MANAGING R&D AND RISKYPROJECTS

LOUIS ANTHONY COX , JR.Cox Associates and Department

of Mathematical andStatistical Sciences,University of Colorado,Denver, Colorado

Department of Risk Analysis,University of Colorado,Denver, Colorado

INTRODUCTION

Research and development (R&D) projectsare inherently risky. Investors in R&Dprojects are often uncertain about theprobability of eventual technical success,the costs and time needed to succeed,competitor activities, and market acceptanceand financial rewards if a technical successoccurs. Quantitative risk models can helpto characterize and manage R&D risks andto answer such practical risk managementdecision questions as the following:

• R&D Project Scheduling and Manage-ment. How to order the activities withina project, decision rules for when toabandon a project.

• R&D Project Selection. Which projectsto fund.

• R&D Investment Strategy. Howintensely or quickly to pursue R&D.

• R&D and Intellectual Property. Howto manage the results of R&D (e.g.,through licensing and patent systems)to create incentives that will benefitsociety.

This article surveys methods for quantify-ing and managing R&D risks.

Wiley Encyclopedia of Operations Research and Management Science, edited by James J. CochranCopyright © 2010 John Wiley & Sons, Inc.

MINIMIZING R&D PROJECT RISKS BYOPTIMALLY ORDERING ACTIVITIES

A very simple model of an R&D projectdivides it into multiple activities, eachhaving a known cost for attempting it and aknown probability that it can be successfullycompleted if it is attempted. An R&Dmanager may wish to minimize the expectedcost to either successfully complete the wholeproject or to learn (by trying activities andlearning that they fail) that it cannot becompleted. The problem of sequencing theproject activities to achieve this goal can besolved easily in certain cases.

Example: Optimal Sequencing of Activi-ties in a Risky Project.

Setting: Suppose that an R&D project can becompleted successfully only by successfullycompleting both of two activities, A and B.The cost to attempt activity A is cA = 1 costunit; the cost to attempt B is cB = 2 cost units;and the conditional probabilities of success-fully completing these activities, if they areattempted, are pA = 0.8 and pB = 0.5, respec-tively. The two activities may be attemptedin either order. The value of successfullycompleting the project (i.e., of successfullycompleting both A and B) is V = 10 benefitunits (on a scale commensurable with thecost units).

Problem: (i) What investment strategymaximizes the expected value of investmentin this set of R&D activities? (ii) What is theexpected value of this R&D project?

Solution: (i) Attempting A first, and then B ifA succeeds, yields an expected net value of

(cost to attempt A)+(probability A succeeds)

× (cost to attempt B after A succeeds

+ probability that B succeeds

× value obtained if B and A succeed)

1

2 MANAGING R&D AND RISKY PROJECTS

= −cA + pA × (−cB + pBV)

= −1 + 0.8 × (−2 + 0.5 × 10) = 1.4 units.

Symmetrically, attempting B first, andthen A if B succeeds, yields an expected netvalue of

− cB + pB × (−cA + pAV)

= −2 + 0.5 × (−1 + 0.8 × 10) = 1.5 units.

Since 1.5 is the higher value (and ispositive), the optimal strategy is to attemptB before A, and the expected monetary valueof the R&D project (if the optimal strategy isused) is 1.5.

More generally, trying A before B yields ahigher expected value than trying B before Aif and only if

− cA + pA(−cB + pB × V) > −cB

+ pB(−cA + pAV), or, equivalently, if

cB(1 − pA) > cA(1 − pB).

That is, for a project with positive expectedvalue, activities should be attempted in orderof decreasing failure-probability-per-unit-costratio (i.e., in order of decreasing ci/(1 − pi),where i = A or B in this example); this deci-sion rule holds for any number of activities.(Projects with negative expected value shouldnot be attempted at all, if the goal is tomaximize expected value.)

The preceding example is especiallysimple because completing the projectrequired all of the activities in it to becompleted. The only decision was the orderin which to attempt them. More generally,there may be several alternative ways tosuccessfully complete an R&D project. Asubset of activities is called a path setif completing all of the activities in itsuffices to successfully complete the project.A minimal path set is one in which noproper subset of activities is a path set.The project succeeds if and only if all of theactivities in at least one minimal path setare successfully completed. If minimal pathsets are disjoint, then an optimal (expectedvalue-maximizing) investment strategy is

to attempt alternative minimal path setsin decreasing order of success-probability-per-unit-expected cost (where the successprobability for a minimal path set is theproduct of the success probabilities of theactivities in it and the expected cost of theminimal path set is calculated assumingthat activities within each minimal pathset are sequenced in decreasing order offailure-probability-per-unit-cost ratio, as inthe preceding example). Investment in aproject should cease as soon as no minimalpath sets with positive expected valueremain.

These ideas can be extended to projects inwhich activities cannot be attempted in anyarbitrary order. Suppose that precedence con-straints among activities restrict the order inwhich they may be attempted. It may benecessary to complete some before others canbe attempted. Suppose that these constraintsare represented by some acyclic graph, whereeach edge represents an activity and eachactivity can be attempted if and only if all ofits predecessors have been successfully com-pleted. The project succeeds and its benefit isobtained if and only if at least one path is suc-cessfully completed from a starting activity(one with no predecessors) to an ending activ-ity (one with no successors). In this quite gen-eral framework, the optimal (expected utility-maximizing) investment strategy for a deci-sion maker with linear or exponential utilitycan still be found by assigning to each activ-ity a number called its index (by generalizingthe failure-probability-per-unit-cost ratio inthe preceding example) that can be computedquickly from the cost to attempt, successprobability, and precedence constraint data.The optimal decision rule is to attempt activ-ities in order of decreasing index until eithersuccess is achieved or no activities with pos-itive indices remain [1]. Many other exten-sions of index policies (also called Gittinsindex policies) have been developed for situa-tions with discount rates, randomly evolvingopportunity sets, and relatively sophisticatedmodels of risky projects, such as Markov deci-sion processes and multiarm bandit decisionproblems [2,3].

MANAGING R&D AND RISKY PROJECTS 3

OPTIMIZING R&D PROJECT PORTFOLIOS

Optimally sequencing the activities withinan R&D project can maximize the expectedutility of investing in it, by minimizing theexpected time or cost to either complete it,obtaining its benefits, or to discover thatthis cannot be done, if such is the case.But even after such within-project optimiza-tion, the problem of choosing a subset ofavailable R&D projects to fund—often frommany proposals—remains. Quantitativeapproaches to optimizing investment in pro-posed risky projects to maximize resultingnet benefits over time include the following:

• Combinatorial Optimization Models.These models search for combinations ofselect and reject decisions to maximizethe net value of the selected portfolio ofprojects, given budget constraints andpossible interactions and dependenciesamong the projects. Large-scale non-linear 0–1 programming and mixedinteger programming models have beendeveloped for this purpose and are prac-tical with current optimization technol-ogy and computational resources [4,5].

• Improving an Existing Portfolio. Givenany proposed portfolio of risky projects,optimization algorithms can seek tobuild a modified portfolio with preferredrisk-return characteristics by addingor deleting projects and modeling howsuch additions and deletions shiftthe predicted (simulated) probabilitydistribution of net return from theentire project portfolio, taking intoaccount interactions among projects [6].

• Continuous Dynamic Optimization.In continuous optimization models,explicit optimal investment formulascan be developed and interpretedas equating appropriately definedmarginal returns across investmentsin different projects. This leads todynamic resource allocation strategiesfor projects that may have statisti-cally dependent, dynamically evolvingmarket payoffs, assuming that partialinvestment in a project can generatepartial returns [7].

In general, optimization of R&D projectportfolios when there are strong interactionsamong projects (e.g., due to shared subsetsof activities or interdependencies amongtheir technical success probabilities and/ormarket values if successfully completed)provides a rich set of challenging prob-lems for sophisticated, computationallyintensive, optimization-based approachesto risk management. Promising approachesinclude simulation-optimization and robustand multicriteria optimization methods forportfolio selection, together with financialevaluation models that recognize the realoption value of risky projects that can beabandoned if they become unattractive. Thepharmaceutical and energy industries havedeveloped and applied many such models [8].

As a practical matter, R&D portfolio opti-mization models can require potentially bur-densome input data on project investmentopportunities and their interactions (e.g., onoverlapping tasks or substitute or comple-ment effects for benefits of different projects),especially since the number of possible inter-actions grows exponentially with the numberof projects. To ease this burden, some recentwork has explored the use of approximate(fuzzy) descriptions of potential future cashflows in assessing project portfolio values ina real options framework, leading to a fuzzymixed integer programming model for opti-mization of R&D portfolios [5].

OWNER VERSUS MANAGER INCENTIVES INR&D PROJECT MANAGEMENT

In the simplest case of a single minimal pathset and no precedence constraints, expectedvalue is maximized by attempting the ‘‘mostrisky’’ or ‘‘most difficult’’ activities first, thatis, those with the highest failure-probability-per-unit-cost ratios. This strategy minimizesthe expected cost of discovering that suc-cess is impossible, if such is the case. How-ever, rewarding a manager for successfullycompleted activities may create an incentiveto postpone high-risk activities as long aspossible, increasing the manager’s expectedreward but increasing the expected cost ofunsuccessful projects. Projects that should

4 MANAGING R&D AND RISKY PROJECTS

be abandoned may be continued too longif managers postpone attempting high-riskactivities until ones that are more likely tosucceed have been completed. Conversely,managers may abandon projects too soonand/or may invest too little effort in makingthem succeed (from the owner’s perspective)when effort and success probability are themanagers’ private information.

Such incentive problems (which areinstances of moral hazard and principal–agent conflict problems) can be largely over-come by evaluating partially completed R&Dprojects using a real options framework andthen compensating R&D managers accordingto these evaluations. More specifically, com-pensating R&D managers using appropriateadjusted residual income measures (withcapital charge rates that are contingent onmanager reports of estimated profitability,recognizing that these may be distorted bymanagers in an attempt to obtain greatercompensation) allows an effective separationof R&D investment decisions by owners andeffort allocation decisions by R&D managers.Such compensation rules optimally balanceincentives to invest in risky R&D againstincentives to abandon unfavorable projects insome specific models of owner and managerinformation and incentives [9].

OPTIMAL INTENSITY OF INVESTMENT INCOMPETITIVE R&D PROJECTS

When a company undertakes R&D to obtaina competitive advantage, time pressurefrom competition (especially in a ‘‘winnertakes all’’ patent and intellectual propertyenvironment) may make it worthwhile toinvest simultaneously in multiple alternativeapproaches (e.g., in multiple minimal pathsets). This stochastically reduces the time,but stochastically increases the cumulativeexpenditure, until either success is achievedor no attractive paths forward remain.

Exactly how intensely a company shouldinvest in R&D to maximize expectedprofit depends on how intensely competitorsinvest. Hence, quantitative models of optimalinvestment intensity are often formulated asdifferential games in continuous time, with

the competing firms deciding at each momenthow intensely to invest in R&D based oninformation available so far. In such com-petitive R&D models, details of R&D projectactivities are typically suppressed, and R&Dprojects are represented by relatively simplemodels such as functions showing how thecumulative probability (or, equivalently, thehazard function) for successful completion ofa project varies with the cumulative amountinvested. For example, in the simplest case,each increment of cost or effort creates a fixedprobability of successful completion (e.g.,successfully finding a new process, drug, or soon); if it does not, then the next increment ofcost or effort produces the same probability ofsuccess, and so forth. In this case, the proba-bility of succeeding within a budget of t unitsof cost or effort is just 1 − exp(−pt), wherep reflects the success probability per unit ofcost or effort. (In more general models, if it isassumed that the most promising approachesare tried first, then p is a decreasing func-tion of t.) In these models, incrementalinvestment purchases incremental successprobability, and more rapid expenditureshasten the time either until success occurs,it becomes optimal to abandon the project, orno investment opportunity remains. Typicalconclusions from such models are as follows:

• Competitive rivalry increases R&Dspending by each competitor when thebenefits of the first breakthrough arecaptured by the firm that achieves it[10].

• If patent protection is incomplete (e.g.,reflecting positive externalities fromincreased knowledge) and/or there areopportunities for licensing so that thebenefits of innovation may be sharedeven by noninnovators, then the effectsof competition on the overall pace ofinnovation are ambiguous. Only somefirms may invest in R&D, and socialwelfare may be either increased ordecreased compared to the ‘‘winnertakes all’’ situation [11].

Such strategic models of competitiveR&D investment and resulting project valuecomplement real options approaches that

MANAGING R&D AND RISKY PROJECTS 5

treat competitor actions as exogenouslyspecified and then optimize a firm’sabandonment decisions (i.e., choice of whenand whether to exercise the ‘‘option’’ toabandon). Such models typically assumethat remaining cost-to-complete is uncertainand evolves according to a random processas R&D proceeds [12].

CONCLUSIONS

Project portfolio selection, project manage-ment, and incentive design problems posechallenging practical applications for quanti-tative risk management methods. The stakesfor effective risk management methods inR&D and other risky projects are high, asthe same set of risky project opportunitiescan lead to either profits or losses, dependingon how well the risks are managed throughproject selection and management.

Although sophisticated quantitativemethods for modeling and managing R&Drisks (see R&D Risk Management) havebeen developed, as summarized in thisarticle and pursued further in the references,applying such methods in practice, withrealistically limited and uncertain data andestimates of potential future R&D costsand benefits continues to be challenging.Yet, it is of great importance in areas suchas pharmaceuticals, high technology, andenergy, where portfolios of risky projects(see Managing A Portfolio of Risks) oftendrive company value. Therefore, furtherdevelopment of practical methods for R&Drisk characterization and risk managementdecision making will probably remain anactive and rewarding area of both theoret-ical and applied risk management for theforeseeable future.

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