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DYNAMIC SYSTEMS
Lecture-08
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Static Systems
• Decision processes have been studied
(Static Systems)
• Concerned with making a single decision
at a given point in time (usually at
present)
• For the case of a periodic decision –it is
considered that the future is stationary,
hence each decision is identical to the first
one.
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Dynamic Systems
• The time element is explicitly incorporated into
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the decision process
Problems studied involve a sequence of decision
points over time
The future is not stationary (but dynamic)
Hence, the state of the system changes over time
Each future decision point may face a different
state of the system
Hence, consecutive decision are not identical
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Dynamic Systems
• How long into the future we should look?
• How long is the planning horizon?
• Planning horizon is the length of time that
the model covers
• For dynamic situation, the choice of the
planning horizon becomes more critical
• The sequence of decisions is called the
decision policy
• Objective: Finding the best sequence of
decisions
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Planning Horizon
• Number of weeks, months, or years
covered by the model
• What is the most appropriate length for
dynamic models?
 The longer the costlier data collection and the
computation of the optimal policy
 Keep as short as possible
• Systematic sensitivity analysis with regard
to the time interval covered may help in
assessing the effects of future events on
the initial set of decisions
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Planning Horizon
• Aim of Modeling Dynamic Situations
 To determine the best set of decisions for
which a firm commitment has to be made at
the beginning of the planning horizon
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Planning Horizon for Seasonal
Process
• The nature of the problem may strongly suggest
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a suitable length for planning horizon
This is the case for decision problems subject to a
seasonal pattern for some of their inputs.
For example: A hydro reservoir (p.359)
 The planning horizon is one year
 A natural break between consecutive seasonal cycles (at
the end of the season the reservoir is empty)
 Carry over from one cycle to the next
 Create an artificial break between consecutive cycle
(p.360)
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ROLLING PLANNING HORIZON
• For the case with no natural breaks or end
points, a rolling planning horizon approach
is used.
• A planning horizon T periods is used to
determine the initial set of optimal
decisions
• Then, the decisions are implemented and
their effects state of the system recorded
• The problem is again analyzed based on
the update state of the system (See
Fig.14-1)
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PLANNING HORIZON
LEAD UP TIME
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Implementation of the decision may not be
instantaneous –takes several days, weeks, or
months
Need to be planned prior to the planning horizon
(a lead-up time)
Also, time needed for developing the overall plan
Hence, this development time is also part of leadup time
A lead-up time becomes part of the effective
planning horizon
The effective planning horizon consists of two
parts - the lead-up time and the active planning
horizon
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CASE: CRYSTAL SPRINGS MINERAL
WATER COMPANY
• Situation Summary
• Choice of Planning Horizon
• Influence Diagram
• Spread Sheet Mathematical Model
• Finding The Optimal Production Plan
• Considerations for Practical
Implementation
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