Socio -organo complexity and project performance

Available online at www.sciencedirect.com International Journal of Project Management 29 (2011) 808 – 816 www.elsevier.com/locate/ijproman Socio-organo complexity and project performance Dimitris N. Antoniadis a,⁎, Francis T. Edum-Fotwe b , Anthony Thorpe b a b Carillion Ltd., London, UK Department of Building and Civil Engineering, Loughborough University, UK Received 31 January 2011; accepted 15 February 2011 Abstract Technical complexity has always been considered a factor which affects project performance. Scheduling and other mechanisms have been proposed which allow for the management of these effects. However, the effect of the complexity of interconnections, and in particular those caused by social interfaces and boundaries between the various teams, have not been investigated. Socio-organo complexity is caused by interconnections which if not managed could lead to a reduction in performance. Understanding the characteristics of complexity of interconnections, how these affect project schedule performance and what deductions can be extracted, will enable the development and implementation of innovative actions and tools that will support the management of the effects of complexity through the respective processes. The authors present results of five case studies, with UK construction organisations, which demonstrate that the effects of socio-organo complexity of interconnections have similarities with the behaviour of underdamped control systems. The results from the study have significant implications for the way socio-organisational issues are managed but will also enable parallels to be drawn between the fields of project management and control systems. © 2011 Elsevier Ltd. and IPMA. All rights reserved. Keywords: Complexity; Interconnections; Projects; Performance; Control systems 1. Introduction Construction projects, and in particular mega projects, often involve a large number of parties and subsequently interconnections. These interconnections can generate complexity which, however, has defined characteristics (Lucas, 2000b). Complexity on projects has been researched extensively in the last decade and a number of proposals have been made in terms of managing its effects (Gidado, 1996; Williams, 2002; Lillieskold and Ekstedt, 2003; Geraldi, 2008; Girmscheid and Brockmann, 2008). In terms of the relationship between complexity and project schedule performance and although heuristic considerations exist, which suggest an exponentially decaying/inverse correlation, very little has been done in identifying the exact relationship. Furthermore, most of the ⁎ Corresponding author. Tel.: +44(0) 7754522049. E-mail address: dnanton00@googlemail.com (D.N. Antoniadis). studies have been carried out on the technical side and very little has been investigated in terms of the socio-organisational aspects of complexity of interconnections and its effects, especially when implementing processes such as selecting team members, structuring the project team, or the management style adopted. Within this paper the authors present the results from five case studies investigating the effect of socio-organo complexity on project schedule performance. The case studies, part of a wider study into socio-organo complexity, were carried out in the UK construction industry with some major organisations. The results indicate that the relationship, although one of an inverse correlation, does not resemble a straightforward exponential decay curve but rather one of an underdamped transient motion. The verification of this relationship not only confirms the non-linearity of project management, especially regarding socio-organisational issues, but it can also be proven very powerful considering the potential extrapolation and implementation of techniques already proven in the field of systems control. 0263-7863/$ - see front matter © 2011 Elsevier Ltd. and IPMA. All rights reserved. doi:10.1016/j.ijproman.2011.02.006 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 809 2. Background The management of projects transpires in a complex environment (Bertelsen, 2004). The application of complexity theory to the management of projects can, therefore, enable the systematic consideration of the conditions that give rise to such complexity. A number of authors have indicated that interfaces generate complexity (Baccarini, 1996; Gidado, 1996; Williams, 2002), however complexity can be associated more with the interconnection structures that link various objects and not the objects themselves (Lucas, 2000a). As a result, considering the prevailing conditions in projects the argument can be easily juxtaposed to the project environment. In one sense, project management can be considered as optimisation of the structuring of the interconnections that link up the delivery systems and subsystems. Understanding the characteristics of these interconnections, especially from a socio-organisational standpoint and how these affect the project performance, can contribute to the design of more efficient project delivery systems. In particular, it should enable project managers to respond with the necessary actions and improve the setting up of projects, the management style adopted and the decisionmaking process. Lucas (2000b) has suggested that complexity arising from interconnections reflects distinct characteristics. The 16 characteristics directly relevant have been mapped onto project conditions and detailed description has been presented in Antoniadis et al. (2006). Construction projects are typically characterised by complexity; under time and/or cost pressure and requiring both creativity and cooperation and which, for most projects, reflects a dynamic process involving non-linear procedures (Bertelsen, 2004). Previous analyses of complexity in construction projects have been conducted mainly from a technical perspective (Gidado, 1996; Lillieskold and Ekstedt, 2003) and not directly addressing the effects of complexity on project schedule performance. Only recently has the subject of complexity been linked to non-technical project aspects such as communication, behavioural and social issues (Geraldi, 2008; Girmscheid and Brockmann, 2008), again though not directly linked to the effects of socio-organo complexity of interconnections on project schedule performance. Empirically/heuristically it is presumed that as complexity increases performance drops (inverse correlation) and the expected graphical output resembles that of an exponentially decaying curve (e.g. e−x ) or a curve similar to an overdamped system such as that presented in Fig. 1 below. Fig. 1, depicts the theoretical harmonic oscillations of systems as these come under the influence of various damping devices. The overall concept of motion represented in Fig. 1 can be described by the equation: d2 xð t Þ dxðtÞ + 2ζωn + ω2n xðtÞ = 0 d2 t dt ð1Þ Fig. 1. Harmonic oscillator with damping. Various cases are depicted, from underdamped to overdamped. As presented in http://www.scar.utoronto.ca/~pat/ fun/NEWT1D/PDF/OSCDAMP.PDF. 1981) which are expressed by the general mathematical function: h i      ð2Þ x = Aeð−ζωtÞ sin ω √ 1−ζ2 t + a where: • • The first part of Eq. (2), [Ae(−ζωt)], expresses the exponential decay element and the second part, [sin(ω(√(1 − ζ2t)) + a)], expresses the circular frequency element (Beards, 1981). Therefore, depending on the outcome of the investigation there could be some correlation between the effect of socioorgano complexity of interconnections onto project schedule performance and the effect of damping on transient motion. Also, since much of the socio-organisational complexity is associated with the organising and the management of projects these areas form the focus of investigation in this paper. 3. The investigation The review established the need for further investigation of the relationship between socio-organo complexity of interconnections, in particular the processes of selecting team members, structuring project teams and the management style adopted, and project schedule performance. Therefore the following Study Question (SQ) was formulated: SQ 1: Socio-organo complexity of interconnections is inversely correlated to project schedule performance. In order to investigate the above question it was decided to conduct a carefully developed, closed design (Yin, 2003), multiple case study approach, for 9 weeks or two project reporting periods, with an adaptive and flexible feedback mechanism. The importance of implementing multiple case studies was based on the fact that: Fears of uniqueness and artificial conditions surrounding the case(s) are minimised; and • To enable literal replication logic (Yin, 2003). • Using the equation of motion (Eq. 1) the graphs depicted above (Fig. 1) are a combination of two motions (Beards, ω = undamped natural frequency ζ = damping ratio 810 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 In considering all the above, it was decided that the most appropriate method to investigate the study question would be to monitor and record the reasons for delay of the activities to be performed in the predefined time and the tool to be used would be the project programme. Progress would be monitored weekly by the PM and/or the appropriate Team Leader and reasons for delay would be selected from a pick list. Working programmes would have to be at the appropriate level of detail so that the length of delay could be reasonably recorded and reported weekly. Pre-arranged meetings with the researcher would enable clarification of any queries, checking clarity of data recorded in the performance log supplied and confirming correctness of process followed. An extensive pick list of ‘reasons for delay’ was developed, focusing essentially on the three areas under investigation (Table 1 presents an extract from this list). Each reason was coded and linked to one or more of the 16 complexity characteristics for ease of use by the case study PMs. Reasons for delay(s) due to issues/causes raised in the past were also available from the pick list and when/if used Table 1 Extract from list for ‘Reasons of activity delay’ given to case study project managers. Code Complexity characteristic D300 D700 B300 Self-reproduction Emergence Undefined values —structure D100 Co-evolution —team C500, Attractors/ C300 non-equilibrium C402 Non-linear —structure C420 Non-linear —management D400 Downward causation —team selection D410 Downward causation —structure D420 Downward causation —management B100 Unpredictability D110 C210 Co-evolution —structure Instability —structure C101, Autonomous agents —team C310 Non-equilibrium —structure C211 Instability, D510 Mutability, D511 D500 D520 D800 Phase changes Reason R01—lack of appropriate level of induction R03—team cohesion R04—inter-team issue (please elaborate) R06—lack of flexibility within the team R08—no expertise within the team—external input requested R09—structure of team required improvement R10—authoritative approach caused problem in team R11—team selection could have been better in terms of tackling the task R12—definition of work structure needed clarification R13—line of command needed clarification R14—problem from initial phases of project re-surfaced and caused delay R16—communication between team and others R17—clarity of communication/instruction cause confusion to the team which took some time to react to the misunderstanding R18—restriction in people availability did not allow for appropriate level of expertise R19—unexpected activity due to: R20—non-availability of material R21—change in higher level programme R22—causing an upset in the team (who probably did it again) R23—caused by unreasonable insistence by others R24—caused by not ‘listening’ to team feedback/expertise the PMs would be asked to elaborate during the pre-arranged meetings. Particular interest was paid to those issues since ‘unpredictability’ (one of the 16 complexity characteristics) or incumbent pathogens (Busby and Hughes, 2004) causes increase in complexity. Also, various scenarios were identified so that these can be discussed with the PMs, in order to determine instances where complexity had a compounding effect. In terms of the approach taken to measure the performance the ‘simple method’ shown below was discussed and agreed with participants: Activity performance = (Duration Planned ∗ % performance reported); and • Total performance = (Σ of duration achieved / Σ of Duration Planned) irrespective of the time elapsed for the activity to be completed. • Five major construction organisations (clients and contractors) accepted to participate. The number of case studies was considered appropriate because, as Yin (2003: 32) states, ‘if two or more cases are shown to support the same theory replication may be claimed and results will be considered more potent.’ Board Directors were briefed on the requirements and asked to put forward projects at the three different phases of the project lifecycle—feasibility, construction and commissioning—and the case study PMs to have 10 or more years of experience. After discussions with Board Directors the case study projects were selected and the respective PMs were briefed extensively on the purpose and the process to be followed. PMs were asked and they provided general information about their project and a number of weekly meetings between the researcher and case study PMs were arranged. To prove the relationship between project schedule performance and complexity, and in particular for the 16 complexity characteristics, the data from the multi-case studies were analysed following Yin's (2003) five evidence techniques and also a number of graphs were plotted including ‘weekly % drop in performance against reason of delay’, ‘frequency of occurrence of coded reasons for delay’ as well as ‘frequency of complexity characteristics causing delay’. The results from the case studies will be deemed acceptable if replication is established between two or more cases (Yin, 2003) but also by carrying out validation interviews with PM practitioners from different organisations. 4. Results Implementation was over a period of 10 months (2007– 2008) and presentations were given to respective Board Directors on the aims and objectives of the research and the case studies. The details of projects put forward by the companies are shown below in Table 2. Representative results from two of the five case studies are given below. The significance of the drop in performance in case study G2.1 can be seen in Fig. 2, which displays ‘Cumulative 811 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 Table 2 Case study contributors by project stage. Company— case study Project stage Description G1.3 G1.1.2 G1.1.4 G2.1 G1.2 Feasibility Design/early construction Construction Construction Commissioning Waste water treatment works Terminal forecourt extension Redevelopment of lounge Building—28 luxury flats Chemical removal plant 2003). The results (Figs. 3 and 4) indicate clearly the inverse correlation between socio-organisational complexity of interconnections and project schedule performance and therefore prove the study question raised. Also the curves in Figs. 3, 4, and 5 resemble accurately the theoretical curve of underdamped transient motion (see Fig. 1 above). Furthermore from the results it is evident that: The shapes of the project schedule performance curves, in particular for those case studies in construction (with the exception of case study G1.1.4 which faced extenuating circumstances and the team never had the chance to recover), follow that of the underdamped transient motion curve. • The results for the case studies at the earlier and latter phases of the project lifecycles G1.3 and G1.2 do not overrule/distort the overall outcome. Actually, the exponential decay shape of the feasibility (Dsgn) case study and the slightly underdamped shape of the commissioning (cmsng) case study underpin the findings. • As described by Moore (2002:66 and 90)—in the team effectiveness curve—at the early phase of the project, performance is higher as the team comes together. This can be observed in case study G1.3 Dsgn where the percentage drop is reduced by 9%. • Similarly at the commissioning phase, team members become anxious about the future, the next project, the new team and other soft issues (Moore, 2002) and thus, as commissioning approaches, performance drops. Eventually, the ‘key players’ (the commissioning team—as described by the G1.2 PM) deliver the project. • Planned’ and the ‘Cumulative Achieved’ durations for the case study period. As can be seen only 43% of the planned activity time (or 252 days of the 590) was achieved and as a result the PM had to delay a number of fit-out tasks. Overall results, in terms of drop in performance, as well as the average from all five case studies, are presented below in graphical form. Two tables of results with all the complexity characteristics that affected performance, by sub-process investigated, are drawn and shown below. Table 3 indicates the frequency of occurrence of each characteristic, which was represented by one or more corresponding causes of delay, and Table 4 presents an analysis of complexity characteristics causing delay by subprocess investigated. The results were validated by conducting saturation interviews with project management practitioners from different organisations and from the levels of Project Director to PM. All interviewees, having reviewed the results, accepted the findings as a true representation of the current status and the issues they face when delivering projects (Antoniadis, 2009). 5. Analysis In order to extract inclusive and integrated deductions as well as establish replication, the analysis of the case study results is conducted holistically rather than each one in isolation (Yin, The results indicate that as the effects of the complexity characteristics on each activity monitored increase, performance drops and, as remedial actions are implemented, the effects are managed and keep the project performance at a plateau. All case study curves, irrespective of the project phase, support this finding. Thus the results confirm replication. Results from case Number of Complexity characteristics & % Drop in Performance 0% 0% 14 10% 13 13 13 20% 12 11 10 12 30% 10 10 43% 8 50% 52% 49% 55% 6 50% 50% 56% 58% 55% 60% 6 70% 4 Drop in Performance Num of Complexity characteristics 2 0 40% 80% 90% 100% 0 Wk0 % Drop in Performance Num. of characteristics 11 wk1 Wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 Fig. 2. Case study G2.1, % drop in performance against number of complexity characteristics that affected performance. 812 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 Number of Complexity characteristics & % Drop in Performance 10 0% Drop in Performance Num of Complexity characteristics 9 10% 7 7 30% 7 40% 6 5 5 5 59% 5 58% 5 58% 62% 4 67% 57% 50% 60% 61% 65% 70% 72% % Drop in Performance 20% 8 Num. of reasons 0% 80% 2 90% 0 0 Wk0 wk1 Wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 100% Fig. 3. Case study G1.1.2, % drop in performance against number of complexity characteristics that affected performance. study G1.2—commissioning phase—provide further evidence of the point made above. Actually the case study, with the continuous increase in performance, also presents the stage after the plateau. As the project reaches completion and complexity is dealt with the number of complexity characteristics causing delay are gradually reduced in number and performance increases. As time elapses and activities are not completed, various measures are taken to overcome the performance problems. For example, additional resources might be ‘pulled in’, or other activities deferred, as is the case with G2.1 where the PM had to delay groups of fit-out activities to a later stage. Therefore, expected performance and, in particular, project monitoring techniques such as Earned Value, the Cost Performance Indicator (CPI) and Schedule Performance Indicator (SPI) Table 3 Frequency of occurrence of complexity characteristics which affected performance per case study and project stage. Construction Feasibility Commissioning Case Case Case Case study study study study 1.1.2 1.1.4 2.1 1.3 Unpredictability Non-standard Undefined values Autonomous agents Instability Non-equilibrium Non-linear Attractors Co-evolution Self-modification Self-reproduction Downward causation Mutability Non-uniform Emergence Phase changes B1 9 B2 B3 C1 9 C2 5 C3 9 C4 8 C5 D1 16 D2 D3 D4 17 D5 17 D6 D7 D8 9 9 9 6 9 13 6 4 3 9 12 6 Case study 1.2 8 9 8 7 8 9 5 12 9 14 18 6 16 6 18 4 4 5 1 7 could be used to present a more complete picture. These, however, are beyond the scope of this paper. As data from the case studies were analysed, it became apparent that, due to the corrective actions taken by the project teams, most of the graphs resembled that of an underdamped transient motion (as per Fig. 1), which is a combination of an exponentially decaying curve together with a circular frequency curve (Beards, 1981). The performance curves of two case studies, G1.1.4 in construction and G1.3 in design (see xFig. 6), can be depicted by the exponential decay curve, whereas those of case studies, G1.1.2 in early construction, and G2.1 in construction, can be depicted by the function of the underdamped transient motion, which combines both elements of Eq. (2). Thus, not only has replication been established but also consistency, with an already proven and established theory. The only case study that does not accurately conform to these curves is G1.2 which was at the commissioning phase. However this can be explained by the fact that the project was essentially complete just after week 4 of the case study period. Nevertheless, considering the initial deep drop and the gradual recovery, it can still be regarded and represented by an equation of ‘underdamped’ transient motion but in a slower cyclic mode. From a brief analysis regarding the impact of complexity characteristics, using the information provided in Table 3 above and for those case studies in construction, the complexity characteristics with the highest frequency of occurrence are detailed below together with the relevant explanation: B1: Unpredictability. This represents the importance of the initial project conditions which, if not managed appropriately, could lead to chaotic conditions occurring later on during the projects (see also pathogens and incubation period, Busby and Hughes, 2004); • C3: Non-equilibrium. Represents the various ‘pulls’ (contractual, behavioural, stakeholder influences, company • D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 Table 4 Analysis of complexity characteristics causing delay by sub-process. Phase Construction Case study Selecting team members G1.1.2 Unpredictability (B1) Autonomous agents (C1) Non-equilibrium (C3) Non-linear (C4) Co-evolution (D1) Phase changes (D8) G1.1.4 Unpredictability (B1) Autonomous agents (C1) Non-equilibrium (C3) Non-linear (C4) Attractors (C5) Co-evolution (D1) Selfmodification (D2) Emergence (D7) G2.1 Unpredictability (B1) Autonomous agents (C1) Instability (C2) Co-evolution (D1) Downward causation (D4) Mutability (D5) Design G1.3 Undefined values (B3) Autonomous agents (C1) Instability (C2) Non-linear (C4) Co-evolution (D1) Downward causation (D4) Emergence (D7) Commissioning G1.2 Autonomous agents (C1) Non-equilibrium (C3) Co-evolution (D1) Self-modification (D2) Structuring the team Management style Instability (C2) Non-equilibrium (C3) Co-evolution (D1) Downward causation (D4) Mutability (D5) Phase changes (D8) Instability (C2) Non-equilibrium (C3) Co-evolution (D1) Downward causation (D4) Mutability (D5) Phase changes (D8) Downward causation (D4) Mutability (D5) Phase changes (D8) Instability (C2) Non-equilibrium (C3) Co-evolution (D1) Mutability (D5) Phase changes (D8) Mutability (D5) Phase changes (D8) Instability (C2) Non-equilibrium (C3) Co-evolution (D1) Mutability (D5) Phase changes (D8) politics and management pressures, to mention but a few) that occur in projects from the multiple contributors. These, depending on the situation, will establish semi-stable modes with ‘players’ (attractors) who will attempt to influence the project at the opportune moment; • D5: Mutability. It is typical of random mutations to occur in projects. Project Managers have to identify and manage them. Further detailed results are presented in Antoniadis (2009). An immediate observation of the results extracted in Table 4 is the lack of complexity characteristics affecting the sub-process of management style adopted for the case studies in design and commissioning. Also of interest, is the commonality of two complexity characteristics, mutability and phase changes, which affected all three case studies in construction. A comment that could be made regarding the former observation is the relevance of the findings to the Traveller's Dilemma, people choose or reflect on the events for their own benefit or exposure, as opposed to the benefit of the company/organisation for which they work (Basu, 2007). Further analysis and discussion on the effect complexity characteristics have on project schedule performance will not be conducted here as the purpose of this paper is to demonstrate the relationship and discuss the significant implications that emanate from the relation between socioorganisational complexity of interconnections and project schedule performance. The latter is covered in the next section. 6. Discussion The detailed case study results and analysis presented undoubtedly confirm replication. Another observation is that as the effect of complexity of interconnections increases, or is not managed, project performance decreases. The results indicate a significant percentage drop in project performance for the case studies in construction, 57% drop, (see Fig. 6) as well as all case studies, 39% drop, (see Fig. 5). This raises a number of points regarding project managers' performance and how this can be improved, the levels of training and the tools available to them which will enable them to successfully and satisfactorily manage the project. Other more generic questions that are raised from the case study results are: What has happened in the last 15 years in UK, since the Latham report, in terms of improving performance of construction projects? • Has complexity of interconnections increased considerably in the construction industry in the last 15 years? • If project management has remained stuck in a time warp in the 60s (Morris, 1994) due to the influence of the machine metaphor (Morgan, 1997), how would new initiatives such as PRINCE 2 and certification improve performance? • Non-equilibrium (C3) Attractors (C5) Co-evolution (D1) 813 814 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 Modelling Performance Wk0 wk1 Wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 Cum. Planned Du Cum Achieved Du 700 600 590 400 300 252 Total Dus 500 200 100 0 Fig. 4. Case study G2.1. Modelling of performance based on Total Duration achieved against time taken. As the case study data were extracted and analysed, it became apparent that, due to corrective actions taken by project managers, the curve resembled that of an underdamped transient motion. Thus the results confirm, through the well established theory of vibration analysis and control systems, the higher order and non-linearity of project management. This correlation should enable collaboration between the two disciplines and facilitate a number of activities such as establishment of variables and how these could be ‘translated’/ used by project management. With the above in mind, some simple thoughts for further discussion are presented below. Using the correlation between project performance and control systems a model can be generated where, by using the appropriate levels of natural frequency, the complexity characteristics could be used as damping devices (‘dampers’). The value allocated to each characteristic/damping device, and for the corresponding project management sub-process, could be generated from tools designed to manage each complexity characteristic. The whole approach could resemble the treatment prescribed by psychiatrists who use a range of The results indicate a direct link between project performance and induced socio-organisational complexity of interconnections and the investigation examined the causes of delay due to each individual characteristic for the areas investigated. However, the characteristics of complexity of interconnections are/should be common to all other project management sub-processes, e.g. monitoring and control, efficient use of resources, etc. Thus, more than one complexity characteristic can have the same cause of delay and similarly, the same cause of delay could belong to more than one subprocess. Therefore, it is feasible that other sub-processes contribute to the drop of performance recorded. The overall drop recorded does not change, but the contributory factors could simply be wider than those presented in this investigation. Understanding how each complexity characteristic affects each sub-process and identifying actions so that it can be managed, as described in other parts of the research (Antoniadis, 2009), enables PM practitioners to take precautionary steps at the appropriate time. Case Study Performance comparison 0% CS G1.2 - Cmsng CS G1.3 - Dsgn CS G1.1.4 - Cnstr 40% CS G1.1.2 - Cnstr CS G2.1 - Cnstr 60% % Drop in Performance 20% 80% 100% wk0 wk1 wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 Fig. 5. Case studies summary results. Drop in performance due to the effects of complexity. 815 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 % Drop in Performance - Average of all Case Studies 0% 0% 40% 37% 40% 40% 39% 40% 37% 39% 40% 39% 60% % Drop in Performace 20% 80% 100% wk0 wk1 wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 Fig. 6. Average % performance drop for all case studies. different medicines to counteract each other in order to achieve the required outcome. Therefore, and using the vibration control formula as a guide, a solution would be to: a) Minimise the circular frequency element [sin(ω(√(1 − ζ2t)) + a)], b) Identify the values of the damping ratio (ζ) and natural frequency (ω), which then c) Make the exponential decay function to equal A (see formula 2 above). Thus: Ae(− ζωt) = A In project management this idealistically is interpreted as performance at 100%, or otherwise 0% drop in performance. From the above it can be deduced that: eð−ζωtÞ = 1 which therefore meansð−ζωtÞ = 0 However, the variables t and ω cannot be equal to zero, as every system has a natural frequency and the element of time is one of the basic factors in the project life cycle. Therefore: ζ = 0 This indicates that those stages that are, in their majority, governed by the exponential decay function should have the damping ratio equal to zero. In terms of the circular frequency function, this will also have to be equal to zero (0), which means that the lag between the displacement vector and the force vector is zero (0). So:      sin ω √ 1−ζ2 t + a = 0 If from the above ω ≠ 0 and ζ = 0    ⇒ω √ 1−ζ2 t + a = ωð√ð1–0ÞÞ + a =  ω + a So sin(± ω + a) = 0, and ∴ðω + aÞ = 0⇒a = −ω; ð3Þ or ð−ω + aÞ = 0⇒a = ω ð4Þ From Eq. (3) above, theory indicates that we have a critically damped system towards which most of the systems are aiming. In project management terms the above can be graphically depicted as shown in Fig. 7. Therefore, with some elemental thinking a number of simple actions can be taken to define different variables for understanding non-linearity for which the means can be developed that will help practitioners reduce the effect of any type of influence on the project management performance. It is also possible to utilise and combine concepts developed by system dynamics to enable the management of the effects of complexity in projects. Δt A Minimise drop in performance and reduce the spread of response ∴minimise Δt by adjusting behaviours, fast enough response, reducing wasted effort, faster implementation and acceptance of change. t Fig. 7. Graphical depiction of underdamped control systems curve applied to project performance. 816 D.N. Antoniadis et al. / International Journal of Project Management 29 (2011) 808–816 7. Conclusions Five case studies were conducted in construction projects, which covered all phases of the project life cycle. Causes of delay, based on the three sub-processes investigated, were considered and the results proved the inverse correlation between complexity of interconnections and project performance. Thus the empirical deduction that project performance declines as complexity increases is proven. Replication was established between all five case studies with some minor variations for the projects in early design and commissioning. The results indicated a considerable overall average drop in performance as complexity of interconnections increased significantly. Analysis of the causes of delay indicated the dependence of project schedule performance on the subprocesses investigated and the 16 complexity characteristics. However, the interlinked properties of the characteristics and those of the reasons for delay did not allow for establishing singularity of results, or otherwise overcoming the difficulty of identifying singular characteristics as causes of the drop in performance. Furthermore the detection of the significant drop in performance is attributed to the fact that the case studies sought and extracted details that are not reported frequently, or seen as small issues that will be overcome, otherwise known as ‘the devil is in the detail’. The level of training and implementation of appropriate actions, when selecting project team members, structuring the project team and when considering the management style to be adopted, is also questioned by the results obtained. Therefore the industry will need to consider improving the timing and the approach taken to implement appropriate techniques. Construction organisations will also need to consider how to improve adjusting of behaviours and speed of response, reduction of wasted effort and improving acceptance of change in order to minimise the effect of complexity of interconnections. In considering the current approach to the three areas investigated, which are linked directly to socio-organisational issues, it can be argued that the effect of not implementing these has a considerable impact and is interrelated throughout the complexity characteristics. The non-linearity of project management is also reflected through the effect of the complexity characteristics. Therefore, a requirement is identified for developing a framework that will enable the management of the effects of complexity by means of its characteristics. Deciphering and mapping the complexity characteristics to the project management processes enables the consideration and development of the means, as well as the approach, for managing its effects on projects. In addition to establishing the correlation between complexity and project performance, the relationship resembled the behaviour of vibration control systems (non-linear systems) and particularly that of underdamped systems. This provides the basis for further research on the non-linearity of project management processes by examining possible solutions based on systems control theory. Further research could be conducted in: Establishing an approach that will identify variables which can be used in known systems formulae, thus enabling PMs to manage and improve project performance. • Supporting the establishment of project management axioms based on the systems dynamics theory, thus providing a further theoretical basis for supporting project management as a profession. • References Antoniadis, D.N., 2009. Managing complexity in project teams, PhD Thesis, Loughborough University, UK. Antoniadis, D.N., Edum-Fotwe, F.T., Thorpe, A., 2006. Project reporting and complexity. In: Boyd, D. (Ed.), Proceedings of 22nd Annual Conference ARCOM, UCE Birmingham. September. Baccarini, D., 1996. The concept of project complexity—a review. International Journal of Management Reviews 14 (4), 201–204. Basu, K., 2007. The traveller's dilemma. Scientific American 296 (6), 68–73 June. Beards, C.F., 1981. Vibration Analysis and Control System Dynamics. Ellis Horwood, Chichester. 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