Is organizational conflict inevitable?

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International Journal of Project Management 26 (2008) 773–788

Resource allocation under uncertainty in a multi-project matrix environment: Is organizational conﬂict inevitable? Zohar Laslo a

a,*

, Albert I. Goldberg

b

Department of Industrial Engineering and Management, Sami Shamoon College of Engineering, Beer Sheva, Israel b Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, Israel Received 20 February 2007; received in revised form 10 September 2007; accepted 2 October 2007

Abstract The matrix structure has become the primary organizational means for maintaining an eﬃcient ﬂow of resources in multi-project environments. Critics of the matrix, however, describe an inherent propensity for conﬂict among managers that substantially limits its eﬀectiveness. Conﬂicts occur not only between the divergent interests of project and functional managers, but also among diﬀerent project managers in a multi-project setting. A system dynamics simulation was developed for a such complex high-tech environment, a milieu with high uncertainty in meeting project deadlines and with intensive competition over ‘‘scarce’’ resources. Expected net beneﬁts were calculated for each of the organizational groups under diﬀerent work proﬁles. Findings from the simulation suggest that not all conﬂict is realistic. For some project objectives, higher organizational performance can be achieved when managers learn that they have no basic diﬀerences in real interests and they can agree upon a resource allocation policy. 2007 Elsevier Ltd and IPMA. All rights reserved. Keywords: Project and R&D management; Organization design; Resource allocation systems; Conﬂict resolution; Decision under risk and uncertainty; Multi-objective optimization; Project scheduling; Simulation; Design of experiments

1. Introduction High-tech companies must cope with considerable uncertainty in order to survive in a dynamic environment. These conditions led to the development of matrix structures that were designed to better keep up with rapid advances in technology [20]. Built-in propensities to conﬂict within the matrix structure with its two-dimensional control system of both functional and project management, however, can bring about less than optimum performance [56,12,37]. The traditional approach to project management considers projects as being independent of each other. Yet, in a multi-project environment the vast majority of the projects compete for resources with other projects and thus the overall strategic eﬀort of a corporation is directed at ﬁnd*

Corresponding author. Tel.: +972 8 6475640; fax: +972 8 6475643. E-mail addresses: [email protected] (Z. Laslo), [email protected]. ac.il (A.I. Goldberg). 0263-7863/$30.00 2007 Elsevier Ltd and IPMA. All rights reserved. doi:10.1016/j.ijproman.2007.10.003

ing ways to deal with possible resource insuﬃciencies [10]. Planning decisions must be made to enable the organization to set resource requirements for activities and then to meet these needs by leveling resources through the hiring, ﬁring and subcontracting. Scheduling the allocation of available resources to projects will determine the start and completion times of the detailed activities. As a consequence, compromises must often be made in order to fulﬁll overall organizational goals. The issue of interrelationships between organizations, individuals and projects was recognized by Van der Merwe [58] who suggested a solution through coordination of activities among projects in a matrix-based structure. In matrix management, people with similar skills are pooled for work assignments. Project managers ﬁnd that they must work closely with other managers in order to complete a project. Functional managers, in contrast, have diﬀerent goals, objectives, and priorities than project managers, which must be addressed in order to complete a job.

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Hendrix et al. [22] found a multi-project situation causes problems in the allocation of scarce resources (i.e. manpower) to a diversiﬁed project portfolio. They suggest ﬂexible resource planning to take into account the availability of scarce resources and the need for special knowledge. Tong and Tam [57] introduced a fuzzy optimization of labor allocation by genetic algorithms, and Wu [61] introduced a fuzzy linear programming approach for manpower allocation among projects within matrix organization. The matrix organization attempts to combine the advantages of functional structures with product oriented structures so as to create synergism by a shared responsibility between project and functional management. Matrix management allows for a greater ease in loaning an employee to another project without making the change permanent. It is therefore easier to accomplish work objectives in an environment where task loads are shifting rapidly between departments. Conﬂicts will develop when incompatible objectives are held by project managers and functional managers. The diﬀerent objectives are based on functional managers’ focus on long-term eﬀectiveness while project managers concentrate on more immediate accomplishments [51,1]. As a consequence, project managers seek to obtain resources to meet any unanticipated circumstance by either expanding existing capacities or contracting for services from external suppliers. In contrast, functional managers oppose indiscriminate accumulation of assets by a project and usually reject attempts to outsource work because of possible underemployment of ﬁrm personnel. A multi-project environment adds another set of disagreements when project managers compete against each other for the allocation of scarce resources [49,46]. If a number of projects are started concurrently, the resource capacities necessary to guarantee the achievement of one project’s objectives may impede allocations to other projects and reduce the overall successes of the organization [27]. As a consequence, there may be particularly intense internal lobbying activities for available resources [3,8]. Furthermore, attempts to optimize resource allocations are complicated by diﬀerences in project activities, due dates, and the nature of penalties for projects that fail to meet their objectives [38,42]. Despite the scholarly critique highlighting a potential for conﬂict because of divergent managerial interests, the matrix structure has persevered [7,29]. A sample of high technology ﬁrms in the American Southeast revealed that 69% continued to employ this format [41], and 71% of 540 development projects reported by members of the Project Management Institute persist in the use of matrix structures [32]. In a textbook on strategic organizational diagnosis and design, [5] recommend the matrix conﬁguration for environments high on equivocality, complexity, and uncertainty. The search for an optimal matrix structure to resolve conﬂicts proved diﬃcult: one research study found that a balanced locus of inﬂuence in a matrix was the best solu-

tion [23], while another research study ascertained the opposite, that an equal balance of power in a matrix led to conﬂict escalation [13], and other research considered a project matrix form to be best for reaching successful performance [31]. After more than three decades of research on the subject, none of the possible matrix forms proved to be clearly more successful [23,31]. It seemed the only way to accept matrix structures as the standard format for high-tech organizations would be through the development of various conﬂict resolution techniques: such as compromise, accommodation, avoidance, collaboration, or the use of explanations/social accounts [48,53]. A need for techniques for resolving conﬂicts, however, assumes the existence of ‘‘real’’ conﬂict. This research explores the possibility that in many work situations, the assumption of contradictory interests may be mistaken. While full agreement among all participants may be unachievable, it is still possible that erroneous conceptions fuel many conﬂicts, while in fact there may be many unrecognized common interests. 2. Empirical investigation An investigation took place at seventeen leading Israeli industrial organizations active in the industrial sectors of electronics, electro-optics, software, pharmaceuticals and construction. All the companies were organized around matrix structure principles. The objective of the research was to study the implementation of the matrix structure in organizations with various work proﬁles. Most of the companies had a very interesting history of changing organizational structures. For example, an electro-optics company was established in a merge of two companies: the dominant company was managed through a hierarchical functional structure, while the second company utilized a hierarchical project/product structure. The merged company chose the widely held functional matrix for its R&D division of more than 500 scientists, engineers and technicians. Two years later, facing detrimental project delays due to a shortage of specialists and skilled engineers, the company decided to prioritize projects for available resources. After four years expanding company resources, the R&D division moved to a project matrix structure, i.e. projects were proclaimed as proﬁt centers and functional units as cost centers. In the generic pharmaceutical industry we found that the receipt of large orders for medical products led to the implementation of a partial project matrix structure beside the traditional implementation of a functional matrix. In one of the electronics companies, a reduction in orders brought about a move from a project matrix structure to a functional matrix structure. From these cases, as well as from others in this investigation, we learned that management sees diﬀerent options for organizing their matrix structures. The probability of project programs meeting timetables and not exceeding allocated budgets was found to be

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inﬂuenced by three conditions: ﬁrst, on the need by projects for scarce resources; second, on the extent to which activities needed personnel from diﬀerent functional areas; and third, on the degree of uncertainty regarding the time necessary to complete activities. There seemed to be patterns in the special conditions found among companies in the same sector. Hence, projects involving R&D in the electro-optics sector are usually characterized by scarce resources, manpower from diﬀerent functional areas, and an inability to estimate duration required for the completion of the project activities. In contrast, electronics sector companies tended to need personnel from the same functional area, while the pharmaceutical sector (generic medicine project division) showed a more predictable time for activity durations (preparing facilities, manufacturing). However, irrespective of the conditions for a single project, high variations were found regarding the characteristics of each project when considering a multi-project framework at any particular company. 3. Conceptual and methodological framework 3.1. Three conﬂict confrontation fronts The readiness to change organizational structures is particularly important in an environment characterized by rapid changes in the nature of the competition while at the same time oﬀering new technological advantages. Upper management may choose to centralize decision making and provide greater resources to particular projects, give control over budget decisions to functional managers, or provide more freedom to individual projects to make use of similar resource allocations [28]. Theoretical models have indeed shown that modulating between temporary governing structures may provide the greatest eﬃciency [45,52]. Studied companies made use of three resource allocation policies: policies diﬀered by the extent to which project requirements were satisﬁed and whether or not priorities were set for some of the projects: 1. Proﬁt and cost centers policy (PC policy): A project matrix structure is established in which project managers have the power to make resource decisions [30]. Project managers have full control over decisions regarding their project budgets and use this power in order to obtain full satisfaction of all project needs [2]. A shortage of available resources is met through either an expansion of the organizational resource capacities or by outsourcing for short-term needs. 2. Comprehensive allocation planning policy (CA policy): A functional matrix structure is constructed that gives functional managers the power to make resource decisions [30]. Functional managers assign staﬀ for highest organizational eﬃciency without consideration to the possible greater importance of certain projects to the company. All projects receive equal priority in the allo-

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cation of existing resources (the same price, no preferences or priorities), and as a consequence, all project managers obtain only partial satisfaction of staﬃng requests. Resources are allocated according to existing company capacities and outsourcing practiced only when it does not threaten the full utilization of in-house resources. 3. Directed priorities policy (DP policy): Project priorities are set within a balanced matrix structure [30]. Greater power goes to high priority project managers and to functional managers when they deal with low priority project managers. The DP policy often found in a high-tech environment because of the need for ‘‘scarce resources’’ unobtainable from external subcontractors [35]. As a result of this situation, limited organizational capacities must be shared among sponsored projects that must meet the conditions of a contract and projects that are internal ventures outside the framework of contractual commitments. The directed priorities policy introduces unequal treatment for projects based on their centrality to the company’s objectives: customer sponsored projects usually receive higher priority in order to meet contractual commitments, while internal corporate ventures must manage with partial satisfaction of their presumed resource needs [40]. Built-in conﬂict within the matrix structure originates from a desire of organizational participants to improve their chances for success by strengthening their power within the organization. The behavior of each group of participants – the functional managers, the sponsored project managers, and the internal venture project managers – can be explained as due to the perception of and propensity to take risks regarding how alternative resource allocation policies favor their objectives [54]. Traditional matrix literature recognized only one potential arena for confrontation: between functional managers, and project managers. This research, however, describes three potential confrontations within matrix organizations (shown in Fig. 1). The preference to convert from a PC to DP policy: The PC policy is the internal venture managers’ favorite resource allocation policy and they will try to retain it. On the other hand, sponsored project managers will try to convert a PC policy to their favorite policy, the DP policy. Functional managers would be ready to support sponsored project managers’ choice of a DP policy if they see no chance to obtain their favorite, the CA policy, so as to prevent the introduction of a PC resource allocation policy perceived as worst for them. The preference to convert from a DP policy to CA policy: The DP policy is the sponsored project managers’ favorite resource allocation policy and they will try to hold on to it. Functional managers will try to move from a DP policy to their favorite policy, the CA policy. Internal venture project managers would be ready to support functional managers in the change to a CA policy in

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PC

PC

Functional U.

1 conflict front

Sponsored P. Functional U.

Sponsored P. Internal P.

CA The traditional system of conflicts

Internal P.

DP

Functional U.

3 conflict fronts

Internal P. Functional U.

Sponsored P. Internal P.

Sponsored P.

CA

The system of three conflict forms

Fig. 1. Possible conﬂict systems within matrix organizations.

order to preclude adoption of a DP policy that they perceive as worst for them. The preference to convert from a CA policy to PC policy: The CA policy is the functional managers’ favorite resource allocation policy and they will try to retain it. Internal venture project managers will try to convert a CA policy to their favorite policy, the PC policy. Internal venture project managers will be supported by the sponsored project managers who wish to convert to their favorite, the DP policy, but will be ready to compromise and accept a PC policy in order to eliminate the worst option for them, a CA resource allocation policy. Alliances among the three vested interest groups in a multi-project setting are unstable since each allocation policy initiates new forces for change. In such a situation, matrix structures retain a high potential for conﬂict as each conversion provides new bases for disagreement. But the high-tech environment is highly uncertain and a drive to obtain additional resources could prove dysfunctional to a project seeking such advantage. Hence, the bases for conﬂict may prove unrealistic and this will be further explored in the rest of this paper. In the empirical investigation, functional and project managers were found to assume that agreement upon a balance of power is unachievable. In seeking advantage, managers involved in R&D may consider a speciﬁc policy as beneﬁcial to their position. But their expectations will often be mistaken because of inadequate information about real-time conditions and the payoﬀ outcomes of actions in a dynamic environment. This absence of essential information is caused either by ambiguous causality

or by a complexity that prevents a full evaluation of the eﬀects of actions [47]. 3.2. Expected net beneﬁts The perceptions of diﬀerent participants about the potential gains or losses to their positions due to a chosen resource allocation policy are summarized in the Expected Net Beneﬁts (ENB). Based on the evaluation of their situation, they will compete over what they perceive to be a limited pool of organizational resources. This competition for resources becomes a driving force for high intensity conﬂicts within matrix structures [56]. Top management will consider the ENB for an entire organization when choosing an appropriate organizational resource policy [21]. Once a preferred resource allocation policy has been decided upon, however, this policy will confer greater dominance to either functional managers or project managers [15]. The policy chosen is particularly crucial for overloaded matrix organizations where an excessive number of projects place a strain on the resource allocation capacity of the ﬁrm [43]. Project managers are expected to manage organizational resources on a given activity within the constraints of contract or scheduled time, cost of the allocated resources, and performance expected by end of project [26]. Considering performance as an inﬂexible parameter, a project manager’s ENB can be described by two basic objectives or by any combination of these two objectives. Minimization of delay losses (objective function a): Management may aim at a minimum level of delay losses. Not meeting a time schedule can result in ﬁnancial losses

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to the organization, disruptions of other project schedules, and customer dissatisfaction with the company’s work. Even when sponsored and internal venture projects entail the same objectives, outcomes may diﬀer when management diﬀerentiates between projects of high priority and projects of low priority. Minimization of direct labor costs (objective function b): The retention of only those workers essential for the expected work is a routine management objective. In meeting this objective, an organization minimizes the cost of direct employment of personnel. This eﬃciency measure will diﬀer when projects are given high priority or low priority. The ENB of functional managers relies on the budgeting for appropriate staﬀ, allocation of available personnel resources according to project need, and the supervision of job performance. Unpredictable needs for project personnel imperil functional unit eﬃciency when: (1) personnel become superﬂuous because projects have no further use of their work specialization, (2) non-productive capacities increase due to the hiring of staﬀ for short-term objectives that are not needed for future needs (e.g. the additional cost of retraining personnel), and (3) lost opportunities for future employment of company personnel because of hasty outsourcing. Thus a functional managers’ ENB can be deﬁned by a multi-objective function as follows: Minimization of functional unit total costs (multi-objective function e): The fundamental objectives of functional units are: (1) minimizing wasted labor costs, (2) minimizing manpower expansion expenses, and (3) avoiding losses from unnecessary outsourcing. For this analysis, a function was selected that gives equal weights to a combination of the three objectives.

3.3. A system dynamics model Conﬂict in matrix structures is diﬃcult to examine empirically because the variables of interest are an integral part of a complex organizational system where it would be impossible to obtain an adequate variety of situations. Therefore, a simulation was seen as the best method for investigating claims about the inappropriateness of matrix structures because of inherent conﬂict and the continued usage of this structure by many R&D organizations. A simulation allows a limitless number of comparisons where a real organization would resist intervention because of its possible consequences. Hence, many more variables are controlled than would be possible in a study of real organizations. There was only a need to discover speciﬁc situations in which conﬂict need not be an automatic response in order to have a better understanding of the continued use of matrix structures.

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The simulation aimed at discovering equilibria in circumstances where there are few participants but they have alternative strategies with unexpected payoﬀs. In modeling such situations, payoﬀs represent money that presumably corresponds to an individual’s utility. This study assumes that players act rationally to maximize their wins (‘‘homo economicus model’’). While humans often act either irrationally, or act rationally to maximize the wins of some larger group of people (altruism), the discovery of possible outcomes where conﬂict need not rationally occur will raise questions regarding assumptions about the built-in propensity for conﬂict in matrix structures. Forrester’s theory (known as ‘‘system dynamics’’) provides a means to understand the payoﬀ outcomes of each ‘‘player’s’’ actions in such a high-tech environment [14,35]. What makes using system dynamics diﬀerent from other approaches to studying systems is the use of feedback loops. In its simplest sense, system dynamics focuses on information that is transmitted and returned that occurs throughout the progress of a process, and the system behaviors over time that result from those ﬂows. The feedback loops create the nonlinearity found so frequently in complex dynamic problems. Running ‘‘what if’’ simulations to test certain policies on such a model, enables us to study reinforcing processes – feedback ﬂows that generate exponential growth or collapse – and balancing processes – feedback ﬂows that help a system maintain stability. A model describing a dynamic ﬂow of resources in a multi-project system can be used to evaluate the impact of alternative resource allocation policies on conﬂict within matrix organizations [44]. The system dynamics feedback loops may provide unexpected results. The probability of a project meeting a scheduled due date within a ﬁxed budget cannot be estimated for high-tech projects because of uncertainty about the resources/time needed to complete any one activity and the extent to which freed resources can be used to expedite the work of other activities. In such a situation, giving full satisfaction to all assumed project requirements at the ﬁrst stage of a project may actually bring about delays because of an inability to meet unexpected and unmet resource requirements at later stages because of constrained budget conditions. In contrast, projects with only partial satisfaction of requirements may under crisis conditions obtain additional resources in order to prevent delays. Some conﬂicts over resources therefore become unnecessary since feedback loops reveal that project managers may succeed without all the resources initially believed to be essential. On the assumption of ‘‘homo economicus model’’, system dynamics feedback loops for alternative resource allocation policies provide three possible results for a given ENB: (1) the feedback loops might not contribute new information that could inﬂuence decisions regarding a participant’s favorite allocation policy, (2) the feedback loops might reveal that a preferred allocation policy is not as advantageous as previously thought and therefore leads to neutrality, and (3) the impact of the feedback loops

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might even demonstrate that a previous position was wrong and reverse a participant’s position about which policy to favor. Therefore, system dynamics enables the generation of optimized decision-making models that deﬁne diﬀerent conﬂict systems. Realistic conﬂict: Conﬂict in which rational decisionmaking is consistent with participants’ ENBs, thus, one side can improve his/her ENB by changing to a more favorable resource allocation policy and the other side reduces their ENB when losing a struggle to retain a favorable policy. Unnecessary conﬂict: Conﬂict in which at least one of the involved sides has a rational expectation that winning the struggle over a resource policy will improve or worsen his/her ENB, but the other side has nothing to lose from the favored policy. Thus without two opposing interests, a struggle can be avoided. Unrealistic conﬂict: Conﬂict based on one side misperceiving an existing situation. A diﬀerence in interests is presumed when in fact there is no real clash between their ENB and the other side’s preferred resource policy. Instead of a struggle, there can be an agreement beneﬁcial to both sides.

4. The simulation model A system dynamics model for simulating the ﬂow of resources in a multi-project uncertain environment was developed for our study in order to explore the impact of

1 st pushing force Organizational task

alternative resource allocation policies on participant beneﬁts in organizations with a variety of work proﬁles. As shown in Fig. 2, the model simulates the stages performed by a project manager before the interference of the top management as well as the stages in which the project program, i.e. the available resources, is impacted by the organizational capacities and the completion on these capacities. The model assumes a non-linear completion of the projects, taking in consideration the feedback loop caused by the uncertainty in obtaining timekeeping and utilization of the budget. The model considers periodic and repetitive ‘‘present view’’ planning that deﬁnes project updated milestones, and thus, allows the re-planning of timetables, updating requirements for resources and reallocation of these resources among the project activities. Such a simulation provides precision and insight which cannot be obtained otherwise and enabled the collection and analysis of performance data of events such as the end of planning period or the completion of one of the projects [4]. The model follows a deﬁnite procedure and therefore performance data can be free of noise factors involving unspeciﬁed variables (the detailed simulation procedure is shown in Appendix A.). 4.1. Database The simulation model required a complete deﬁnition for projects (see Step 1 in Appendix A for deﬁnition). Projects with random characteristics in multi-project systems were sampled and introduced into the simulation model [33,34]. Two possible resources were assumed in the simulation as necessary for project activities: (1) a ‘‘normal resource’’

2 nd pushing force Resource allocation policy

Adjusting resource capacities Consequent period

Planning a resource unconstrained program

Determining the resource requirements

Allocating resources among the projects

Consequent period Accelerating motion

Dynamic scheduling during each planning period

Consequent planning Latest period

Latest period

ENB computation for each organizational participant

Initial period Initial organizational resource capacities

Fig. 2. A model of the ﬂow of resources that allows an evaluation of the impact of resource allocation policies on participants’ ENBs.

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with the capacity for enlargement in a short response time (during one scheduling period) or reinforcement by immediate outsourcing; and (2) a ‘‘scarce resource’’ in which an increase in capacity would require a longer response time (two scheduling periods) and cannot be obtained by outsourcing. For the simulation developed in this research, project networks were designed with 6 ordinal nodes, and then a reduction made to 9 arrows from the 15 arrows possible between each pair of the 6 ordinal nodes. The location of the 9 arrows in each of the project networks was determined by a random sampling – see Step 1.1. in Appendix A. For each network, the necessity for the execution of each activity of two types of resources was sampled (normal resources, scarce resources, both normal and scarce resources, or none) – see Step 1.2. in Appendix A. Each resource required for executing an activity were assumed to have the lowest staﬃng of one unit and the highest possible staﬃng of four units. A pair of values was sampled for each activity, the lower value was considered as the expected normal staﬃng for activities at the minimal execution speed, while the higher was considered as the expected crash staﬃng for activities at the maximal execution speed – see Step 1.3. in Appendix A. Three additional values were sampled for each activity, two represented the most optimistic and most pessimistic evaluation of the normal duration distribution function [16], and the third was the expected crash duration. The sampled values sorted in decreasing order were considered respectively as: (1) the ‘‘pessimistic evaluation’’ of the normal duration, (2) the ‘‘optimistic evaluation’’ of the normal duration, and (3) the expected crash duration [34] – see Step 1.4. in Appendix A. The project lead times for this simulation were considered as the length of the critical paths assuming expected normal activity durations, and the budgets as the average costs related to the execution of all activities in normal speeds and in crash speeds – see Step 1.5. in Appendix A. In a simpliﬁcation of the simulation, 3 pairs of projects were considered as possible scenarios. Each pair of projects represents two types of projects, the sponsored project and the internal venture project. Among each pair of projects one of them was determined as the prioritized sponsored project – see Step 1.6. in Appendix A. The sampled characteristics were used to obtain diﬀerent work proﬁles for each project [33]. The basic characteristics that deﬁne the work proﬁle vary for diﬀerent R&D projects, depending on marketplace conditions and the degree of existing technological development. Three important characteristics were selected from the large number of possibilities for this simulation to establish a work proﬁle. These characteristics were: Asset speciﬁcity requirements (V1): Measured by the proportion of scarce resources. Multi-disciplinary activity (V2): Measured by the average number of functional areas participating in the performance of each activity.

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Time duration variance (V3): Measured by the average activity duration variance. Each attribute received only two values: low (L) or high (H). These values deﬁne vectors within a work proﬁle, such as H,L,H, describing a project population with high asset speciﬁcity requirements, low multi-disciplinary activity, and high time duration variance. This procedure provided a complete set of 8 work proﬁles for each of the three pairs of project networks. Each simulation was performed simultaneously for the pair of sponsored and internal venture projects, both with identical work proﬁles. 4.2. Resource-unconstrained planning Initial introduction of the project’s resource needs requires the preparation of an ‘‘optimal’’ program that is conceptualized as unconstrained by existing resources and expected to deliver ﬁnal results with a 95% chance constraint to accomplish the project at or before its due-date – see Step 3 in Appendix A. Final cost should also be within a pre-given chance constraint to be either lower or equal to the budget set for the project at this early stage. Objectives are presumed attainable by optimizing available budget among project activities. An appropriate planning technique was sought for a simulation of such a virtual program. The commonly used critical path method (CPM) of time-cost tradeoﬀs [24,25] could not be used because it relies on a deterministic model and for that reason does not ﬁt the stochastic nature of R&D activities. The PERT statistical approach [39], with nonalternative network projects and activity durations, provides considerable chance variation, but does not make use of any cost parameters. A PERT statistical approach based on Monte Carlo simulation [18] allows a redistribution of the budget among activities so as to shorten project completion time, but provides an incomplete solution since it includes stochastic time but retains deterministic cost parameters. Other planning approaches were rejected because of excessive complexity. This included the GERT approach, with purely stochastic alternative outcomes at certain nodes, the corresponding optimization procedure based on Monte Carlo simulation [50,9], the CAAN model [16], and the more problematic GAAN model [17] with its optimization procedure [19]. Finally, the design structure matrix framework was also ruled as inappropriate because it incorporates partially overlapping activities within its schedule simulation [55,6]. R&D programs are best characterized by a stochastic CPM because of the high degree of uncertainty in planning. This planning approach can be developed through the integration of a regular CPM with its time-cost tradeoﬀs and a PERT statistical approach to obtain distribution functions for activity times [34]. Its corresponding optimization procedure allows a decision maker to manage simultaneously both the time and cost chance constraints.

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The regular CPM time-cost tradeoﬀ allocates supplementary budget to critical activities that can be speeded up so as to reduce the time need to complete the project. The procedure is iterative, recognizing critical paths at each step. Activities on current paths are evaluated on the basis of time-cost tradeoﬀs, and obtain further budget allocations when this action can reduce project completion by one working day. The iterative procedure enables the most economical attainment of objectives. The unpredictability of actual activity durations makes it impossible to deﬁne critical paths in stochastic models. Through the use of a Monte Carlo simulation [59], 1000 sets of project activity durations are generated that convert the stochastic problem into 1000 deterministic problems. This large number of possible scenarios allows for the calculation of the criticality of the project activities, i.e. the probability of an activity being on a critical path. The activity with highest criticality becomes favored for additional budget. It is rare that alternative activities will be found with the same criticality. However, in such a case, the critical activity with the lowest curve slope in a timecost tradeoﬀ will be given preferential treatment. Iterations based on the Monte Carlo simulation were repeated until meeting the cost chance constraint. 4.3. Resources: requirements, allocations and capacity adjustments Since a divergence occurs in R&D projects between planning and execution, four equal planning periods of 65 working days were designed to update project programs based on remaining tasks to be performed and on the remaining available budget. The updated project programs determine the usage of resources day-by-day during the project life cycle and outline project resources requirements. Updated project programs furnished present and future resource requirements – see Step 4 in Appendix A. Total requirements were compared to current internal capacities and adjustments made to meet needs. The adjustment of the organizational capacities was performed separately for normal and scarce resources. A decrease of capacities was initiated immediately for normal resources with a further elimination of unemployed capabilities. Unused normal resources can be safely eliminated because of the availability of outsourcing without time delays – the purchase of normal resources do not call for additional delay due to manpower training and installation of new equipment. In contrast, an enlargement of normal resources took place when planning showed their employment for 3 sequential allocation periods. Scarce resource capacities that cannot be purchased externally were reduced only if there was no planned employment for them during the following 3 allocation periods. Scarce resources not in project programs during a following allocation period remained temporarily in the functional unit payroll so as to be available for future employment – see Step 5 in Appendix A.

Current scarce resources, current normal resources, and external normal resources (outsourcing) were allocated among sponsored and internal projects on the basis of one of the possible resource allocation policies: the PC policy, the DP policy, and the CA policy. Algorithms were developed for the three diﬀerent resource allocation policies. Each algorithm was based on the resource allocation decisions typical to each of the policies and on organizational capacity planning [36] – see Step 6 in Appendix A. 4.4. Dynamic scheduling under resource constraints After each of the projects had received its allocated resources, the simulation schedules repeatedly the project activities. The dynamic scheduling of project activities under resource constraints is implemented according to the SPAR1 procedure [60]. SPAR1 is based on the MINSLK (minimal slack) heuristic dispatching rule that was found to be the most eﬀective principle for attaining the objective of minimal project completion time [11]. Since the activity durations are not predicable beforehand, a sampling of 1,000 activity duration sets was performed for each project. The number of dynamic schedules was performed on the basis of the status of the project and the current resource capacities during each of the 4 allocation periods – see Step 7 in Appendix A. 5. Expected net beneﬁt computations For each set of activity durations, performance is measured in relationship to the extent to which the schedule was met and the degree to which resources were being utilized eﬃciently. Lateness and lack of full utilization of resources have economic costs. An ENB is calculated on the expected average costs of the 1,000 runs for each objective. During the running of the simulation over 4 planning periods in each of the 72 tests (8 work proﬁles · 3 pairs of network structure · 3 resource allocation policies) the detailed expenses of both projects and the functional unit were computed for diﬀerent objectives as follows: 1. Delay losses of project i (ai): Where 1 is a sponsored project and 2 is an internal venture: measured by a substitute which is the value of the project’s volume of work not completed by its due-date The end of planning period four was assumed to be a common due-date of project 1 and also of project 2 (Di=1, 2 = 4 · 65 = 260). A substitute was used instead of a direct measure because the simulation is not continued beyond four planning periods ai¼1;2 ¼

2 X

C j U i;j ðDi Þ;

ð1Þ

j¼1

where j is the type of the resource (1 is scarce type, 2 is common type), cj is the resource value per day, Ui, j(Di) is

Z. Laslo, A.I. Goldberg / International Journal of Project Management 26 (2008) 773–788

where Ri,2(p) is the outsourced capacity of common resources during planning period p (provided by the simulation).

the remaining volume of work in project i to be performed by type of resource j at the project due-date Di = 260 (provided by the simulation). 2. Direct labor costs of project i (bi): Measured by the value of staﬃng over the four planning periods plus the value of the unaccomplished work by the end of the fourth planning period 2 XX C j ½T S i;j ðp 6 4Þ þ W i;j ðp > 4Þ; ð2Þ bi¼1;2 ¼ p

6. Conﬂict analysis This research sought to ﬁnd those balances of power between organizational groups that might reduce the intensity of conﬂict within matrix structures. The results provided by 72 simulations were analyzed in order to ascertain:

j¼1

where p is the planning period, T is the duration of each of these periods (assumed as T = 65), Si, j(p) is the jth type of resource staﬃng in the ith project during planning period p (provided by the simulation), and Wi, j(p) is the planned volume of the jth type work in the ith project during planning period p (provided by the simulation). 3. Wasted labor costs (b3): Measured by the value of unemployed staﬀ (i.e. the organizational resources that were not allocated to the projects) over the four planning periods " # 4 X 2 2 X X C j T M j ðpÞ S i;j ðpÞ ; ð3Þ b3 ¼ p¼1

j¼1

1. To what extent do participant utilities depend on the choice of a project objective and the speciﬁc work proﬁle – to be evaluated via multi-way analyses of variance? 2. If a choice of diﬀerent project managers’ objectives for each given work proﬁle can inﬂuence agreement regarding a balance of power between participants (i.e. agreement to a speciﬁc resource allocation policy) and consequently decrease the intensity of conﬂict within a matrix structure – to be evaluated via multiple-range tests?

i¼1

6.1. Multi-way analysis of variance of the eﬀects of work proﬁles on the preferences for diﬀerent resource allocation policies

where Mj(p) is the jth type of resource total number employed in the organization during planning period p (provided by the simulation – see Fig. 2), assuming initial values of Mj(0) as the average request for resources per planning period 1 X2 U i;j ð0Þ: ð4Þ M j ð0Þ ¼ i¼1 4T 4. Manpower expansion expenses (c): Measured by the number of new personnel for each planning period, multiplied by the recruitment cost of each employee to the organization 2 X 4 X M j ðpÞ M j ðp 1Þ if M j ðpÞ > M j ðp 1Þ; c¼ 0 otherwise: j¼1 p¼1

The work proﬁle of a project predisposes managerial preferences for speciﬁc resource allocation policies. In a high-tech environment, this includes a need for scarce resources (asset speciﬁcity requirements), a concurrent involvement of several resources in the same task (multidisciplinary activity), and a high degree of uncertainty (time duration variance). Through a multi-way analysis of variance (shown in Table 1), the inﬂuence of the eight viable combinations of the three work attributes was examined for diﬀerent objectives and for each resource allocation policy. The presence of four-, three-, or two-way interactions determines the need for multi-range tests for homogenous groups that allow an evaluation of the utilities to be gained or lost from changing resource allocation policies. A multi-way analysis of variance showed that all three attributes of a high-tech work proﬁle inﬂuence the impact of allocation policies on the performance of each organizational participant. The involvement of scarce resources –

ð5Þ 5. Losses averted from precipitous outsourcing (d): Measured by the value of the volume of the work performed by outsourcing over the four planning periods d ¼ C2

4 X 2 X p¼1

Ri;2 ðpÞ;

781

ð6Þ

i¼1

Table 1 The eﬀects of work proﬁles on the preferences of resource allocation policies (multi-way analysis of variance, p < .05) Objective

a1 a2 b1 b2 e

The alternative resource allocation policies and: Required asset speciﬁcity

Multidisciplinary activity

Time duration variance

Four-way interaction p < .05 N.S. N.S. N.S. N.S.

Three-way interaction p < .05 Two-way interaction p < .01 Two-way interaction p < .01 N.S.

Two-way interaction p < .05 N.S. Two-way interaction p < .01

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measured by required asset speciﬁcity – was recognized in the empirical investigation as a source of additional conﬂict fronts, but in this analysis did not inﬂuence preferences for allocation policies signiﬁcantly except as part of a four-way interaction. On the other hand, as shown in Table 1, the multi-disciplinary activity – the attribute that represents the complexity, and the time duration variance – that represents the uncertainty, have mostly signiﬁcant multi-way interactions with the resource allocation policies. In the case of objective function a1, a four-way interaction (p < .05) was found between the resource allocation policy and all three work attributes. In the case of the objective function a2, a three-way interaction (p < .05) was found between the resource allocation policy, the multi-disciplinary activity, and the time duration variance. In the case of objective functions b1 and b2, two-way interactions (p < .01) were found between the resource allocation policy and the multi-disciplinary activity, and between the resource allocation policy and the time duration variance in the case of objective function e. In the case of objective function b1, a two-way interaction (p < .05) was found between the resource allocation policy and the time duration. 6.2. Simulated utilities in the conversion of resource allocation policies (multiple-range tests) Positive and negative utilities for changes in resource allocation policies were identiﬁed through multiple-range tests performed separately for each work proﬁle as they related to the various objectives. Separate tests were performed when a work attribute or a combination of work attributes interacted with diﬀerent resource allocation polices (as shown in Table 1). In the case of a four-way interaction, eight work proﬁles were examined (each work proﬁle mean was based on three computed values), in the case of three-way interaction, four work proﬁles were examined (means based on six computed values) and in

the case of two-way interaction, two work proﬁles were examined for each interaction (means based on 12 computed values). The results of these tests (p < .05) are shown in Table 2. Assuming that each of the organizational participants has the initiative to improve his/her utility, realistic conﬂicts between participants derive from signiﬁcant and opposing policy conversion utilities, while coherent utilities provide agreements, and compromises can be easily achieved where the conversion utilities are not signiﬁcant (N.S.). Table 2 demonstrates the functional managers’ ENBs after taking into consideration the eﬀect of the feedback loops. In the endeavor to minimize functional unit costs (objective e), their utilities might be insigniﬁcant for some work proﬁles in the conversion of a PC policy to a DP policy, or vice versa. In other possible policy conversions (a DP policy to a CA policy or vice versa, and a CA policy to a PC policy or vice versa) the feedback loops have no impact on the functional manager utilities. Table 2 shows no possible reversal of the functional manager utilities for the various work proﬁles, a positive utility does not become negative and a negative utility does not become positive. There is also no reversal of utilities for project managers when they endeavor to minimize expected delay loses (objectives a1 and a2). Results from the simulation show that if project managers deﬁne eﬀectiveness as their single objective, organizational participants in some work proﬁles should not have any reason for becoming involved in a conﬂict. Thus, conﬂict intensities can be reduced. On the other hand, results of the simulation in Table 2 make it obvious that for project managers who are concerned with project eﬃciency (aim at minimizing direct labor costs, objectives b1 and b2), there will be a reversal in support for or against policy conversions for most work proﬁles. These changes can be the source for diﬀerent coalitions which can agree upon an organizational resource allocation policy.

Table 2 Simulated utilities in the conversion of resource allocation policies (multi-range tests for homogeneous groups, p < .05) Policy conversion

Objective

Work proﬁle (L = low, H = high L,L,L

L,L,H

L,H,L

L,H,H

H,L,L

H,L,H

H,H,L

H,H,H

PC to DP

a1 a2 b1 b2 E a1 a2 b1 b2 E a1 a2 b1 b2 E

N.S. Negative Negative N.S. N.S. Negative Positive Positive N.S. Positive Positive Positive Positive N.S. Negative

N.S. Negative Negative N.S. Positive Negative Positive Positive N.S. Positive Positive N.S Negative N.S. Negative

Positive Negative Positive Positive N.S. Negative Positive N.S. N.S. Positive N.S. N.S. Negative Negative Negative

Positive N.S. Positive Positive Positive Negative Positive Positive N.S. Positive Positive Positive N.S. N.S. Negative

N.S. Negative Negative N.S. N.S. Negative Positive Positive N.S. Positive Positive Positive N.S. N.S. Negative

Positive Negative Negative N.S. Positive Negative Positive Positive N.S. Positive N.S. N.S. Negative N.S. Negative

Positive Negative Positive Positive N.S. Negative Positive N.S. N.S. Positive N.S. N.S. Negative Negative Negative

Positive N.S. Positive Positive Positive Negative Positive Positive N.S. Positive N.S. N.S. Negative Negative Negative

DP to CA

CA to PC

Z. Laslo, A.I. Goldberg / International Journal of Project Management 26 (2008) 773–788

Table 2 provides two diﬀerent organizational conﬂict systems for each work proﬁle and for each combination of participants’ goals. For example, Fig. 4 illustrates the conﬂict system for work proﬁle H, H, H where the three parameters are all high (required asset speciﬁcity, multidisciplinary activity, and time duration variance) for the combination of goals a1, a2, e as well for the combination of goals b1, b2, e. The outcomes from the simulation of alternative participants’ actions under uncertainty establish what should be rational preferences. Hence, some of the participants have no real interest to become involved in some conﬂicts based on the initiation or blockage of policy conversions. Moreover, participants may have reason to change their resource allocation policy preferences as shown in Fig. 1. This provides an opportunity for coalitions to form with an agreed organizational resource allocation policy. Fig. 3 demonstrates two situations: (1) where the objective is to minimize delay losses, i.e. goals combination a1, a2, e, and (2) where the objective is to minimize direct labor costs, i.e. goals combination b1, b2, e. In the ﬁrst situation, where project managers seek a minimization of delay losses, some of the participants have no obvious interest to be involved in conﬂicts by initiating policy conversions or blocking them. Fig. 4 shows that in this situation, internal project managers should be indiﬀerent to the conversion from a PC policy to a DP policy that is initiated by the coalition between managers from sponsored projects and functional units. In addition, for this objective of minimizing delay losses, managers of sponsored projects

Grade the activities by MSLK

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and internal projects no longer have a real need to convert a CA policy to a PC policy. Thus, conﬂict can be reduced but still an agreement cannot be made among all parties on one resource allocation policy since one realistic conﬂict remains: managers of internal projects and functional units remain opposed to the initiative of managers of sponsored project to convert a CA policy to a DP policy, and vice versa. In the second situation, where project managers seek a minimization of direct labor costs, change is possible in resource allocation policy preferences. When participants take into consideration the complexity and the uncertainty of the resource ﬂow, a reversal in utilities is possible. As a consequence, they should be less susceptible to conﬂict and ready to join coalitions on preferred policies. Managers of internal projects are no longer threatened by a conversion of a PC policy to a DP policy and may be ready to join managers from sponsored projects and functional units in initiating this policy conversion. In a similar shift in perceptions, managers of sponsored projects and internal projects who previously blocked the conversion of a PC policy to a CA policy may be ready to join functional units in support for this conversion. Furthermore, conﬂict is reduced because managers of sponsored projects no longer have a substantive reason to block a conversion from a DP policy to a CA policy. In the search for an agreed upon policy, a combination of goals a1, a2, e cannot lead to a stable equilibrium (see Fig. 4). A choice of a PC policy will motivate functional managers to strive for a change to any of the other alloca-

Are the required resources available?

Choose the first activity in the list

yes

Schedule the activity

no no Is it the eligible activities list empty?

yes Stop no no

Update eligible activities list

Freeze the used resources

yes

Is the completion date within the period?

Move to the next completion date

Is it the last activity in the list?

yes

Start date Fig. 3. Simulating the periodic projectns performance.

Retain completion date & remove activity from the list

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PC

PC

Sponsored P. Functional U.

Sponsored P. Internal P. Functional U.

Functional U.

1 realistic conflict

Internal P. Functional U.

DP

Sponsored P.

Sponsored P. Internal P. Functional U.

An agreed upon policy

CA

Project's minimization of delay losses (goals combination a1,a2,e)

DP

Internal P. Functional U.

CA

Project's minimization of direct labor costs (goals combination b1,b2,e)

Fig. 4. Realistic conﬂicts and an a greed upon policy for the work proﬁle H, H, H considering diﬀerent project objectives.

tion policies, a choice of the DP policy will encourage internal project managers and functional unit managers to try for a change to a CA policy, and a choice of the CA policy will persuade sponsored project managers to make every eﬀort to change to a DP policy. In contrast, a combination of goals b1, b2, e allows equilibrium for a CA resource allocation policy since none of the participants have a ‘‘real interest’’ to struggle for a change from a CA policy to another policy. Thus, a CA policy provides a possibility for reaching agreement on a single allocation policy in a situation where all managers support a combination of goals b1, b2, e. Further analyses showed that any goals combination (1 x)a1 + xb1, (1 y)a2 + yb2, e, 0 6 x 6 1, 0 6 y 6 1 decrease substantially the possibility of realistic conﬂict and lead to an agreed upon CA policy, if x > 0, and or y > 0. 7. Discussion Conﬂicts believed to be unavoidable are assumed to reduce the eﬀective performance of matrix structures because project managers and functional managers struggle for greater control over the allocation of organizational resources. As a consequence, organizations do not unite around one resource allocation policy and fail to adopt one of the three standard matrix forms as a preferred organizational structure. In a high-tech environment, however, coalitions are possible because of three confrontation fronts: between managers of projects with high priority (usually sponsored projects), managers of projects with low priority (usually

internal ventures), and functional managers. In order to obtain more favorable resource allocation policies, two of the three parties can form an alliance: for instance, project managers with low priorities joining with functional managers in a confrontation against the interests of high priority project managers. But, such coalitions are usually unstable because shifts in allocation policies lead to changes in interests of the partners. A diﬃculty of predicting the full consequences of each resource policy in a dynamic environment has become a serious complicating factor in attempted alliance formation. Disagreement among managers over resource policies, however, may turn out to be unrealistic as the attainment of a favored allocation policy may actually damage a project. For instance, a project can obtain full staﬃng in the early stages of a project in order to more quickly meet a due date but then have inadequate resources to meet unexpected problems at later stages of the work. On the other hand, partial staﬃng in the early stages of a project can increase the risk of missing a completion date, but provide a better possibility of having resources allocated at later stages for meeting unbudgeted diﬃculties. The simulation developed in this research introduced the concept of a ﬂow of resources within an organization during the scheduling process under alternative resource allocation polices. Resource requirements were set for pairs of random projects with work proﬁles consisting of diﬀerent sets of three attributes – asset speciﬁcity, multidisciplinary activity, and time duration variance. The dual objectives of meeting both a time schedule and of preventing a project from exceeding its budget are considered jointly in a high-tech environment with the interaction of

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these objectives under conditions of uncertainty requiring a consideration of feedbacks loops during the scheduling process. The results of the simulation allow for the calculation of the expected net beneﬁt to be obtained by each participant for diﬀerent resource allocation polices as they relate to various work proﬁles and project objectives. Considering that a participant’s motivation to change a policy or obstruct possible change derives from the expected net beneﬁt, his/her position regarding change should be based on the beneﬁts to be obtained from each potential struggle. Thus, potential conﬂicts can be recognized as realistic conﬂicts when two sides have diﬀerent interests, unnecessary conﬂicts when only one side stands to gain from a conﬂict, and unrealistic conﬂicts when agreement would increase expected net beneﬁts for both sides. In a situation where project managers seek primarily to minimize losses caused by not meeting a project deadline, then the outcomes of actions are fairly predictable under conditions of uncertainty for each of the work proﬁles. The feedback loops accordingly may turn presumed realistic conﬂicts into unnecessary conﬂicts but not into unrealistic conﬂicts. Thus, a reduction of conﬂict within the matrix is achievable but a fully agreed upon resource allocation policy is still impossible for those in the three conﬂict fronts. On the other hand, if the eﬃcient utilization of allocated resources becomes a shared objective, the feedback loops for some work proﬁles may change ‘‘most likely’’ outcomes of project activities into ‘‘unclear’’ outcomes. This would change outcomes considered as advantageous to disadvantageous, and vice versa. The simulation identiﬁes the work proﬁles where conﬂicts can be seen as unnecessary, or even unrealistic, and allows consensus to be reached on a comprehensive allocation planning policy. As a consequence, managers seeking to make more eﬃcient use of their resources – and beneﬁt from inter-project cooperation – can agree on a functional matrix as the preferred organizational structure. The simulation on the ﬂow of resources in a multi-project setting and under conditions of uncertainty provided the means to examine the possibility of unnecessary and unrealistic conﬂicts. An awareness of ‘‘real interests’’ can lead managers to agree upon an allocation policy. In making visible to managers how they can best meet resource concerns, this study should contribute to a reduction of conﬂict in the matrix management of high technology ﬁrms. Irrespective of the interesting ﬁndings regarding possible agreement over resource allocations policies among managers in matrix organizations, a simulation can never be the reality, it can only reﬂect it. This study assumed ‘‘homo economicus’’ participants and a management policy directed at the maximization of expected organizational net proﬁt. ‘‘Noises’’ such as friendship or antagonism among participants may change the results. Nevertheless, this research provided evidence for the problematic nature of assumptions about conﬂict in matrix structures and possi-

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bly explaining the continued use of this organizational structure in high-tech organizations. Appendix A. The simulation procedure

Step 1 – determining the organizational task 1.1. Determine the partial ordered set (POSET) of activities in which a network graph describes activities denoted by arrows, starting from one event and ending at another event, both denoted by nodes (PERT/CPM – activity-on-arrow scheme). 1.2. Determine the required resources for executing each project activity and their type (normal or scarce). 1.3. Determine the minimal resource staﬃng for the accomplishment of each activity in the minimal and maximal execution speeds (this determines the expected costs of activities for the minimal and maximal execution speeds – the ‘‘normal cost’’ and the ‘‘crash cost’’ [24,25]). 1.4. Evaluate the ‘‘optimistic’’ and the ‘‘pessimistic’’ estimations of the ‘‘normal duration’’ [34]) and the expected ‘‘crash duration’’ of each activity, corresponding to the minimal and the maximal execution speeds [34]. 1.5. Determine the time/cost constraints: (1) the project’s due date, (2) the chance constraint to meet it, and (3) the allocated budget. 1.6. Determine the project’s priority position within the company’s projects list. Step 2 – determining the resource allocation policy (choose 1 from following procedures: PC, CA, or DP) PC For each of the resources, compare the total requirements vs. the available capacity in the current planning period. If full satisfaction is possible: Allocate the required capacity to each of the projects and the remaining capacity keep in the functional unit (as unemployed capacity); Otherwise: For ‘‘scarce’’ resource: Allocate the available capacity among the projects by keeping equal proportions of satisfaction. For ‘‘normal’’ resources: Outsource the incomplete capacity and allocate the required capacity to each of the projects. CA For each of the resources, compare the total requirements vs. the available capacity in the current planning period. If full satisfaction is possible: Allocate the required capacity to each of the projects and the remaining capacity keep in the functional unit (as unemployed capacity);

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Otherwise: Allocate the available capacity among the projects by keeping equal proportions of satisfaction. DP For each of the resources, compare the total requirements vs. the available capacity in the current planning period. If full satisfaction is possible: Allocate the required capacity to each of the projects, and keep the remaining capacity in the functional unit (as unemployed capacity). Otherwise: For ‘‘scarce’’ resource: Allocate capacity to satisfy as much as possible the requirements of the most prioritized project (according the list determined in Step 1.6), with the remaining capacity repeating to satisfy the requirements of the second in the list, then these of the third, and so on. For ‘‘normal’’ resources: Allocate capacity to fully satisfy the requirements of the prioritized projects also if outsourced reinforcement is required; then, allocate the remaining initial capacity to satisfy as much as possible the ﬁrst non-prioritized project in the list, the second, and so on. Step 3 – planning a resource unconstrained program 3.1. Sample a duration for each of the project activities from a normal distributed population bounded by the ‘‘optimistic’’ and the ‘‘pessimistic’’ durations (1.4, if not replaced meanwhile by 3.4). 3.2. Relating to the set of the project activity durations (3.1) and the precedence constraints (1.1), calculate the critical path length (project’s lead-time) and identify the activities on the critical paths [24,25]. 3.3. Repeat 3.1–3.2 999 times, and then calculate the probability of meeting the due date (1.5) and the criticality of the project activities, i.e. the probability of an activity being on a critical path. 3.4. Choose the most critical activity that has not yet reached its maximal execution speed (1.4) speed its execution by one unit of budget, and adjust its ‘‘optimistic’’ and ‘‘pessimistic’’ durations to the current execution speed [34]. 3.5. Repeat Steps 3.1–3.4 until meeting the chance constraint to accomplish the project on time, or meeting the budget constraint (1.5). Step 4 – determining the resource requirements 4.1. Express the ‘‘optimal’’ execution speed of the project activities as determined in Step 3 in terms of expected activity duration and allocated staﬀ to activity. 4.2. Deploy the needs during the project’s life cycle for each of the resources, assuming expected activity

duration as deterministic times and assuming ‘‘earliest start’’ scheduling of eligible activities. 4.3. Calculate the project’s average need for each of the resources in each planning period, which are the project’s periodic requirements for resources. Step 5 – adjusting resource capacities 5.1. Sum up the periodic requirements (4.3) of all projects for resource. 5.2. Compare the total requirements for each resource in each planning period to the current resource capacity. 5.3. Adjust the organizational capacities of each resource. If the current resource capacity disables the full satisfaction of the requirements: Expand the capacities of the succeeding planning periods to the expansion response time by: The average shortage during the expansion response time plus the average shortage/ redundancy in the 3 following planning periods if the sum shows shortage, for scarce resource, or, the average shortage/redundancy in the 3 following planning periods if the sum shows shortage, for normal resource. Discharge the capacities of the succeeding planning periods to the discharge response time by: The average shortage/redundancy in the 3 following planning periods to the discharge response time the sum shows redundancy. Step 6 – allocating resources among the projects 6.1. Choose one of the alternative resource allocation policies: the PC policy, the CA policy, or the DP policy – the chosen policy will be valid throughout the makespan. 6.2. Allocate the initial organizational capacities in the initial planning period, or the adjusted resource capacities in the consequent planning periods (5.3) according to the appropriate decision-making procedure (2.PC, 2.CA, or 2.DP). Step 7 – dynamic scheduling during each planning period 7.1. Sample a duration for each of the project activities from a normal distributed population bound by the ‘‘optimistic’’ and the ‘‘pessimistic’’ durations (1.4, if not replaced meanwhile by 3.4). 7.2. Schedule repeatedly under resource constraints the project activities considering that each activity uses resource capacities as determined in 4.1 (allocated staﬀ to activity) and during the sampled duration (7.1) according to the SPAR1 procedure [60] that is based on the MINSLK (minimal slack) heuristic dispatching rule that was found to be the most

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