Multidimensional Opportunity Analysis

Introduction

Identifying, evaluating and communicating opportunities should be a best practice for every business investment analysis.  Fundamentally, business investment decisions are initiated for two reasons – to increase the potential for gain or to reduce the possibility of loss.  Investments result in a range between two possible outcomes, incurring either a benefit or a loss; the break-even point, no net loss or gain, may be considered a positive result for preservation of resources.  Investment decisions, even when proactively seeking an improvement to add value, typically focus towards mitigating potential negative outcomes and, deliberately or not, apply a risk mitigation approach intended to reduce the possibility of loss.  The Project Management Institute (2017) defines project risk as, “an uncertain event or condition that, if it occurs, has a positive or negative effect on one or more project objectives” (p. 307).  The positive effect may be classified as opportunity which could support value maximization – the return outweighs the cost (Dixit & Pindyck, 1995).

The Department of Defense (2017) states, “Opportunities are potential future benefits to the program’s cost, schedule, and/or performance baseline, usually achieved through proactive steps that include allocation of resources” (p. 43).  Kendrick (2015) also stated, “The primary meaning of opportunity related to a project involves the value anticipated from the project deliverable”.  In addition to project opportunity, Frederick, Novemsky, Wang, Dhar and Nowlis (2009) defined opportunity costs as, “The unrealized flow of utility from the alternatives a choice displaces” (p. 553).  Examining forgone potential opportunity Baratta (2007) stated, “The basic premise behind this metric is that as soon as we are aware that there is an opportunity to realize a defined business benefit by making some change in our business, then every moment that passes without that change being in effect, represents a lost benefit, a missed opportunity.  Therefore, we need to measure lost opportunity just as much as adherence to an estimate, which may actually be wrong.”

Though risk identification and associated risk management plans are often mandated in order to minimize loss, an opportunity model – to include opportunity costs and passed up potential opportunities – is typically not included in decision-making apart from possibly a lean component of SWOT analysis.  Formalizing the opportunity model would not only better inform investment decisions, but may also improve economic efficiency if selected opportunities result in resources more productively employed.  For example, the opportunity to reduce redundancies among business units might yield greater value than the potential return on alternative investment decisions taken by the individual business units.  An opportunity model should illuminate such strategic possibilities for decision maker consideration.  Strategic business decisions to further organizational objectives must go beyond narrowly considering the downside based on the traditional risk analysis paradigm.  Risk is characteristically evaluated as the relationship of the scales for two variables – probability and impact, represented as conventions (x) and (y) respectively.  Applying a similar approach for opportunity analysis, with the inclusion of a third variable scale (z) for investment resources, would enable more detailed decomposition into multidimensional components to identify potential options or reveal hidden value.

Traditional Approach

Investment decisions focusing on risk tolerance often base decisions on simplistic single-point green (low), yellow (medium) and red (high) visual indicators which are typically represented in the form of a five-cell-by-five-cell color-coded table derived from probability and impact scales.  Each of the 25 cells in the risk matrix heat map provides the measure of risk derived from associated qualitative translations of likelihood from “not likely” to “near certainty” and consequence ranging from “minimal impact” to “critical impact.”  As a business investment decision support tool, the color-coded representation is rudimentary for presenting opportunity and ineffective for articulating quantified risk.  Industry employs more complex models, often accompanied with statistical analysis; for example, weather forecasting calculates the likelihood for a significant number of variables to estimate impacts such as precipitation, temperature, and cloud cover (National Weather Service, n.d.).  Variables having linear relationships also allow for linear optimization programming models to minimize total risk while meeting goals (Lawrence & Pasternack, 2002).

Depending upon the type of investment – i.e., real estate, financial instruments, capital equipment, etc. – compound opportunity or risk statements should be normalized into single actionable events or conditions, and complex scenarios may be further decomposed into interrelated components.  Deconstructing opportunity and risk into constituent elements down to root cause(s) can be time consuming and may not be practical for every situation.  Subject matter experts (SME) are a good source for identifying and assigning accurate values to the opportunity decision variables, and recommending key variables to focus on.  The fundamental risk variables of probability and impact are important two-dimensional approach starting points, yet remain exiguous without correlation to investment constraints for informed allocation of resources.

Improving cost, schedule and/or performance is often equated to offsetting or decreasing negative impacts.  Risk mitigation is a reactive plan against potential loss or under performance while an opportunity strategy is proactive for possible gain or over performance in which – for the purpose of this review – the opportunity model axes boundaries separate mutually exclusive positive and negative return space.  Fundamentally, risk is based upon the likelihood of an event occurrence and the resulting impact of something bad.  Worst case risk outcomes occur in negative space, though scenarios could be evaluated that while remaining in positive space the results attain less than optimal goal outcomes.  In such situations, risk and opportunity overlap in the positive space.  For example, a risk might be stated as, “The probability that 1^st fiscal quarter earnings will not reach the 5 percent estimate.”  Earnings of less than zero would be negative (loss), while greater than zero but less than 5 percent – though below the target – would still be positive (gain).  Net positive values could be examined for opportunity.

Risk and opportunity are inverse – risk worsens and opportunity improves as probability and impact increase.  Euclidean three-dimensional cube space (x, y, z axes) affords an infinite number (n) of two dimensional plane values; incorporating time (t), which will not be presented here, could also provide a measure of change order.  While brainstorming often hypothesizes possibilities based upon unconstrained resources, the practical application of available investment resources for risk mitigation and opportunity exploitation, while remaining defined as the area within the three-dimensional space, limits the collection of useful points to a smaller range of numerical values narrowed by the resource scale.  Uncertainty (x), which exists for both risk and opportunity, is the probability expressed as a positive value between 0.0 (cannot occur) and 1.0 (certain occurrence); as risk is a tentative future event, 0 and 1 denote definitive results and are not included.  Impact (y) may have a negative (risk) or positive (opportunity) effect, calculated as an interval numerical value (which may be derived from an ordinal scale such as low, medium and high).  Available resources (z) further bounds opportunity within the positive impact space.

Opportunity Defined

Opportunity (O) represents the value placed upon a potential benefit, such as typical project control metrics that deliver net savings derived from improved cost or schedule results.  More difficult to specify are intangible benefits derived from faster decision-to-answer time or improved organizational performance in essential planning, organizing, directing and controlling operations.  However, reducing investment uncertainty for intangible benefits is possible as indicated by Hubbard (2014) and applied to an investment risk simulation example (Frum, 2017).  SME knowledge, supplemented with historical and industry statistics, may be a reliable source to both articulate the benefit variables such as cost/schedule/performance and also to accurately define the probability and impact variable numerical values.

Lowercase theta ᶿ from the Greek alphabet can represent the opportunity model, supported by the mathematical proof for the existence of an opportunity when defining the opportunity statement.  Calculating the quantitative value for an opportunity ᶿ – the opportunity score – permits plotting the x, y and z coordinates.  Though missed opportunity may also be quantitatively determined, as no actual loss to the balance sheet occurred, only the value of potential opportunity will be studied.  Achieving the potential opportunity may require either explicit (actual) cost, or implicit (tradeoff) equivalent cost had the resources been applied to alternate benefit options if available; implicit value would equate to (opportunity cost = selected option cost – not selected next best alternate option cost).

Equivalent opportunity cost examination in which diverse opportunities are compared based upon some common value, at least at an exploratory order of magnitude, is necessary to more definitely determine that the selected opportunity is valued above any alternate opportunities.  For example, an investor examining certificates of deposit at various financial institutions may consider not only the interest rates but also 24/7 account access, customer support, length of deposit requirements, physical versus on-line only commerce, etc. – all factors evaluated against a common and consistent quantitative scoring method – in choosing one institution over another.  The opportunity model ᶿ assumes to be true that for each type of opportunity, whether comprised of one or more constituent criteria, there is only a mutually exclusive single best choice possible to maximize return value, the selection cannot be divided such as a linear programming feasibility solution for constrained optimization or as an investor choosing to place a combination of funds in two or more CDs.

Opportunity Model

After a potential opportunity has been identified, the opportunity must be correctly stated – concisely and accurately defined – to proceed to numerical evaluation.  Simply stating that the organization wants to increase production while becoming more efficient is a general goal too ambiguous for measurement.  The opportunity must provide a specific, well defined and assessable value.  Adding specificity such as increasing production by 10 percent while becoming 5 percent more efficient within 12 months is a quantified outcome objective.  If the organization pursues an opportunity, then accurate, relevant, practical and computable performance measures must be applied to quantified resources for input, process, output and outcome to evaluate expected results.  The organization’s strategy is an appropriate starting point in which mission priorities, objectives and initiatives – all predetermined to be important to the organization – can inform opportunity construction, leading to selecting the most promising from possible alternatives.

Should investment in some combination of each opportunity be possible, then a linear programming maximizing/minimizing function might be applied to derive the optimal mix of resources.  As stated by Martinich (1997), “Constrained optimization models are mathematical models that find the best solution with respect to some evaluation criterion from a set of alternative solutions” (p. B2).  Comparing opportunities may be further challenging when the units of measure (M) are not equivalent.  For example, an investment that leads to improving senior leader decision time may need to be compared against employee training that improves processing time; for the former, direct access to data may reduce decision time from days to hours by visualization of metrics, while the latter might improve customer support by faster turn-around time for product purchase requests.  The organization would benefit from each alternative but resource constraints allow for just one investment selection.

Decision Variables.  Opportunity options – primary and alternate, if applicable – may be dissimilar, making comparison and choice decisions more challenging.  To calculate opportunity cost among dissimilar options, the quantity of resources required for each possible selection becomes the basis for comparing alternative choices.  The options must first be reduced to their equivalent per unit basis, such as the miles per gallon gasoline equivalent (MPGe) used by the Environmental Protection Agency to compare electric to gas vehicle fuel economy and average distance traveled per unit of energy consumed.  Reduce the opportunity expression to equivalent terms.  For example, when selecting the best value (most cost effective purchase) for protein among beef, fish or chicken, the protein per 100 grams of each does not provide all the necessary information for a decision.  Setting aside all other factors, consider on average that per 100 grams, beef contains approximately 36 grams of protein, fish provides 26 grams, and chicken has 18 grams – the logical component among the variables is protein.  Then determining the equivalency based upon cost per gram of protein enables improved opportunity selection among multiple candidates, indicating beef would be the best value; such as:

Opportunity equivalency (O_e), where ó is defined as logically equivalent.

Protein equivalency A_n ó Opportunity B_n ó Opportunity C_n

·         per 100gm: meat_36g ó fish_26g ó chicken_18g

O_e, setting the national average prices per 454 grams (1 pound):

·         beef = $2.49 = $0.55 per 100gm with 36 gm protein = $0.015 per gm protein

·         fish = $3.99 = $0.88 per 100gm with 26 gm protein = $0.034 per gm protein

·         chicken = $3.18 = $0.70 per 100gm with 18 gm protein = $0.039 per gm protein

Opportunity cost (O_c) = (selected option cost) – (not selected next best alternate option cost).

·         O_c = | (beef at $0.015 per gm protein) – (fish at $0.034 per gm protein) |

·         O_c = $0.019 per gm protein; selected O = beef

Objective Function.  

·         Opportunity cost O_c = |O_c – !O_c|, where O := !O and the quantity n of unit of measurement M = n x [M] = n[M]

·         O ó !O, opportunity alternatives that may or may not be homogeneous but allow for like or equivalent comparison and analysis based upon a common equivalent unit of measurement

·         unit of measurement M, allows for the multiple n of cost M for the same base units

Constraints.  Examples of limits or restrictions include: How much can be afforded to invest; How much can be afforded to lose to attain the desired effect; Is the opportunity time-bound; How many units of each type can be processed per person per unit of time; Are there legal specifications?  Opportunity constraints for a business with billion dollar earnings are likely not the same as a small owner-operator business.  Constraints must be well documented to determine if opportunity equivalency comparisons are appropriate.  Opportunity identification should also establish threshold cost-benefit performance measures such as those taken from strategic objective targets, existing performance and practice measures, resource or capacity constraints, legal or policy standards, analysis of similar organizations, industry statistics or best practice benchmarks.  The threshold should define that point at which if the organization can do better, then how much better per unit invested?  The costs avoided or dollars gained by a program must be defined.

Monte Carlo simulation is an excellent quantitative method for determining the likelihood of a potential opportunity over a range of values.  The subject-matter expert (SME) plays an essential role in determining opportunity, uncertainty, impact and constraints within their areas.  Figure 1 illustrates a hypothetical business opportunity simulation, indicating that for 10,000 simulations there is a 90 percent likelihood that the annual ROI will exceed about $46 million and a 10 percent probability that the annual ROI will exceed about $50 million, with a median (50 percent likelihood) expected annual ROI of about $48 million.

Opportunity Triplet

Representing the opportunity theta ᶿ values as ordered triplets (x, y, z) consisting of a scenario that characterizes the business objective and numerates the variable quantities will permit mathematically solving the ordered triple in ways meaningful to real world applications.  For example, the organization might determine the risk associated with a phishing and social engineering attack as the average impact cost of $1.6 million (M) and the likelihood of a targeted user clicking on the malicious attachment or link at 0.02736, with the risk value = ($1.6M x 0.02736) = $43,776.  Examining potential opportunities to reduce or offset the attack risk may yield increased cost savings (spend less than $43,776 for training) and training benefits (more flexible training scheduling) for performing security awareness and training in-house rather than outsourcing; for example, where,

x = possibility expressed as a probability; based upon best empirical data.

y = impact requires an accurate, meaningful and quantitative measurement in order to answer the business impact question: How significant would the benefit or value of the opportunity be to the organization?  A basic impact scale similar to the risk likelihood criteria described by DoD (2017) in Figure 2 would assess opportunity based upon Likert scales ranging from ‘minimal impact’ to ‘critical impact’.  Likert scales are ordinal, meaning the importance can be ranked but not accurately interpreted mathematically and would require corresponding numerical (interval) levels ranging from 1 (minimal) to 5 (critical).  The organization should develop standard impact rating criteria for evaluation consistency.  The SMEs as domain knowledge authorities provide insight in assessing impact as they are typically more knowledgeable than others regarding consequences within their area.

z = investment resources in which the z axis represents the positive range of potential opportunity values based on assets available such as funds, personnel and time to pursue objectives.  As previously expressed, a common unit of measurement is required to determine opportunity value (opportunity cost = selected option cost – not selected next best alternative option cost).

The (x, y, z) ordered triplet of numbers in this model represents point P on the axes within the positive coordinate space (+,+,+) corresponding to the top-right-front first octant.  In Cartesian geometry with three mutually perpendicular axes, the area of positive z coordinates with equal probability would take the shape of a cube as depicted in Figure 3.  After establishing the ordered triplet variable values, determining the opportunity value is a relatively straightforward point computation as shown in Table 1; which shows that Opportunity 1 would require a higher investment but could yield a higher result with O_c = ($22,500 – $12,000) = $10,500.  Varying the value of z represents a range of opportunity values along the z coordinate axis.  As with the example illustrated in Figure 1, more detailed analysis and simulation could be performed to arrive at population mean, standard deviation, confidence intervals and similar evaluations.

  

Table 1
Comparing Two Different Opportunities with Cost as Unit of Measure
Variable	Opportunity 1	Opportunity 2
x (likelihood)	0.75	0.60
y (impact)	3	4
z (investment)	$10,000	$5,000
ᶿ = (x) x (y) x (z)	$22,500	$12,000
Note. Opportunity Cost Oc = (O1 – O2) = ($22,500 - $12,000) = $10,500

  

Opportunity Plane

Another consideration of positive opportunity space could be the property of opportunity aggregate group (g) in which each z coordinate, should more than one exist, would be elaborated to include differentiating detail(s) for further examination and exploitation.  The (x, y, z) ordered triple numbering convention would share the same z value with either or both x and y values, varying to produce differentiating characteristics of the specific individual opportunity.  Each initial triplet such as (x8, y8, z8) and additional triplet such as (x1, y3, z8) extending from the initial triplet will determine a straight line, and all differentiating characteristic triplets in which z remains constant (i.e., z = 8) will lie in the same unique (x, y) plane surface as spatially illustrated in Figure 4.  The range of an individual opportunity option would be the difference between the worth assigned to the highest and lowest triplet values for which z = constant as listed in Table 2.  For example, a gambler with a single $100 chip to wager must decide whether a win with one roll of the dice (O₁), one card draw (O₂) or one slot machine spin (O₃) would yield the best desired outcome.

  

Table 2
Comparing Three Opportunities in One Group with Same z Value
Variable	Opportunity 1	Opportunity 2	Opportunity 3
x (likelihood)	0.75	0.60	0.40
y (impact)	3	4	5
Z (investment)	$100	$100	$100
ᶿ = (x) x (y) x (z)	$225	$240 (highest)	$200 (lowest)
Note. Opportunity Range = (O2 – O3) = ($240 - $200) = $40

  

Conclusions and Recommendations

Commercial enterprises in competitive markets continually seek opportunities to grow their businesses; both opportunity recognition and opportunity exploitation are positively associated with innovations (Kuckertz, Kollmann, Krell, & Stöckmann, 2017).  Opportunity is incorporated into the capital budgeting decision based upon economic analysis of investment projects such as cost-benefit analysis (Bierman & Smidt, 2012, p. 8).  The absence of market forces generally deprives the motivation to pursue opportunity and innovation which is often accompanied by change and disruption.  Opportunity as described by DoD (2017a) covers 5 pages including a single opportunity management vignette, whereas risk management covers 23 pages.  DoD acquisition program guidance states risk 212 times and opportunity 4 times (DoD, 2017,b).  The difference allotted to the two topics reveals the prominence placed on mitigating the downside and lack of emphasis on exploring and quantifiably articulating the upside, effectively incentivizing risk aversion, apart from offices specifically focused on innovation.

The basic high-level risk model typically depicts a 5x5 cell matrix in which the combination of likelihood and impact determine a color coded risk level for low (green), moderate (yellow), and high (red).  As a business investment decision support tool, the color-coded representation is ineffective for articulating quantified risk probability distributions for a range of possible outcomes for any meaningful choice of action.  Beyond signaling candidate areas for in-depth analysis, the same approach is also an insufficient opportunity framework, particularly to facilitate goal achievement.  Opportunity estimation must become more than a cursory mirror approach to risk management, communicated as abstract qualitative concepts represented in terms of three colors.

Multidimensional opportunity analysis offers an improved model to quantitatively explore initiatives that may yield potential improvements in cost, schedule reductions, and/or performance.  Measurable opportunity evaluation should become an integral part of Defense acquisition program management and systems engineering, elaborated in a range of policy, regulatory, and statutory directives.

To begin improving cost, schedule, and performance opportunity benefit analysis I recommend the following:

(1) Incorporate opportunity equivalency and opportunity cost in Department of Defense guides that address opportunity particularly in the Acquisition field;

(2) Require the opportunity theta model based upon ordered triplets in which x represents possibility expressed as a probability, y represents impact requiring an accurate, meaningful and quantitative measurement, and z represents investment resources for all potential investment decisions exceeding $1 million. 

Published in Defense Acquisition: July-August 2019 (http://www.dau.mil/library/defense-atl/DATLFiles/Jul_Aug2019/Frum.pdf)

References

Baratta, A. (2007). The value triple constraint: measuring the effectiveness of the project management paradigm. Paper presented at PMI® Global Congress 2007—North America, Atlanta, GA. Newtown Square, PA: Project Management Institute.

Bierman Jr, H., & Smidt, S. (2012). The capital budgeting decision: economic analysis of investment projects. Routledge.

Department of Defense (DoD). (2017a). Risk, issue, and opportunity management guide for defense acquisition programs. Retrieved from https://www.acq.osd.mil/se/docs/2017-rio.pdf

DoD. (2017b). Operation of the Defense acquisition system. Retrieved from http://acqnotes.com/wp-content/uploads/2014/09/DoD-Instruction-5000.02-The-Defense-Acquisition-System-10-Aug-17-Change-3.pdf

Dixit, A. K., & Pindyck, R. S. (1995). The options approach to capital investment. Real Options and Investment under Uncertainty-classical Readings and Recent Contributions. MIT Press, Cambridge, 6.

Frum, R. (2017, November-December). How to improve communication of information technology investments risks.  Defense AT&L, 44-48.

Frederick, S., Novemsky, N., Wang, J., Dhar, R., & Nowlis, S. (2009). Opportunity cost neglect. Journal of Consumer Research, 36(4), 553-561.

Hubbard, D. W. (2014). How to measure anything: Finding the value of intangibles in business. John Wiley & Sons.

Kendrick, T. (2015). Project opportunity: risk sink or risk source? Paper presented at PMI® Global Congress 2015—North America, Orlando, FL. Newtown Square, PA: Project Management Institute.

Kuckertz, A., Kollmann, T., Krell, P., & Stöckmann, C. (2017). Understanding, differentiating, and measuring opportunity recognition and opportunity exploitation. International Journal of Entrepreneurial Behavior & Research, 23(1), 78-97.

Lawrence, J. A., & Pasternack, B. A. (2002). Applied management science: modeling, spreadsheet analysis, and communication for decision making. New York: Wiley.

Martinich, Joseph S. 1997. Production and operations management: An applied modern approach. New York, New York: John Wiley & Sons, Incorporated

National Weather Service. (n.d.). Welcome to the statistical modeling branch. Retrieved from https://www.weather.gov/mdl/StatisticalModeling_home

Project Management Institute. (2017). A guide to the project management body of knowledge (PMBOK® Guide) - sixth edition. Retrieved from https://www.pmi.org/pmbok-guide-standards/foundational/pmbok#