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Inferential Statistics Methods and the Computer-Based Approach to Project Management

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Inferential Statistics Methods and the Computer-Based Approach to Project Management Inferential Statistics Methods and the Computer-Based Approach to Project Management Gordana DUKIĆ Josip Juraj Strossmayer University of Osijek, Faculty of Philosophy Department of Information Sciences Lorenza Jägera 9, 31000 Osijek, Croatia Mate SESAR Ph.D. Student Josip Juraj Strossmayer University of Osijek, Faculty of Agriculture Department of Agroeconomics Trg Sv. Trojstva 3, 31000 Osijek, Croatia Ivana SESAR Student Josip Juraj Strossmayer University of Osijek, Faculty of Agriculture Department of Agroeconomics Trg Sv. Trojstva 3, 31000 Osijek, Croatia ABSTRACT INTRODUCTION Project management is a discipline of outstanding Successful operation of any organization is directly importance, especially in cases when a certain task related to project realization. Projects as such can serve requires substantial human, technical and financial different purposes, e.g. they can result in shortening the resources to be accomplished. When estimating project time required for a certain activity, cost reduction, quality duration and its costs, as well as identifying its critical improvement, increase in sales, or improved working path activities, project managers can gain crucial support conditions. There are numerous determinants of the from computer simulation. The decision-making model concept 'project', two of which will be pointed out here. presented in this paper is based on the assumption that G.H. Blackiston [9] refers to projects when speaking of activity durations can be defined as random variables that activities that result in new or changed products, services, follow a triangular or beta PERT distribution. In order to environments, processes and organizations. According to estimate project duration as accurately as possible, the H.A. Levine [12], a project is a group of tasks, performed proposed computer-based model envisages a higher in a definable time period, in order to meet a specific set number of simulation sets. By using the analysis of of objectives. This author believes that a project is variance (ANOVA) and post hoc comparisons we are characterized by being a one-time program, by its life able to determine simulation sets whose averages of cycle, work areas that can be categorized in certain tasks, project duration have no statistically significant budget, using multiple resources, and possibly the need to differences. After their frequency distribution is formed, establish a special organization or to cross the boundaries we can calculate the confidence interval for the mean of the traditional one. Although the issues of project project duration, which is one of the key pieces of management is directly connected to the development of information in project management. human civilization, modern project management, based on scientific approach and systematic application of Keywords: project management, computer-based technological achievements, came into being only in mid- approach, decision-making model, computer simulation, 20th century. Over the past few decades, different random variable, ANOVA, post hoc comparisons, organizations, including non-profit, public and confidence interval for the mean project duration government institutions, have recognized the importance of project management. In today's turbulent conditions, efficient realization of any complex task is inconceivable without this discipline. Project management can be defined as the application of stochastic one. The procedures used within these methods relevant logic and tools to planning, directing, and to determine the critical path, the expected project controlling a temporary endeavor means of planning and duration, and the slack are available in numerous control (M.M. Helms (eds.) [5]). In line with the Project publications (R. Bronson, G. Naadimuthu [2], F.S. Management Body of Knowledge (PMBOK), J.P. Lewis Hillier, G.J. Lieberman [7], H.A. Taha [17]). Within the [13] defines project management as the application of proposed decision-making model, activity durations are knowledge, skills, tools and techniques to project defined as random variables that follow a triangular or activities to achieve project requirements. It follows from beta PERT distribution (F.E. Williams [19], C. the above that project management encompasses a wide Hendrickson [6], J. Fente, K. Knutson, C. Schexnayder spectrum of different concepts, tools and techniques [4], P.A. Jensen [8]). In order to estimate project duration designed to facilitate the efficient achievement of planned as accurately as possible, and to identify the activities on objectives. the critical path, the model envisages repeating a number of simulation sets. This procedure is inconceivable According to E. Verzuh [18], project management can be without a computer and appropriate program applications. divided into five main functions: selection, definition, planning, control and close out. During selection, a Project managers can significantly improve their project is assessed regarding its purpose and benefits, its decision-making by using inferential statistics methods objectives are being related to the organization's strategic (D.-E. Lee, D. Arditi [10], D.-E. Lee, J.J. Shi [11], G. goals, and resource constraints are determined. Having Dukić, D. Dukić, M. Sesar [3]). In the model analyzed selected the project, the organization identifies all the here, the simulation sets whose averages of project stakeholders interested in its performance, appoints duration have no statistically significant differences are people in charge, and draws up the required documents. determined by means of the analysis of variance They list the objectives, constraints, management (ANOVA) and post hoc comparisons. These are then the structure, performance benchmarks, and all the other facts basis for calculating the confidence interval for the mean or assumptions that are important for completing the project duration, which is one of the most valuable pieces project. In this way, the project has been defined. This is of information for project managers. followed by the planning stage, including a detailed description of the activities, their schedule, an estimate of project costs and duration, as well as other required PROJECT PLANNING USING CPM/PERT resources, especially personnel. Within the control function, the project progress is monitored, establishing The aim of the CPM and PERT methods is to provide an possible departures from the set plan, which requires analytical framework for scheduling the activities. feedback between particular phases. If there are Therefore, there are four key values to be determined departures from the plan, the project team takes within both of these methods: the earliest start time (ES), corrective action. An important aspect of this function is the earliest finish time (EF), the latest start time (LS) and communication of the control bodies with the project the latest finish time (LF). They are calculated on the team and all the other stakeholders. Close out is the last basis of estimated duration of each activity (Dij). In this phase in project implementation. As a function, it way we can obtain the elements required to create a includes disbanding the team that worked on the project network diagram. An example of such a diagram, where and dismantling the project infrastructure. There should the nodes are marked with A, is given in Figure 1. be a systematic follow-up of the outcomes achieved in the realization phase. If these outcomes do not meet the organization's requirements, project management needs to A(1) be put in place again. As its efficiency is closely related 1 ES1 LF1 D 0 1 to the available management information, an area that D D 4 1 A(0)3 A(4) merits special attention within project management is the D D 34 modeling and construction of an adequate database. ES0 LF0 A(3) ES4 LF4 02 23 D A(2) ES3 LF3 ES LF RESEARCH METHODOLOGY 2 2 The decision-making model presented in this paper is Figure 1. An example of a network diagram based on project management techniques. The two best known, CPM (Critical Path Method) and PERT (Project The basic difference between the CPM and PERT Evaluation and Review Technique), are the starting point methods lies in the way how activity duration is for the model we have developed. The former belongs to determined. Whereas CPM is based on a single time the group of deterministic methods, whereas the latter is a estimate, within PERT, three time estimates are given for every activity - optimistic (a), most likely (m) and ⎛ T − μ{}E( j ) ⎞ pessimistic (b). In such a case, the expected duration of P()D{}E( j ) ≤ T = P⎜ z ≤ ⎟ ⎜ σ 2 {}⎟ each activity (i, j) is calculated by means of the formula: ⎝ E( j ) ⎠ 1 Dij = ()a + 4m + b With the increasing number of activities the parameter 6 approximation is improving, and with it also the estimate If the earliest start time of the first activity is marked with of probable completion of an event within the set ES0, then it must be ES0 = 0. The earliest start time of any timeframe. activity (ESj) is determined in the following way: {} ES j = max ESi + Dij , for all i entering into j. SIMULATION OF ACTIVITY DURATION i BASED ON A TRIANGULAR AND BETA PERT DISTRIBUTION The latest finish time of an activity (LFi) can be calculated as follows: In comparison to the CPM method, the usage of PERT can only slightly decrease the risk of inaccurate estimate LFi = min{}LF j − Dij , for all j leaving from i. j of project duration and its costs, as well as of the incorrect identification of activities on the critical path. The activity is critical if it satisfies the following The reason for this is that, when using PERT in project conditions: planning, only one time estimate is taken into account, namely the one obtained by calculating the expected 1. ESi = LFi duration of an activity. What is disregarded in this way are all the possible subcritical paths, which could be 2. ES j = LFj generated due to wrong estimates of this value. Hence, − = − = 3. ES j ESi LFj LFi Dij the initial model based on the PERT method needs to include the concept of computer simulation.
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