Searching For Resilient Project Structure Judyta Ciemcioch Grzegorz Ginda AGH University of Science AGH University of Science and Technology and Technology Cracow, Poland Cracow, Poland judyta.ciemcioch@gmail.com gginda@zarz.agh.edu.pl Abstract—Project optimization often deals with simple Possible scale of project optimization depends mainly on minimization of its makespan and cost for a given order of the assumed order of project components. The role of order of project components i.e. project structure. However, project project components is nevertheless often neglected. And as a execution effects may be improved at most with the application result – project optimization results in a suboptimal project of appropriate project order. The problem of the utilization of implementation only. appropriate project structure is nevertheless often neglected. This is why project optimization efforts usually result in Possible project disruption caused by adverse changes in suboptimal project implementation. Moreover, the actual surrounding environment are usually neglected while effects of optimized project depend on possible disruptions in optimizing a project due to project analysis complexity. surrounding environment. The meaningful disruptions may Hence the actual appearance of project disruptions result in have different e.g. financial and other resource-based, societal, optimized project implementation performance which is far environmenal nature etc. It is necessary, therefore, to make away from expected performance. Considering possible project disruption-proof. This is why a framework for the project disruptions during project optimization becomes framework that is capable of delivering project structure that important, therefore, to ensure expected project makes project implementation resilient to possible disruptions implementation effects that are at least close to the expected is presented in the paper. effects in the presence of disruptions. It seems that, because to the fundamental role of applied project structure for final Keywords—project management, project structure, disruption, performance of project implementation, the application of resiliency appropriate choice of the structure would to make project resilient to possible disruption resulting from changes in surrounding environment. I. INTRODUCTION Rising of diverse natural, societal, political, and technical Projects are used in diverse areas to obtain different goals. threads cause that resiliency to uncontrollable changes in Successful project implementation depends on careful project surrounding environment becomes more and more interesting preparation and project management. However, the topic for scientific research [1]. However, up to our uncontrolled influence of continuously changing surrounding knowledge, despite an urgent need for providing reliable tools environment, contemporary complex projects are for resilient planning of project implementation, no proposal implemented in, may disrupt actual project implementation currently addresses coping with improving project resiliency effects as well. For example, such influence may result from to disruptions changes in surrounding environment by means changing fiscal, political, societal and environmental issues. of proper project structure choice. This is why a framework This is why the implementation of contemporary complex for project optimization which is capable of delivering a projects should be prepared in a way that makes such project project structure that makes project resilient to possible resilient to possible disruptions in as much as it is only surrounding environment-induced disruptions. Thus, the rest possible. of the paper is structured as follows. The second section is Projects are optimized to provide necessary means for the devoted to tentative assumptions. The elements of actual best possible project implementation results. Project disruption-aware project optimization framework are optimization is aimed at obtaining the best possible levels of presented in the third section. Final conclusions are included project characteristics – makespan, cost etc. Limits of in the last section. available resources are included in this regard. The optimization results in a project implementation timeline. II. TENTATIVE ASSUMPTIONS Resulting project timeline deals with the applied order of A project consists of n components. The components are project components – activities that make obtaining necessary related to one another by an obligatory precedence order. The intermediate project implementation results – intermediate precedence order decides if each pair of project components goals – possible. An order of project components is called may be applied only in sequence or in any way. Note that project structure in the paper. A permissible project structure number of possible admissible project structures may rise a results from pre-order of project components. The pre-order is lot with the cardinality of a set of project components. defined by obligatory precedence of project components. Once the implementation of project component starts it doesn’t stop until its successful end. The same deals is true in Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) the case of the implementation of project components. Each Γ− = Γ+ () project component is responsible for some intermediate goals. The goal may be achieved by means of using different This is why one of them is sufficient to describe obligatory possible ways (modes). The application of each mode order of project components. requires utilization of some resources. The resources deal with manpower, equipment, materials, space, financial means Structure of project is defined by a digraph G(U,V) and a etc. Actual availability of resources is limited and may corresponding n by n matrix G, where U denotes digraph’s change in time. However, it is assumed that once a given vertices and V – digraph’s arcs. Note that in the case of all resource is engaged, it becomes entirely involved in the above mentioned digraphs vertices (nodes) represent project implementation of a project component til its successful components while the arcs – the precedence of project completion. The availability of resources may be limited in components. both time and space. Note that limited nature of resources A notion of a network S(G,Φ,Ψ) is applied to express needed by project components may cause delays in actual actual project implementation. The network is based on a start of project component implementation. digraph G. Symbols Φ, Ψ express sets of attributes describing Implementation of project components may undergo project components and sets of attributes which define their disruptions resulting from changes in surrounding economic, immediate precedence, respectively. societal, technological, political, fiscal environment and The effects of project implementation are expressed by a natural phenomena. Disruptions may result in diverse adverse set of meaningful attributes. The set may include casual effects: delays, cost overruns, unnecessary blocking of tangible project attributes: makespan, cost, starting date, due resources, a need for etc. Possible modes for project date as well as other original tangible attributes e.g. level of component implementation may differ in actual sensitivity to the utilization of available resources. The application of disruptions. intangible project attributes is also possible. All in all, project Several attributes may be applied to assess the effects of implementation attributes result from actual network S. project implementation. Both tangible attributes (makespan, However, they may be also directly influenced by changes in cost etc.) and intangible attributes (influence on surrounding surrounding environment. environment etc.) may be applied in this regard. Level of To provide necessary means for recommending project project attributes results from attributes levels obtained for implementation and assess project implementation quality, a individual project components. The attributes can be utilised vector function F is introduced. The function makes final to assess the effects of the implementation of overall project recommendation of project implementation(s) possible. The and its components. recommendation is results from a multi-level optimization Note that clear recommendation of best project with the following goal function: implementation involves making several decisions at once. The decisions deal with the indication of appropriate: • project structure;   G    0 S    min  min min F S (G, Φ,Ψ ),  ( )      () • modes for the implementation of project components which also define required resources; where: Γ denotes a set of permissible project structures, θ0 is • project starting date. a starting date for actual project implementation, and ω(t) expresses the influence of surrounding environment which III. PROJECT IMPLEMENTATION MODELLING changes in time t. A. Princples The goal function is accompanied by a set of constraints imposed on considered attributes of whole project and its The application of flexible and universal means is components. Considered optimization problem belongs to the welcome to model project implementation in a comfortable general class of multi-criteria multi-mode resource- way. A notion of a joint directed graph (digraph) is applied, constrained project scheduling problems [2]. It is nevertheless therefore, as a basis for description of both obligatory a peculiar and unique class instance because it considers precedence of project components and a project structure. intangibles and unknown influence of surrounding Note that a digraph may be expressed by a matrix. The actual environment. application of such digraph representation facilitates project optimization process a lot. It is visible from goal function (2) that consecutive optimization levels deal with individual decisions. The The digraph of predecessors Γ- and digraph of successors decisions pertain to the choice of appropriate: Γ+ are applied to express admissible precedence of project components. The digraphs may be expressed by • Project structure. a corresponding binary n by n binary matrix of (project component) predecessors Γ- and a corresponding n by n • Starting date for actual project implementation. binary matrix of (project component) successors Γ+, • Actual modes for project components. respectively. The matrices are strictly related to each other: Note that higher level decisions impose considerable restraints on permissible lower level decisions. Goal function is intentionally given in a general form (2). permissible project structures. The first inner loop pertains to This is because such form allows to make use of both tangible simulations of changes in surrounding environment. It and intangible project attributes while optimizing project contains two inner loops. The outer one allows to consider implementation. Moreover, the general nature of the goal influence of actual allocation of modes to project components function (2) doesn’t favour use of any particular optimization on project implementation outcomes. The inner one deals model class and opens presented framework to the wide with the influence of starting date θ0 on the outcomes. Note family of optimization model classes. that replying of calculations for different starting dates makes sense because of possible time-dependent changes in B. The optimization surrounding environment. Several challenges arise while considering the The application of each tuple consisting of considered: optimization of project implementation. The main problems deal with the need for: • project structure G, • Considering all permitted project structures and • surrounding environment state ω(τ), modes for project components. • actual mode allocations to project components, • The use of both tangible and intangible project • starting date θ0. attributes. results in a network S corresponding with a distinct project • The influence of surrounding environment. implementation. The pair-wise comparison of the attributes of The problems impede optimization efforts. Monte Carlo such project implementation with attributes of previously simulations were finally chosen to generate permitted project identified non-dominated project implementation(s) to check structures, to select actual modes for project components and if it is a non-dominated in the sense of Pareto-efficiency. If to simulate changes in surrounding environment. A notion of so, it is applied to update the set of non-dominated project Pareto efficiency-based dominance and pair-wise implementations. nS. Note that the identification of new non- comparisons helped to address a need for use of both tangible dominated project implementation may also require and intangible project attributes. deepening nS update by removing project implementations which become dominated by the newly added project START implementation. Note that to obtain reliable results and facilitate calculations core simulations should be carefully prepared. Generating permissible Several experimental simulation runs are needed, therefore, to project structure identify appropriate probability density models and to indentify necessary parameters e.g. number of required core Surrounding environement simulation runs. Particular care is indispensable with regard state generating to the preparation of simulations of surrounding environment Search for the best project structures state. This is because the reliability of the framework is extremely sensitive to any inadequacy in capturing Allocation of modes surrounding environment state reality [3]. Multiple repetitions in surrounding environment to project components of optimization framework is also recommended to consider Simulation of changes as much possible permitable project implementations as possible. Starting date update The optimization of project implementation may result in Mode allocation Starting date variation one or a set of several non-dominated candidates for the recommended project implementation. In the latter case there Set of the best networks appears problem which dominated project implementation to recommend for final application? Pair-wise comparisons may nS update prove helpful in this regard, again. The ability to consider difference in importance of project implementation attributes End End End End is nevertheless needed here. NO Loop Loop Loop Loop Loop ???? For example, a multi-attribute value theory-based technique like Saaty’s AHP [4,5] may prove to be a relatively YES easy to use tool. Another possibility deals with the application of a outranking-based technique like Bran’s PROMETHEE STOP [6]. There are also some well known strategies of psychological origin available e.g. intuitionistic heuristic Fig. 1. Illustration of general idea of proposed framework techniques like Tversky’s semi-lexoicogrpahic strategy and aspect-wise elimination strategy [7,8]. Note that some The general scheme for proposed optimization framework additional limitations imposed on main or auxiliary project is presented in Fig.1. Four embedded loops are applied in this implementation attributes may also help a lot in the regard. The outermost loop deals with the generation of identification of the most valuable project implementation. To avoid pitfalls with regard to the identification of the There are also several FLOSS options available that seem really best non-dominated project implementation alternative, suitable for the implementation of the proposed framework. the application of sensitivity analysis is recommended. The For example example, GNU OCTAVE - a multi-platform analysis can deal with the influence of different decision scientific programming language system available at support tools or differences in preferences toward different https://www.gnu.org/software/octave provides necessary project implementation attributes. means for matrix, numerical and simulation analysis. A general two-stage framework for final recommendation Another suitable option is provided by core programming of project implementation (Fig.2) consists of two stages languages with useful extensions. It seems that, due to which are devoted to: universality and rising popularity, the application of van • The identification of non-dominated project Rossum’s Python programming language should be implementations. recommended in this regard. Python implementations are freely available at web page dedicated to the language: • Final indication of the most advantageous non- https://www.python.org. dominated project implementation. C. Software implementation IV. CONCLUSIONS Complexity of proposed framework makes software Contemporary projects are implemented in specific multi- application support indispensible. Fortunately, the dimensional surrounding environment. The complexity of development in information and communication technology interactions with surrounding environment result in a delivers a lot of possible options available that are capable of considerable dependence of actual project implementation facilitating software implementation of the framework. Many outcomes on actual changes in surrounding environment. of them are freely available under free and libre open source Therefore, it is necessary to plan the implementation of software (FLOSS) framework. For meaningful details consult contemporary projects in a way which would make them for example the Floss for Science initiative presented at resilient to possible changes in surrounding environment as https://flossforscience.com. much as only possible. A framework is thus presented in the paper which is capable of recommending project START implementation which would be resilient to changes in surrounding environment at the highest possible level. The framework makes use of appropriate choice of project structure in this regard. Data input Besides the capability of including tangible and intangible influence of surrounding environment changes, the main merits of the framework cover the ability to include both tangible and intangible effects of project implementation. The The identifiaction of non-dominated framework is also capable of including different possible project implementations uS ways for implementing project components while considering limited availability of necessary resources. Therefore, it seems also to be a tool that considerably improves to the reliability of solutions of wide class of multi-criteria multi- YES -mode resource constrained project scheduling problems. | nS | = 1 ? Universal and comprehensive nature of proposed framework makes it well suited for recommending reliable project structure and a resulting schedule in different areas. NO Actual reliability of indispensable software implementation of the framework heavily depends, however, on the adequacy of Elaboration modeling influence of surrounding environment. Specific of final project implementation implementation of the framework requires, therefore, careful recommendation adjustment to actual needs. Hopefully, the application of available FLOSS tools makes it approachable. Presentation ACKNOWLEDGMENT of final recommendation The authors wish to thank AGH UST for providing financial means for the research and publication of the paper. STOP REFERENCES [1] Y.-P. Fang, E. Zio, „An adaptive robust framework for the Fig. 2. General scheme of the proposed recommendation framework optimization of the resilience of independent infrastructures under natural hazards”, European Journal of Operational Research, vol. 276(3), 2019, pp. 1119–1136. [2] J. Węglarz, J. Józefowska, M. Mika, G. Waligóra, “Project scheduling with finite or infinite number of activity processing modes a survey”, European Journal of Operational Research, vol. 208(3), 2011, pp. 177– 205. [3] M. Dytczak, G. Ginda, N. Szklennik, and T. Wojtkiewicz, “Weather Influence-Aware Robust Construction Project Structure”, Procedia Engineering, vol.57, pp. 244–253, 2013. [4] T.L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill, 1980. [5] E. Rokou, K. Kirytopoulos, “Multicriteria Decision Making for Project Scheduling under Reource Constraints”, Proceedings of ISAHP 2013, June 2013 [paper no.056, available at: https://doi.org/10.13033/isahp.y2013.056] . [6] J.P. Brans, L'ingénierie de la décision: élaboration d'instruments d'aide à la décision. La méthode PROMETHEE. Presses de l’Université Laval, 1982. [7] A. Tversky, “Intransitivity of preference”, Psychological Review, no. 76, 1969, pp. 31–48. [8] A. Tversky, “Elimination by aspects: a theory of choice”, Psychological Review, no. 79, 1972, pp. 281–299.