ERP) system and by identifying the historical behavior and uncer-
tainty of all relevant factors. ese factors include elements such as lead
times, capacities, demand, production, inventory, quality, yields, policies,
and more.
Companies next develop “what- if” scenarios, or what we call hypotheses,
that need to be reinforced or refuted, looking at scenarios such as demand
increasing by 30%, demand decreasing by 30%, lead times increasing or
decreasing, market share to be gained, supplier disruptions, plant dis-
ruptions, complex competitive pricing changes, geopolitical changes, oil
price uctuations, and more. Most probabilistic tools maintain a library
of probability tables that indicate the probability distributions utilized
within the scenarios. If the tools can’t capture historical data for certain
variables, users can posit probabilities of occurrence for certain changes.
With these assumptions codied and historical data in hand, users begin
to run discrete- event simulations across the entire enterprise for every sce-
nario in an eort to review the cause- and- eect outcomes and their statistical
strengths. e outcomes normally take the shape of histograms, sensitivity
curves with condence intervals and probabilities of occurrence along
with risk assessments for each scenario, depicted on the bottom of
Figure10.2. is continuous running of the model, requiring several hun-
dred iterations, can continue until the outcomes, per scenario, are consid-
ered statistically signicant. is task is accomplished through the use of
sensitivity analysis, optimized response curves, and design of experiments
(i.e., a structured and systematic Six Sigma– oriented testing methodology
of the process model).
e outcomes of the scenarios are next prioritized based on their
probabilities of occurrence and their associated risk index. is novel
approach is accelerating SCRM. By combining powerful tools, such as
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