resallocpolicies duration

& ResearchPaper

Effects of Resource Allocation Policies forReducing Project Durations: A SystemsModelling Approach

Zee Woon Lee1, David N. Ford2* and Nitin Joglekar3

1Syska Hennessy Group, 502 Carnegie Center, Princeton, New Jersy, USA2Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas, USA3Boston University School of Management, 595 Commonwealth Avenue, Boston, Massachusetts, USA

Minimizing duration is critical to success in many development projects. Resourceallocation policies during such projects determine the fractions of resources that are tobe assigned to constituent tasks. The choice of allocation policy can strongly influenceproject durations. But policies for reduced project duration are difficult to design andimplement because of closed loop flows of work that generate dynamic demand patternsand delays in shifting resources among activities. Resource demand estimates andresource adjustment times are two policy features that managers can readily alter toinfluence project durations. These features are used to describe allocation policies in arelatively simple project model. Myopic and foresighted policies are distinguished bytheir use (or lack thereof) of rework and multiple backlogs in allocation. Optimal policiesunder perfect and limited managerial control are described by testing myopic andforesighted policies across a range of project complexities and adjustment times underdeterministic and uncertain conditions. Counter-intuitive results from this analysisindicate that minimum resource allocation delay does not produce minimum durations,and increasing uncertainty decreases durations under certain conditions. The model isused to explain these results. Managerial implications and future research topics arediscussed. Copyright # 2007 John Wiley & Sons, Ltd.

Keywords uncertainty; resource allocation; policy design; policy analysis; project management

INTRODUCTION

Completing development projects after theirdeadlines is a common but expensive problemthat has been well documented in the literature(e.g. Scott, 1993). Meeting schedule deadlines is

SystemsResearch andBehavioral ScienceSyst. Res.24, 551^566 (2007)Published online inWiley InterScience(www.interscience.wiley.com)DOI:10.1002/sres.809

*Correspondence to: David N. Ford, Zachry Department of CivilEngineering, Texas A&M University, College Station, TX77843-3136, USA.E-mail: [email protected]

Copyright # 2007 John Wiley & Sons, Ltd.Received 29 September 2005Accepted 23 October 2006

often the most important concern for managers(Wheelwright and Clark, 1992; Meyer, 1993;Patterson, 1993; Lyneis et al., 2001). Two app-roaches to improving schedule performance areprocess improvements and resource management.A variety of process improvement approaches toimproving schedule performance have beenexplored, including dynamic planning and con-current development (Backhouse and Brookes,1996; Pena-Mora and Park, 2001), the use ofinformation technology tools (Joglekar and Whit-ney, 1999), and cross-functional developmentteams (Moffatt, 1998). But the challenges ofmanaging uncertain project conditions and con-straints imposed by cost, product architecture, andproject participant relationships often constrainmanagers’ ability to effectively improve projectsthrough process improvement (e.g. see Joglekaret al., 2001). Therefore resource management isimportant to the timely completion of projects andreducing project durations.

Development projects in general and theresource management of those projects in specificcan benefit from a systems perspective. Develop-ment projects are systems of diverse componentslinked by rich interactions (Simon, 1996). Theseinteractions are as, or more, important to under-standing and controlling project behaviour andperformance as the detailed features of specificcomponents. One result is that project systemsevolve over time in ways that are difficult toexplain and control effectively. Systemsapproaches have been used to perceive andmodeldevelopment projects (Taylor and DaCosta, 1999;Misra, 2002; Alberts et al., 2004) and can provideinsight into how project structures drive beha-viour and performance. The current work appliesthe system dynamics approach. System dynamicscombines servo-mechanism thinking with com-puter simulation to analyse systems (Forrester,1961, 1968; Sterman, 2000). System dynamics isone of several established and successfulapproaches to systems analysis and design (Floodand Jackson, 1991; Lane and Jackson, 1995;Jackson, 2003). It shares many fundamentalsystems concepts with other approaches, includ-ing emergence, control and layered systemstructures. Therefore system dynamics canaddress broad systems concerns such as ration-

ality in systemmanagement (Lane et al., 2004) andorganizing assumptions (Lane, 2000). For examplethe current work includes an investigation of theimpacts of differences between managerialassumptions used in policy design, due largelyto bounded rationality, and conditions experi-enced in practice. As will be illustrated, therelatively formal, mathematically orientedperspective taken by system dynamics providesvaluable opportunities for model and behaviouranalysis.

System dynamics has been applied extensivelyto the investigation of development projects overseveral decades. The methodology is particularlyuseful in this context because of its ability tomodel the delayed information feedback, flowsand accumulations of work, and non-linearrelationships that characterize development(Cooper, 1993a,b,c; Ford and Sterman, 1998).When applied to projects system dynamicsfocuses on how performance evolves in responseto interactions between managerial decision-making and development processes. Systemdynamics has been successfully applied to studythe impacts of a variety of management issues onproject performance, including changes inproject scope (Cooper, 1980; Rodrigues andWilliams, 1997), rework (Cooper, 1980, 1993a,1994), poor schedule performance (Abdel-Hamid, 1988, Abdel-Hamid and Madnick,1991), failures in project fast track implementa-tion (Ford and Sterman, 2003a); and concealingrework requirements (Ford and Sterman,2003b). Specific system dynamics researchrelevant to the impacts of resource managementon project performance includes the work ofCooper (1993a, b, c), Graham (2000) and others onthe importance of early error detection. Thecurrent work focuses on the impacts of resourcemanagement policies on project schedule per-formance.

Development project resource managementcan improve schedule performance by increasingthe quantity of resources, productivity andutilization. Total resource quantities and associ-ated productivities are often limited and difficultor expensive to improve, leaving resourceutilization as a primary management tool toreduce project durations. Managers can have a

Copyright � 2007 JohnWiley & Sons,Ltd. Syst. Res.24, 551^566 (2007)DOI:10.1002/sres

552 ZeeWoon Lee et al.

RESEARCHPAPER Syst. Res.

large effect on resource utilization through thepolicies they use to allocate resources amongdevelopment activities, even when the totalquantity and productivity of resources are fixed.For example a design manager can impact whenall design components are completed by allocat-ing the optimal fraction of the available designersto the initial design of components, the checkingof designs to identify needed changes, and thecorrection or improvement of componentdesigns. Applying too few resources to anygiven activity slows progress and applying toomany can cause crowding that reduces pro-ductivity and wastes resources that could beused more efficiently by other activities. There-fore the effective and efficient allocation of scarceresources among development phases andamong activities within phases is a realisticmanagement opportunity for improving projectschedule performance. The current work focuseson resource allocation policies as a means ofreducing project duration and seeks to improveunderstanding of the impacts of these policies onproject durations through project systems mod-elling and analysis. Sterman’s (2000) descriptionof policies as decision-making rules is adoptedhere. In this context resource allocation policiesare formal heuristics or guidelines which man-agers use to make individual decisions aboutwhere to apply resources. For example the criticalpath method mantra ‘Feed the critical path [withresources]’ is an informal resource allocationheuristic that could be formalized into a policy offilling all resource needs of critical path activitiesbefore allocating resources to other activities.Improved understanding of how resource allo-cation policies impact project schedules canimprove performance.

Despite the potential of improving resourceallocation policies to reduce development dura-tions, relatively little research has investigatedallocation policy design. Resource allocationpolicies can include many types of information,including resource needs across activities andtime, productivities of resource types, and resourceavailability. The current work focuses on howthree policy features impact development projectdurations: (1) whether to base allocations oncurrent or future conditions, (2) how quickly to

adjust resources and (3) how much control toexert over resource adjustment speed. Based onmodel analysis we propose and investigatetuning managerial delays as a potential advance-ment in project management. We investigate theapplication of tuning these delays to resourceallocation policy design. Challenges in the designof resource allocation policies are described in thenext section, followed by background for theinvestigation. The research approach and modelare described in Section 5. How the model wasused and the results of simulations are followedby discussion and conclusions.

CHALLENGES IN PROJECT RESOURCEALLOCATION POLICY DESIGN

The design of resource allocation policies isdifficult because of two inherent characteristics ofdevelopment: iteration and delays in implement-ing allocation decisions. Development processesare iterative by nature. Iteration creates closedloop flows of work in which defects or optionalchanges for improvement are discovered,changes are made, and the work is checked ortested again for additional change requirements.Iteration can greatly magnify the total work effortneeded for completion because rework canexpose or create additional change requirements,which creates more rework etc. An emergingbody of product innovation literature deploys thedesign structure matrix (DSM) methodology toexplore the iteration and allied interdependenceproblems (Steward, 1981; Eppinger et al., 1994;Smith and Eppinger, 1997; Sosa et al., 2004). Thismethodology accounts for iterations by mappingthe dependencies between a value chain ofinnovation tasks in terms of precedence, infor-mation exchange requirements and probabilityof rework. Browning and Eppinger (2002) haveexplored a network using simulation to assesscosts and schedule risks. Helo et al. (2004) havedeployed DSM with systems thinking method-ology to assess economic impacts of uncertaintywithin feedback loops and studied a number ofalternatives in decision-making to possibly avoiditerative situations.


Resource Allocation Policies for Reducing Project Durations 553

Syst. Res. RESEARCHPAPER

Effective and efficient resource allocation foriterative projects or project phases is difficultbecause of challenges in accurately predictingthe sizes of work backlogs, specifically theamounts of work that must be initially com-pleted, work to be inspected or tested todiscover change requirements, and work to bereworked. These work backlogs evolve duringprojects. Consider, for example a design phasewithout the benefits or burdens of starting withpreviously developed work. At the beginning ofthe phase all work packages must be initiallycompleted and none are yet available for qualityassurance or rework. As work is designed thedesign backlog (and the need for designers)decreases and the quality assurance andrework backlogs (and their resource needs)increase, but at different rates. The qualityassurance and rework backlogs later decreaseas work is approved and designs finished.The dynamics of rework cycles make workbacklogs difficult to predict. Given the limita-tions of human cognition (Simon, 1996), especi-ally in managing dynamic systems (Senge,1990), managers cannot predict resource needsaccurately enough for effective resourceallocation.

Delays in making allocation decisions, imple-menting reallocations, and productivityramp-up of re-allocated resources also makeresource allocation policy design difficult.Resource adjustment delays can be large dueto the number of information and physicalactivities that must occur for a complete changein allocation, the time requirements for thoseactivities, and the prerequisite informationneeds in those processes. For example reallocat-ing ironworkers from correcting flawed struc-tural steel connections to inspecting new con-nections requires observing and collectingbacklog sizes and current workforce allocations,forecasting demands for ironworkers, determin-ing desired allocations, informing the supervisorof the new targets, selecting and instructing theaffected ironworkers, the relocation of ironwor-kers and necessary equipment and tools, and theramp-up of iron workers to full productivity intheir new assignments. Intuitively, managersshould incorporate resource adjustment delays

into allocation policies. But several types ofmanagerial errors can thwart these efforts,including the previously discussed challengesin predicting the sizes of multiple interactingbacklogs, the uncertain sizes of actual delays,and the lack of understanding of how demandforecasting and allocation delays impact per-formance. Much of the analytical literature oninnovation project management (e.g. the DSMstudies cited above, with Yassine et al., 2003 as anotable exception) assume there are no resourceallocation delays, that these exchanges areperfectly synchronized, or both. Studies in thesystems dynamics tradition explicitly modeldelays while allocating resources in a varietyof problem settings (Ford and Sterman, 1998;Helo, 2000; Sterman, 2000). In the next section weexplore the literature on how foresight inestimating resource demands and resourceadjustment delays impact project scheduleperformance.

BACKGROUND

Resource allocation research often focuses on asingle resource type (e.g. money, labour, equip-ment, managerial effort) because of the uniqueimpacts of different resource types on perform-ance. For example Shohet and Perelstein (2004)propose a methodology for prioritizing rehabi-litation projects for the allocation of funding.Within individual construction projects resourceallocation is often studied as a special caseof scheduling problems (e.g. the resource-constrained scheduling problem) in which theresource is labour or equipment. These studieshave used heuristics (Gordon, 1983; Hong et al.,2001) and genetic algorithms (Chan and David,1996) in connection with activity modellingto allocate resources1. These approaches fail

1Frequently activity priorities are used to fully meet one activity’sdemand before allocating remaining resources to lower priority activi-ties. This approach appears unlikely to be used extensively in practicebecause managers would be forced to completely neglect some activi-ties that need resources while completely satisfying others and itincreases the discontinuity of allocations, which Joglekar and Ford(2005) found problematic.




to address the dynamic systems nature ofdevelopment projects and focus on scheduling,not resource allocation policies. They thereforecannot fully address the issues describedabove.

Resource allocation can be based on a simpleheuristic: allocate resources to each developmentactivity in the same proportion that the activity’scurrent backlog contributes to the total backlog(e.g. Repenning, 2001). This policy is attractive forat least three reasons: (1) current conditions arerelatively easy to observe and use, (2) currentconditions are easier than forecasted demands todefend to policy critics and (3) basing allocationson current conditions and direct proportions iscognitively simple. But such a policy has at leasttwo important defects. The policy fails to includethe impacts of future changes in backlogs and thegrowth in total effort required due to rework. Incontrast, Joglekar and Ford (2005) recommendbasing allocations on estimates of future resourcedemands that are continuously adjusted basedon current conditions. This approach partiallyaddresses the challenges posed by allocationdelays.

Previous research also supports the import-ant role of delays in controlling dynamicsystems. Structural control system researchershave studied how delays between signals fromsensors and actuators impact structural systembehaviour and found that purposeful timedelays can improve structural behaviour overeliminating time delays (Mahmoud andAl-Muthairi, 1994; Udwadia et al., 2003). Thissuggests that managers can improve scheduleperformance by tuning resource adjustmentdelays to the characteristics of developmentprojects. Control theory and model simulationssuggest that the size of resource adjustmentdelays can also significantly impact durations.But little research has been done to investigate theimpact of resource adjustment delays on projectperformance or the tuning of managerial delaysto project features and characteristics. Noresearch is known to develop or test this concept,and specifically the design of delay sizes forreduced durations, as a potentially significantand inexpensive means of improving develop-ment projects.

RESEARCH METHODOLOGY

Research Approach

The current work uses an experimental approachto investigate the relationship between resourceallocation policies and schedule performance.Individual project characteristics are varied incontrolled conditions to isolate and understandtheir impacts. Most actual development projectsare poor settings for controlled experiments dueto the many confounding features and charac-teristics that are difficult to control. Actualprojects are also generally unavailable for policyexperimentation due to the poor performance ofsome experimental treatments, which are unac-ceptable to project participants. Therefore acomputer model of a development project wasdeveloped and used for experimentation. Thesystem dynamics methodology (Forrester, 1961;Sterman, 2000) was applied to model the flowsand accumulations of work, delayed informationfeedback, and the non-linear relationships thatcharacterize construction projects (Cooper,1993a; Ford and Sterman, 1998).

The model is used to address a single, narrowaspect of development project management.Therefore, the model is simple relative to actualpractice to expose the relationships betweenresource allocation policy structures and projectbehaviours. Although many development pro-cesses and the features of project participantsinteract to determine project schedule perform-ance, only those features that describe resourceallocation policies and the fundamental pro-cesses they impact are included. Simplifyingassumptions about previously investigated pro-ject structures reduce the confounding of results.For example total resource quantities andproductivities are assumed fixed and all workin backlogs is assumed to be available fordevelopment. Simulated performances usingdifferent policies are, therefore, consideredrelative and useful for comparing allocationpolicies and developing insights, but not suffi-cient for final policy design. The literature citedabove investigates the impacts of these and otherfactors influencing performance. This researchapproach allows the investigation to focus on




how specific policy choices and project charac-teristics impact durations. Potential impacts ofrelaxing modelling assumptions on results arediscussed in the conclusions.

A MODEL OF RESOURCE ALLOCATIONIN DEVELOPMENT PROJECTS

The model structure is based on previouslyvalidated models of development project pro-cesses andmanagement as referenced below. Themodel maps the backlogs and flows of work in aproject and the information structures andpolicies used to allocate resources. The inter-actions among the work and information com-ponents of the model describe the use of projectinformation (e.g. work backlog sizes) and man-agerial policies to influence project progress.Individual relationships are specified with rela-tively simple algebraic equations that reflect theinteractions among project components. Becauseclosed form solutions are unknown the beha-viour of the system over time was simulated.

The model has two sectors: a workflow sectorand a resource allocation sector. The workflowsector models project processes through theflows of work (in small fungible work packages)and the resulting changes of backlogs, asinfluenced by project characteristics such asproject complexity. The resource allocation sectordescribes policies for allocating resources andtheir implementation, including delays. Theinteractions between the workflow and resourceallocation sectors describe the use of resourcesand information to control project scheduleperformance (see Lee (2004) for more detail).The model structure is described next. Thecomplete documented model is available fromthe authors or at http://ceprofs.tamu.edu/dford/.

Modelling Work Flows, DevelopmentProcesses and Resource Impacts

The model represents workflows through aproject as a value chain of alternating backlogsand development activities with a rework cycle

(Figure 1). The rework cycle is inherent indevelopment projects and has been modelledand used extensively to explain and improveproject management (Taylor and Ford, 2006;Lyneis et al., 2001; Ford and Sterman, 1998;Cooper and Mullen, 1993; Cooper, 1980,1993a, b, c, 1994). The model used here describesthe flows of work through a new project in whichall work starts in the backlog2 of work needing tobe initially completed (box at bottom of Figure 1).The initial completion of work moves work intothe backlog of work needing to be inspected orchecked by quality assurance (QA) operations(box in middle of Figure 1). Quality assurancedrains this backlog, with a portion of the workbeing discovered to require rework and enteringthe project’s rework cycle. This work enters therework backlog (box at upper left of Figure 1) andremains there until changes are made. Rework isreturned to the quality assurance backlogbecause performing rework can create or revealadditional rework requirements. Work that is notdiscovered to require rework is approved andreleased (at right of Figure 1). The specificworkflow structure used here (Figure 2) wasdeveloped for projects by Ford and Sterman(1998) and has been applied to explain con-current development implementation failure(Ford and Sterman, 2003b) and the role of tippingpoints (Taylor and Ford, 2006) and managerialbehaviour (Ford and Sterman, 2003a) in projectperformance. The project work flow structureshown in Figure 1 is a value chain throughinitial completion, quality assurance, and workapproval and release with a rework cyclethrough the discovery of required rework,rework backlog and rework activity. The fractionof work discovered to require rework is used tomodel project complexity. More complex pro-blems are assumed to require more iteration forcompletion. Quality assurance efforts areassumed to identify all rework needs. See Fordand Sterman (2003a, b) for a more detailed modelof iteration and studies of the impacts ofimperfect quality assurance.

2Because the flows of development activities reflect the completion ofthe activity, the backlogs, as used here, include work in progress aswell as development work that has not yet started.




Project progress depends largely on howmuchwork gets trapped in the rework cycle versushowmuch ‘leaks out’ of the rework cycle throughapproval. But process rates also constrain pro-gress. The initial completion, quality assurance,and rework rates are each a fraction of the ratesallowed if the development process has infiniteresources (i.e. uncapacitated conditions). Unca-

pacitated process rates are described with anaverage processing time that is assumed equalfor all three rates for simplicity. The fractionthat reduces each activity’s progress from itsuncapacitated rate is the rate allowed by theresources allocated to the activity divided bythe rate assuming the activity was allocated allthe resources. Progress rates for the three

Figure 1. A project work flow model

Figure 2. Work backlogs (50% rework and myopic policy)




development activities (initial completion, qual-ity assurance and rework) allowed by resourcesare modelled as the product of the total availableresources (assumed constant), productivities(assumed constant and equal), and appliedresource allocation fractions. Therefore resourcesimpact progress through the application ofallocation fractions to individual developmentactivities. These fractions are determined by theresource allocation policy. This formulationallows uncapacitated progress by an activity ifit is allocated all of the resources, no progress ifno resources are allocated, and progress directlyproportional to resources in between theseboundary conditions. The model generatesrealistic and complex behaviour despite thesimplicity of this formulation. This formulationelucidates the impacts of resource allocationpolicies by isolating the quantity of resourcesallocated as the driver of differences in modelbehaviour.

Modelling Resource Allocation Policies

Resource allocation targets can be based oncurrent or forecasted resource needs. Targetsbased on current conditions use the backlogsimmediately upstream of initial completion,quality assurance, and rework operations asthe basis for allocation. Consistent with Joglekarand Ford (2005) we call these policies ‘myopic’because they do not use future conditions and aretherefore relatively shortsighted. Resource frac-tions in myopic policies are the proportion of thetotal backlog that each current backlogrepresents.

However, as projects progress operationsdrain one backlog as they fill others (e.g. reworksimultaneously reduces the rework backlog andincreases the quality assurance backlog) and therework cycle amplifies the effort required tocomplete the project. Managers who are aware ofthese characteristics may use this understanding(perhaps tacitly) to forecast resource demand.Joglekar and Ford (2005) capture this by basingdemand forecasts on multiple backlog sizesinstead of only the one backlog immediately

upstream of each activity. They refer to suchpolicies as ‘foresighted’. The same nomenclatureis used in the current research. This definition isconsistent with ‘look ahead’ policies and othersimilar terms used by resource allocationresearchers (e.g. Gere, 1966; Holstein and Berry,1970). The use of ‘foresight’ to describe allocationpolicies in the current work does not imply theexplicit prediction of future backlog sizes. But theforesighted policies in the current work doinclude future conditions when compared tomyopic policies by including contributions tobacklogs due to the stock-flow structure and theimpacts of rework over the entire projectduration. Joglekar and Ford (2005) specify howthese are used to develop foresighted policies.While forecasts can be based on extrapolatinghistorical trends (e.g. see Sterman, 2000), extra-polation does not reflect the closed-flow nature ofdevelopment work. The current work usesJoglekar and Ford’s foresighted resource allo-cation policies (see appendix).

As described, the implementation of resourceallocation policies can be delayed after targetallocations have been set. As a simple example,assume quality assurance currently (in week 92)needs 25% of the resources but the projectmanager expects that fraction to increase to50% in week 100. Further assume that it takes8 weeks to implement target allocation decisionsand that (for simplicity) delays take effectcompletely and instantaneously after the delay.To best meet resource needs the project managershould set the target allocation for qualityassurance inweek 92 to 50%, not 25% as indicatedby current demand, and should not wait untilweek 100 when the quality assurance level ofdemand actually reaches 50%. But delays areoften perceived as unfortunate realities ofdevelopment processes and management andthe bounded rationality of managers make theimpacts of delays very difficult to incorporateinto policies (Sterman, 2000). The policies usedhere reflect this by assuming instantaneousadjustments.

In contrast to the delay assumptions used inpolicies, delays experienced during projects(operational delays) may differ significantly fromzero. The model reflects projects in which the




manager assumed instantaneous adjustment butexperienced significantly longer adjustmenttimes, which are potentially realistic scenarios.As will be shown, smaller operational delays donot necessarily generate better performance. Thecurrent work explicitly captures differencesbetween delays assumed in policy design andoperational delays experienced during projectsand focuses on the impacts of operationalresource adjustment times on performance. Inthe model the applications of allocation fractiontargets are delayed with first order exponentialadjustments that move applied fractions towardtargets a fixed portion of the difference betweenthe applied and target fractions each timeperiod. The speed of adjustment is definedby this resource adjustment delay, with largedelays generating slower adjustments and viceversa.

Model Validation and Behaviour

The model was tested for usefulness in evaluat-ing resource allocation policies using three typesof tests of system dynamics models suggested byForrester and Senge (1980) and described bySterman (2000): (1) structural similarity to theactual system; (2) reasonable behaviour over awide range of input values; and (3) behavioursimilarity to actual system behaviours. Basing themodel on previously validated project modelsand the literature improves the model’s struc-tural similarity to development processes andpractices, as do unit consistency tests. Asrecommended by Sterman (2000), simulationsusing extreme parameter values (e.g. no andinfinite resources) were performed in addition tothe inspection of model equations. Modelbehaviour remained reasonable with extremeinput values and across changes in individualparameter values. For example reducing reworkrequirements decreases project durations. Themodel’s behaviour for typical conditions(Figure 2) is consistent with previous projectmodels and practice (e.g. the ‘S’ shaped growth ofwork released). Based on these tests the modelwas assessed to be useful for investigating the

impacts of resource allocation policies on projectschedule performance.

MODEL USE AND RESULTS

Resource allocation policies are described herewith two features over which project managershave significant influence: (1) the use of myopicor foresighted resource allocation policies and(2) the size and uncertainty of operationalresource adjustment delays. Schedule perform-ance under different project conditions is inves-tigated to better describe the impacts of resourceallocation policies on performance and projectconditions on policy effectiveness. Several pro-ject conditions can impact project progress andpolicy effectiveness, including uncapacitateddevelopment activity process durations, totalresource quantities, resource productivities, andproject complexity. The current work focuses onproject complexity, which can significantlyimpact project progress through the rework cycleandwhichmanagers can compare across projectsand therefore use in policy design. Differentamounts of uncertainty in resource adjustmenttimes during a project are also modelled to reflectlevels of managerial control.

Impacts of Resource Adjustment Delays andProject Conditions on Project Schedule

Project managers often cannot perfectly controlresource adjustment delays. One form of thischallenge is a fixed operational adjustment timethat differs from the optimal value. To investigateconditions in which delays do not match optimaloperational values projects were simulated usingmyopic and foresighted policies with projectcomplexities ranging from 0% to 80% likelihoodof rework and resource adjustment delaysexperienced by the project (the operational delay)from 5 to 75 days. For each policy / complexitycombination the optimal operational delay wasidentified as the delay generating the minimumproject duration. Impacts of mean operationalresource allocation delay size and project com-plexity on project duration are shown in Figure 3




for rework fractions of 10%, 30% and 50% usingmyopic and foresighted policies and resourceallocation delays from 5 to 75 days3. Increases indurations vary from 17% of their minimum value(50% rework with a foresighted policy) to over165% (10% rework with a myopic policy).Optimal operational resource adjustment timesvary from 10 to 40 days, increasing with therework fraction. Results with rework fractions upto 80% are consistent but not shown for clarity.These results suggest that the operationalresource adjustment time can strongly impactproject duration and is an important feature ofresource allocation policy effectiveness. Thisimplies and that the selection of target resourceadjustment times is an important part of resourceallocation policy design.

Notice that the relationship between theresource adjustment time and project durationis consistently convex as adjustment times

deviate from optimal values. This result isconsistent across the simulated rework range(0%–80%) and suggests that improving resourceallocation policies by changing adjustment timesis not simply a matter of reducing adjustmenttimes as much as possible. Reducing an adjust-ment time below it’s operational optimal valuewill increase project duration.

Imperfect Control of ResourceAdjustment Delays

Imperfect control of delays by project managerssuggests that resource adjustment times can varyduring a project as well as vary a constantamount from a target delay. Managers mayimpact the amount of this variation in actualadjustment times with the amount of influencethey exert on adjustment processes. Firmlycontrolling adjustment times would generatesmaller variation and vice versa. Uncertainty inresource adjustment delays during a project canreflect the imperfections and purposeful manip-

Figure 3. Project durations versus resource adjustment time

3Comparisons across policy type (myopic vs. foresighted) are notjustified due to the assumption of instantaneous resource adjustmentin the control theory model used to develop foresighted policies.




ulation of managerial control over resourceadjustment times. This is modelled as variationin the adjustment time around its mean duringthe project. Durations were simulated withdelays that were 50% greater than the optimalvalue or 50% less than the optimal value over arange of uncertainty in delays. Variance levelswere changed using coefficients of variation(¼standard deviation/mean) to normalize var-iances to mean values. Three hundred possibleprojects were simulated for each mean resourceadjustment delay value with four coefficients ofvariation (0%, 10%, 20% and 30%) and the projectdurations averaged for each condition.

As shown in Figure 4 for a myopic policy with50% rework, when resource adjustment delaysare not optimal increasing the variance of thedelay generates unusual changes in duration.Intuitively duration is expected to monotonicallyincrease with increasing variance because moreuncertain systems are considered more difficultto manage. But simulated durations increase orremain essentially constant when varianceincreases from 0% to 10%, decrease for variancesfrom 10% to 20%, and then increase again forvariances from 20% to 30%.

This perplexing (and unexpected by theinvestigators) behaviour can be explained byscrutinizing howdistributions of resource adjust-ment times interact with the project’s adjustmenttime/duration relationship (e.g. Figure 3), as

shown in Figure 5 for 50% rework and a myopicpolicy. Results for other complexities and fore-sighted policies are similar. The impact of achange in the distribution of adjustment timesexperienced during a project on durationdepends onwhether it activates more adjustmenttimes that increase duration than it activatesadjustment times that decrease duration, and thesizes of those impacts. The average durationincreases when changing the variance of theadjustment time adds more times to the samplethat increase durations than the change addstimes that decrease durations, and vice versa. Theadjustment time–duration relationship describesthe size of impacts. For example in Figure 5increasing the variance from 10% to 20% addsmore adjustment times near the optimal time of10 days (below the mean delay of 15 days) thatdecrease average durations than it adds abovethe mean time that increase durations. Thisexplains the reduction in average duration whenvariance increases from 10% to 20% in Figure 4.In contrast, increasing the variance from 20% to30% extends the lower portion of the distributionof adjustment times beyond the optimal value,thereby including more times that increaseaverage duration above the minimum. Thereforethe average duration increases. Recognizing andusing the convex nature of the adjustmentdelay–duration relationship and overlaying thedistributions of adjustment times on that

Figure 4. Average project durations across range of variance in resource adjustment times




relationship can explain why average durationsdecrease initially and then increase with increas-ing variance. Counter-intuitively, these resultssuggest that when resource adjustment delaysare not optimal increasing variation can reduceduration by including more resource adjustmenttimes nearer the optimal value.

DISCUSSION AND CONCLUSIONS

A relatively simple dynamic systems model wasused to investigate how a simple, commonstructure of project processes and resourceallocation policies impact durations. Differencesin forecasting resource demands and delays inadjusting resources described resource allocationpolicies. Conclusions are limited by the purpose-ful simplification of the model compared toactual projects and incomplete validation,particularly with actual project data. Despitethe preliminary nature of work, two counter-

intuitive results suggest changes for projectmanagement practice and future research.

First, the results showing that durations areminimized with resource adjustment timesgreater than their minimum values support aconclusion that projects have optimal managerialdelays that may be positive. This recommendsagainst the common perception and practice thateverything should be done as quickly as possibleto minimize durations. The result also impliesthat managers should seek to identify optimaldelay sizes and use them as targets in decision-making, and not assume that all delays should beminimized. Some experienced managers may dothis tacitly and intuitively for some developmentprocesses, adding to the list of cognitive func-tions potentially performed by practicingproject managers but not yet captured in formalmodels. The current work identifies optimalmanagerial delays as a potentially importantconcept for practitioners and a topic for futureresearch.

Figure 5. Resource adjustment delay distributions and project duration versus mean delays




Second, results showed that increasing uncer-tainty in project controls can decrease durationsif delays are not optimal and the delay–durationrelationship is convex by increasing the netamount of work performed near optimal con-ditions. Counter-intuitively, exerting less controlon variance in delays can improve scheduleperformance under some conditions.

An increasing emphasis is being placed onsystematic studies of complexity, uncertaintyand risks in innovation project managementliterature in general (Adler et al., 1995; Loch andTerwiesch, 1999; Braha and Bar-Yam, 2006) andfor the allied staffing decisions in particular(Antoniol et al., 2004; Anderson and Joglekar,2005). However, a majority of these studies havenot focused on the resource allocation delays andvariation in the ability of a management team todeploy productive resources. If managers cannotperfectly control mean delay sizes to theiroptimal values they may, for some projects,improve performance by increasing the variancearound their actual mean by exerting less control.Managers who know that their mean resourceadjustment times are sub-optimal may find itdifficult to purposefully exert less control overthose delays to improve performance. But even inthese cases the insight can provide managerialguidance. Effectively using this insight wouldlikely includemanagerial attempts to manipulatethe reduction of control to apply more adjust-ment times that are closer to the optimal valuethan further from the optimal, thereby improvingperformance more than indicated by the normaldistributions used here. However, this wouldrequire an awareness of the convex nature of theadjustment delay–duration relationship, anunderstanding of the impacts of delay uncer-tainty on duration, and knowing at least thedirection of the optimal value from the meanapplied value. This reinforces the potential valueof identifying, specifying, and understandingdelay–duration relationships and optimal delaysizes and their impacts on performance. How-ever, operationalizing this insight may prove tobe challenging.

Several features of the current work that limitconclusions point to opportunities for futureresearch, including its focus on only one dimen-

sion of project performance (schedule) andmodel assumptions. Demands for resourcesand setting managerial delays are also likely tobe impacted by other project factors such as thecost of changing or maintaining delays of specificsizes. Future research can also expand the modelto investigate the impacts of other projectcharacteristics on resource allocation policyeffectiveness and improve the model to reflectmore aspects of projects as experienced inpractice.

The current work contributes to systemsresearch on projects by introducing the conceptof tuning delays from control theory to projectmanagement through managerial choices ofresource adjustment times. It expands researchon project dynamics by identifying the optimalsizes of managerial delays as a potentiallyvaluable research topic and demonstrating thevalue of understanding the interaction of uncer-tainty and managerial decisions. Tuning man-agerial delays to project characteristics canimprove development project performance.However, this requires an understanding of theimpacts of the dynamic project structures onbehaviour and performance. Projects can beimproved by continuing to develop a deepunderstanding of those impacts, how theyinfluence projects, and how project systems canbe changed to exploit that understanding.

APPENDIX A: FORESIGHTED RESOURCEALLOCATION POLICIES

Joglekar and Ford (2005) use a two-dimensionalResource Allocation Policy Matrix (Figure 6) todescribe policies as the set of relationships

Figure 6. A resource allocation matrix representing amyopic policy (Joglekar and Ford, 2005)




between individual work backlogs and thedevelopment processes that service those back-logs. Each cell value in a Resource AllocationPolicy Matrix defines the relative importance of abacklog (Wc, Wqa or Wrw in Figure 6) on theresources for a development process (InitialCompletion, Quality Assurance, and Rework inFigure 6). The product of each cell value andthe size of the appropriate backlog determine therelative demand for resources by the activity (thecell’s row) due to the backlog (the cell’s column).Allocation fractions are the fraction of the totalrelative demand (sum of all nine relativedemands) needed for each activity (sum of eachrow of three relative demands). Allocationscontinuously change during a project due tothe evolution of backlogs and thereby relativedemands for resources. Myopic policies in whichallocation fractions are directly proportional toonly the current size of the backlog serviced aredescribed with diagonal terms of equal value andzeros as non-diagonal terms (e.g. Figure 6).Assuming equal productivities, myopic resourceallocation policies allocate resources to eachactivity in the same fraction that the activity’scurrent backlog contributes to the total amount ofwork waiting to be done. Foresighted allocationpolicies are described with non-zero off-diagonalterms, which account for the rework in the stockand flow structure and use backlogs in additionto the one serviced to set each activity’sresources.

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