Decisions in an Uncertain World: A Real Options Framework

1
Decisions in an Uncertain World A Real Options
Framework
2
The Problem

• Military is faced with a highly uncertain,
  rapidly changing environment
• Current military acquisition strategy plans for
  most likely outcome
• Leads to integrated, inflexible systems
• Often impossible or very expensive to adapt
• Need a decision making methodology that takes
  uncertainty into account
• Put dollar amount on the value of flexibility and
  modularity
• Consider true lifecycle costs when faced with
  changing and uncertain resource requirements

3
Real Options

• Real Options is a business framework for
  assessing costs in uncertain situations
• An option is the right, but not the obligation,
  to take an action in the future
• Example Options
• Flexibility options remaining flexible for
  future decisions.
• Learning options allowing future decision
  conditional on learning from experiments.
• Waiting-to-invest options allowing to invest in
  the future.
• Exit options allowing to walk away if conditions
  change.
• Options assign value to flexibility

4
Real Options

• But Traditional Real Options not appropriate for
  Military Acquisitions
• evaluates only a single buy/sell decision, not a
  complete acquisition strategy
• Can be opaque
• Assumes that future scenarios will cluster evenly
  around an average value (i.e. a bell curve
  distribution of possible future values)

5
Solution Real Options For Defense

• Handles the impact of rare but significant or
  catastrophic events on costs and strategy
• Provides transparent analysis
• Estimates true cost of existing/alternate
  acquisition strategies (e.g. planning for
  most-likely or worst-case scenarios)
• Discovers the optimal upgrade/downgrade strategy
• Handles complexity in a manageable way

6
Solution Real Options For Defense

• Key Demonstrated Results
• Strategies that commit to an immediate course of
  action in an attempt to cover all possible future
  scenarios (e.g. planning for most-likely or worst
  case scenario) have hidden costs
• In an uncertain world, strategies that wait and
  adapt to current circumstances perform better
• As uncertainty increases, integrated systems,
  which lack flexibility, grow quickly in cost
  relative to modular systems

7
Details

• Focus on example case of Power Supply acquisition
  for a Navy Ship
• Represent predicted future power requirements as
  a lattice of potential values
• Lattice greatly increases transparency
• Visualization of decision points and results
• Makes underlying distribution of values discrete
• Input to Model ships current power
  requirements, and a description of how they
  should vary over time
• Can use arbitrary distribution, builds on Jeff
  Cares work

8
Example Ships Power Requirements Over Time
9
Example Ships Power Requirements Over Time

• Top node represents current power requirements
  99
• Each level in the lattice represents alternative
  possible power requirements for the following
  timestep
• Timestep arbitrary length of time (day, week,
  month, year) depending on desired lattice
  resolution
• 50/50 chance of progressing from a node to either
  of its children
• In this example, theres a 50 chance of having
  power needs of 99 in third timestep, but only 25
  chance of 54 or 635, because there are 2 paths
  from top node to 99 and only one to 54 or 635.
• Notice that numbers change relatively little
  between timesteps on left, dramatically between
  those on right. This represents possibility of
  rare but significant events.
• Next slide shows same lattice extended by one
  timestep. This lattice will be used in next
  couple examples

10
Example Additional Timestep
11
Defining The Acquisiton Environment

• In order to evaluate alternative acquisition
  strategies for fulfilling current and future
  power needs, need to know what power supplies are
  available.
• Power Supplies defined by
• Power Level provided
• Purchase cost
• Maintenance cost per timestep
• Also need to know cost of transitioning between
  two power supplies (cost of an upgrade or
  downgrade)
• Represents cost of installation and possible
  overhaul of other ship systems for compatibility
• Assume power requirements in lattice are minimum
  requirements, and must be met. There is a penalty
  for last minute upgrades (in following example,
  we assume a 10x penalty over standard upgrade
  cost)

12
Available Power Supplies
Normal Upgrade/Downgrade Cost
Last Minute Upgrade Cost
13
Assessing Alternate Strategies

• In the following set of slides well compare a
  number of alternative strategies for acquiring
  power supplies to satisfy the predicted power
  needs in the lattice
• Worst-case scenario strategy
• Most-likely case strategy
• Optimal strategy (as discovered by the model)

14
Building for the Worst Case

• Worst case strategy immediately purchases power
  supply to cover worst case predicted future power
  needs
• In the example lattice, worst case power needs
  are 1200 (bottom right node in lattice)
• Only Power Supply 3 (1200) provides enough power,
  so we purchase Power Supply 3
• Results on next slide

15
Build For Worst Case
Total Expected Cost3592
315 1200
16
Build For Worst Case

• Power requirements shown in white (as before)
• Power provided by power supply at that node shown
  in black.
• Since we always have enough power to cover needs
  we never upgrade, so power provided is always
  1200
• Notice that in the majority of the lattice we are
  significantly over-prepared for our power needs
• Paying purchase and maintenance costs that are
  higher than we need

17
Calculating Expected Cost

• Expected cost is the sum of
• The initial purchase cost
• The cost of any upgrade/downgrade at a node,
  times the probability of arriving at that node
• The cost of maintenance when leaving a node,
  times the probability of arriving at that node
• The average of total lifecycle cost over all
  possible outcomes
• All future costs discounted to current value
  using standard formula
• Cost cost/(1-discountRate)Timestep
• We used discountRate 0.1, but any rate could be
  used
• Additional details in final report

18
Build for Most Likely Case

• This strategy looks at what power needs are most
  likely to be in the future, and immediately
  purchases the cheapest supply that meets those
  needs
• In our example lattice, needs are most likely to
  be between 69 and 177
• Power supply 2 provides 800 power, cheapest
  supply that meets those needs
• Results on next slide

19
Build For Most Likely Case
Total Expected Cost 2614 (Worst Case 3592)
Red quick upgrade
20
Build for Most Likely Case

• Power requirements shown in white (as before)
• Power provided by power supply at that node shown
  in black.
• Less overprepared than in worst case lower
  expected cost
• BUT Notice that the bottom right node is bright
  red. This represents a last minute upgrade. The
  node requires 1200 power, but we came into the
  node with only 800, forcing an immediate costly
  upgrade
• We pay a penalty for being unprepared

21
Optimal Strategy

• Model looks at available power supplies and
  predicted power needs to determine optimal
  acquisition strategy
• Use an approach called dynamic programming to
  search for best of all possible strategies
  (details in final report)
• Does not attempt to meet all needs up front.
  Looks opportunistically for upgrade and downgrade
  opportunities

22
Lowest Expected Cost
Total Expected Cost 1788 (Worst Case 3592)
(Most Likely Case 2614)
Dark Blue downgrade Light red normal upgrade
23
Optimal Strategy

• Power requirements shown in white (as before)
• Power provided by power supply at that node shown
  in black.
• Lowest cost of all three strategies
• Notice dark blue node. This represents a
  downgrade to save on maintenance costs, when
  future power needs likely to be low
• Notice light red node. This represents an upgrade
  to prepare for a likely increase in future power
  requirements

24
Results and Implications

• Optimal strategy significantly cheaper than worst
  case and most likely case
• 50 savings over worst case planning
• 32 savings over most likely case planning
• This is because the optimal strategy is flexible
  in the face of uncertainty
• Worst case and most likely case attempt to cover
  all future possibilities immediately
• Optimal strategy waits for more to be known about
  future resource needs, then adapts accordingly
• Flexible approach allows optimal strategy to
  downgrade to save on maintenance costs and to
  upgrade in anticipation of increased power needs
• Less over-prepared
• Not caught unprepared

25
Custom Strategies

• Besides finding the optimal strategy, our model
  can be used to generate and evaluate custom
  acquisition strategies
• Worst case and Most likely case strategies are
  specific examples
• Allows user to specify acquisition behavior at
  any or all points in the lattice
• Pick a specific power supply to be used at a node
• Request no upgrades or downgrades occur at a node
• Leave node unconstrained (tool picks optimal
  behavior)
• In the example on the next slide the user
  constrains the top node of the lattice to use
  Power Supply 3 (1200 power)
• Power Supply 2 (800 power) was used by optimal
  strategy

26
Custom Strategy 1
Total Expected Cost 3383 (Optimal
1788) (Worst Case 3592) (Most Likely Case
2614)
99 1200
Node constrained to use power supply 1200
315 1200
54 75
99 1200
635 1200
Dark Blue downgrade Light red normal upgrade
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Custom Strategy 2

• As shown on slide 22, the optimal strategy
  upgrades power supplies in preparation for a
  likely increase in future power needs
• The user might decide that they prefer waiting
  and upgrading at the last minute, despite the
  higher cost
• As shown on the next slide, this strategy can be
  created by constraining the node at which the
  upgrade occurs to using the incoming power supply

28
Custom Strategy 2
Total Expected Cost 2583 (Optimal
1788) (Worst Case 3592) (Most Likely Case
2614)
99 800
315 800
Node constrained to Keeping incoming supply
54 75
99 800
635 800
1200 1200
Dark Blue downgrade Red quick upgrade
29
Custom Strategies

• Custom strategies allow the user to
• evaluate the cost of suggested strategies
• Modify the optimal strategy when the user would
  like to make different trade-offs than the model
• get a better understanding of the ways in which a
  suggested strategy will play out, and where the
  costs are coming from

30
Custom Strategies

• In many real world scenarios the optimal result
  may not be the right one to implement
• Optimal strategy does not take qualitative
  factors (e.g. political implications, personnel
  implications, difficulty of implementation) into
  account
• But, these qualitative factors often contribute
  significantly to the overall success of a
  strategy
• Sometimes it makes sense to pay more (use a
  suboptimal strategy) if it leads to higher
  overall likelihood of success
• Ability to specify custom/suboptimal strategy
  allows the user to see how much an extra comfort
  zone or increased probability of success would
  cost them

31
Modular vs Integrated Systems

• Following set of examples demonstrates models
  ability to explore impact of available resources
  (e.g. ship Power Supplies) on acquisition
  strategy and costs
• Specifically look at influence of modular systems
  vs integrated systems on lifecycle costs
• Assume integrated systems are somewhat cheaper to
  build/purchase initially, but prohibitively
  expensive to adapt
• Assume modular systems are somewhat more
  expensive to build/purchase, but are specifically
  designed to be adaptable (i.e. cheap upgrades and
  downgrades)
• Will use a lattice extended to 6 timesteps (next
  slide)

32
Example Ships Power Requirements Over Time
315
54
33
Standard System

• Start with a default case. Standard system is not
  impossible to adapt, but was not designed with
  adaptation in mind
• Provides a point of comparison for modular and
  highly integrated systems
• Available power supplies for standard system
  shown on next slide
• Last minute transitions not shown, but assumed to
  still be 10x standard transition cost

34
Available Power Supplies Standard System
Normal Upgrade
35
Standard System

• Next slide shows optimal strategy and expected
  cost for standard system
• To simplify the lattice, only the power provided
  by the equipped supply is shown, but power needed
  at the node remains the same (see slide 26)
• Dark Blue nodes represent a downgrade
• Light Red nodes represent an upgrade

36
Standard System
Total Expected Cost 5142
800
4000
75
4000
75
400,800
800,4000
75
37
Modular System

• Next, we look at a set of power supplies designed
  to be modular (i.e. cheap to upgrade or
  downgrade)
• We assume that each modular supply costs 50 more
  than its standard counterpart
• Represents the initial cost of designing
  components to be easily adapted and exchanged
• Transition costs are assumed to be low (50) and
  uniform between all supplies
• Available supplies and transition costs shown on
  next slide
• Changes from standard system shown in bold
• Last minute transitions remain 10x

38
Available Power Supplies Modular System
Normal Upgrade
39
Modular System

• Next slide shows optimal strategy and expected
  cost for modular system
• To simplify the lattice, only the power provided
  by the equipped supply is shown, but power needed
  at the node remains the same (see slide 26)
• Dark Blue nodes represent a downgrade
• Light Red nodes represent an upgrade
• Dark Red nodes represent a quick upgrade

40
Modular System
Total Expected Cost 3041
(Standard Cost 5142)
400
800
75
4000
75
400
400, 800,4000
400, 800,4000
75
41
Modular System

• Despite 50 higher initial purchase costs,
  modular system has lower expected cost than
  standard system
• Since modular system is designed to be adaptable,
  last minute upgrades are no longer prohibitively
  expensive
• Modular system can afford to wait until more is
  known about power needs, only upgrading to costly
  system when it is definitely needed (i.e.
  investing in modularity buying a waiting
  option)
• Able to rapidly adapt to changing environment

42
Highly Integrated System

• Finally, we look at a set of power supplies
  designed to be highly integrated
• We assume that each integrated supply costs 50
  less than its standard counterpart
• Represents savings in efficiency of highly
  integrated designs
• Transition costs are assumed to be extremely high
  (10,000) and uniform between all supplies
• Essentially have to scrap and redesign system
• Available supplies and transition costs shown on
  next slide
• Changes from standard system shown in bold
• Last minute transitions remain 10x

43
Available Power Supplies Integrated System
Normal Upgrade
44
Highly Integrated System

• Next slide shows optimal strategy and expected
  cost for integrated system
• To simplify the lattice, only the power provided
  by the equipped supply is shown, but power needed
  at the node remains the same (see slide 26)
• Dark Blue nodes represent a downgrade
• Light Red nodes represent an upgrade
• Dark Red nodes represent a quick upgrade

45
Highly Integrated System
Total Expected Cost 6193
(Standard Cost 5142)
(Modular Cost 3041)
800
4000
800
4000
800
800,4000
800,4000
800,4000
800
46
Results and Implications

• Expected cost of modular system was lower than
  both the standard (default) and highly integrated
  systems
• Expected cost 41 lower than standard system
• Expected cost 51 lower than integrated system
• Modular had lowest total lifecycle costs even
  though initial costs were 1.5x those for standard
  system and 3x those for the integrated system
• Modular system outperformed other two because it
  allowed for rapid, flexible responses to changes
  in the environment

47
Less Uncertain World

• In a world where future needs are known with
  relative accuracy, a modular system may not have
  an advantage
• The following lattice has a much smaller range of
  predicted values for power needs than our
  previous example
• We will look at the modular and highly integrated
  systems again, this time using the new lattice of
  resource needs

48
Example Less Uncertain World
115
52
49
Highly Integrated System
Total Expected Cost 968
400
400
50
Modular System
Total Expected Cost 1165
(Integrated Cost 968)
400
400
75
400
75
51
Implications and Results

• In this case, the integrated system had a
  somewhat lower cost than the modular
• When the future is known, there is less need for
  flexibility
• Model handles tradeoff between purchase cost and
  flexibility

52
Summary

• Real Options For Defense
• Values flexibility
• Incorporates lifecycle costs
• Under both common and rare conditions
• Manages complexity transparently
• Estimates true cost of existing/alternate
  acquisition strategies
• Discovers the optimal acquisition and
  upgrade/downgrade strategy

53
The Tool
54
The Tool

• Icosystem has provided a model of Real Options
  for Defense, as previously described
• Includes Graphical User Interface (GUI)
• Allows for extensive user input and interaction

55
The GUI

• Center of tool displays the models lattice
• Nodes color coded to indicate upgrades and
  downgrades
• color code identical to that in this presentation
• Dark Red quick upgrade
• Light Red upgrade
• Blue downgrade
• Right side panel allows choice of what to display
  in node
• Power needed at node
• Expected cost of this node
• Probability of reaching this node
• Power supply at node
• Hovering over a node displays all node information

56
The GUI - Probability of Node

• User can choose to have each node display its
  probability

57
The GUI

• Right side panel also displays critical results
  of model analysis
• Min, mean, max expected cost
• Min, mean, max expected upgrades/downgrades
• Min, mean, max expected quick upgrades
• Left side panel can be browsed to view current
  available power supplies and their transition
  matrices

Results Display
Left Side Panel
58
Interaction

• Users can double click any node to alter strategy
  at that node
• Pick specific power supply to be used at this
  node
• Request no upgrades/downgrades at this node
• Leave node unconstrained
• User can alter probability of going from node to
  its children (normally 50/50)
• User can also use buttons in right side panel to
  constrain all nodes to using incoming supply or
  to reset all nodes to unconstrained
• Allows user to focus on changing strategy only at
  specific nodes they care about

59
Interaction - Custom Strategy

• Nodes constrained by user are outlined in black

60
Interaction

• Buttons in right side panel allow user to see
  results of optimal, worst case, and most likely
  strategies on this lattice
• User can choose one of three underlying
  distributions to generate the lattice
• Normal (bell curve)
• Log normal
• Power law (as seen in this presentation)

Right Side Panel
61
Summary

• GUI significantly increases usability of ROD
• Previous work on Real Options mostly theoretical
• at best, provided users with Excel spreadsheets
  and equations
• often required them to work out complicated
  calculations and decision trees by hand
• ROD makes it extremely easy for the user not only
  to quickly analyze a variety of potential
  acquisition scenarios, but to actually see where
  the costs in those scenarios are coming from.
• Models user interface allows users to
• explore multiple acquisition strategies,
  including custom strategies
• View many different aspects of results (e.g.
  overall expected cost, expected cost of
  individual nodes, locations of upgrades and
  downgrades)

62
Directions From Here

• Trade-offs between multiple components, and
  multiple sources of uncertainty
• Components that arent mutually exclusive (e.g.
  adding armor on top of existing armor)
• Accounting for interdependencies between
  subsystems (e.g. engine and power supply)
• Joint analysis of research and acquisition
• Research outcomes interact with acquisition
  strategy
• Incorporate changes in cost and availability of
  components over time (e.g. improvements in
  manufacturing process)
• Transition and purchase costs change over time
• Automatically achieving cost and performance
  requirements
• Find parameters that achieve given cost goal,
  e.g. find closest maintenance costs that get us
  below cost X
• Allowing for strategic re-evaluation
• Inputting actual state of world at future time
  points into lattice to update strategy
• Going beyond acquisitions
• Applying ROD to other aspects of military
  decision-making (e.g. recruiting, budgeting,
  research investment)