Project Scheduling Techniques: Probabilistic And Deterministic

Project Scheduling Techniques:Probabilistic and Deterministic

ContentsProject scheduling and types of project schedule . 2Overview . 2Project scheduling techniques . 2Deterministic Scheduling . 3Introduction . 3How it works?. 3Probabilistic Scheduling . 4Introduction . 4How it works?. 6Conclusion . 7

Project scheduling and types of project scheduleOverviewA project is an activity that focuses to create a unique product or service in a definite timeperiod. Project management is a systematic approach to guide project processes for achievingthe target, and project schedule is one of the most important tools that guides for effectiveproject management.Project scheduling encompasses mapping and planning of every phase of a project’s lifecyclefrom initiation to its’ subsequent completion. It should include all terminal elements of theproject, containing its budget, duration, work breakdown structure, etc. When performedsuccessfully, it will allow more efficient time and resource provision to ensure that the projectis managed in a smooth and efficient manner.Time and task management are the knowledgeareas in project management, which define whatwork is to be done, when is to be done, and whoshould be doing. A project schedule generallyconsists of a hierarchy of work to be performed- an estimation of resources required to performtasks, duration and effort involved in performingthose tasks, and cost incurred in completing thework.In scheduling tool like MS Project, thehierarchy of work, known as the WorkBreakdown Structure (WBS), can beeasily developed and thus helps inmanaging the work easily. The toolhelps in estimating the dates and costof each activity which in aggregatecalculates the estimated start andfinish date of the project along withthe total cost estimation of theproject.Project scheduling techniquesThere are various methods involved in displaying and analysing project schedules. Methods of displaying project schedules - Milestone Chart, Task List, Gantt Bar, NetworkDiagram, 2-D Task List, among others.Methods of analysing project schedules - Critical Path, Critical Chain, PERT, ResourceLevelling, Schedule Acceleration, among others.

These methods can be broadly classified under:1. Deterministic Scheduling2. Probabilistic SchedulingDeterministic SchedulingIntroductionDeterministic scheduling is the most commonly used scheduling technique. In this method, theschedule developed is a network of activities linked by dependencies.How it works?The values such as duration, start and finish dates for activities, are deterministic in natureand thus each one is allocated a single value estimation. The estimated values roll up to theproject level to define project duration, along with start and finish dates. The statistical toolgenerally used is Critical Path Method (CPM). As shown in the below figure (Figure 1), thecritical path of a project is indicated in red colour.Figure 1: Schedule with Critical Path -- Red Bars showing Critical PathAccording to CPM, the project is always driven bya list of connected activities having the longestpath, known as the critical path. The projectduration, start and finish dates are calculatedfrom the critical path. The focus is majorly onhow the project is performing on the critical pathactivities, rather than focusing on all activities.MS Project automatically develops theGantt Chart based on the estimateinputs, like activities and duration,along with the constraints like start orfinish dates.Estimations in deterministic scheduling require experience and references of past data. Thechances of successfully completing the project, as per the schedule, greatly depend on theestimations that are deterministic in nature. The number of critical activities may be less thanor equal to the total number of project activities.Consider an example of developing a project schedule with three tasks – design, procurementand development. Following table gives the gn4 daysStartProcurement5 daysWill start after Task 1 is completeDevelopment8 daysWill start after Task 1 is complete

The project duration is estimated using CPM through the below network diagram:Design 4 daysProjectStartProcurement 5 days2S1Development 8 daysEProjectEnd3Figure 2: Network DiagramThere are two paths in the above project:S 1 2 9 days1 3 E 12 daysAccording to CPM, the path with the longestduration is considered as the critical pathand the project duration is equal to theduration of the longest path.Linking various tasks/activities anddeveloping the network diagram using MSProject is an automatic process. This issimply done by defining thepredecessor/successor relations. Thecritical path also gets derived from thenetwork diagram automatically.Here the critical path is S 1 3 E and the project duration is 12 days.According to the above example, totalduration of the project will be 12 days. Theactivities on the critical path need to becompleted for the said duration to completethe project in 12 days, else the project willget delayed.The schedule estimated is deterministic innature. This type of scheduling is used whereone knows what exactly is going to happen.This method is helpful where the projects areof similar or repeat nature.Viewing & having an analysis of thecritical path in MS project can be done inno time - just by selecting Critical Pathoption.Simply having a glance on different Ganttchart representations, Project Managerscan understand the current status of theproject. This also helps them in taking adecision over which part or projectactivities need to be focused on.Probabilistic SchedulingIntroductionThis scheduling technique involves same activities as in deterministic scheduling, such as listingof tasks, allocating resources, estimating duration, defining start and completion dates, andbased on the inputs develop a Gantt chart. The only difference lies in the way of estimatingduration and statistical tool used to develop the schedule.

The three-point estimate in deterministic scheduling - the best case, the worst case and themost likely.Figure 2: Best Case, Most Likely Case & Worst Case EstimationBest case is the estimation where everything goes right, most likely case estimate is whereactivities go on with normal problems and opportunities, and the worst case is where everythinggoes wrong.Statistical tools like PERT (Programmable Evaluation and Review Technique), Monte CarloSimulation, GERT (Graphical Evaluation and Review Technique), are used do estimate projectduration, task dates, project dates, and develop the Gantt chart.PERTThe program (or project) evaluation and review technique, commonly abbreviated as PERT, isa statistical tool for project management, analysis and representation of tasks involved incompleting a given project.Monte Carlo SimulationMonte Carlo are a comprehensive range of computational algorithms that are determined byrepeated random sampling to achieve numerical results.GERTGraphical Evaluation and Review Technique, commonly known as GERT, is a technique ofnetwork analysis used in project management that allows probabilistic treatment of bothnetwork logic and estimation of activity duration.

How it works?In order to understand how a probabilistic schedule is developed, understanding of the workingof statistical tools is necessary.How PERT is used to determine the schedule?The estimation done in PERT is 3-points estimate – Pessimistic (P), Optimistic (O) & Most Likely(M) for each task. In PERT analysis, the duration of a task is assumed to have a beta probabilitydistribution. According to this distribution, the expected task duration and variance of the taskcompletion can be calculated using the following formula:Expected Task duration (d) (O 4M P)/6Variance (v) ((P-O)/6)2Consider the above example and estimate the project duration.Priority/RelationshipTaskNameDuration (in Days)Optimistic (O) Most likely (M)Pessimistic (P)Task 1346StartTask 23.558Will start after Task 1 iscomplete10Will start after Task 1 iscompleteTask 368Apply the above formula to calculate the activity duration (d) and variance (v):OptimisticMost likelyPessimisticExpectedVariance (v)Task Duration(d)Task 134640.25Task 23.55850.125Task 3681080.45Task NameDuration (in Days)The project duration is estimated using the Critical Path Method (CPM). The CPM in this exampleis S 1 3 E, as determined from the network diagram (Figure 2). The expected projectduration in the above example is the sum of expected task durations of Task 1 and Task 3.Expected project duration (µ) 4 8 12 daysThe variability or standard deviation of the project duration is calculated by the followingformula:Variability in Project Duration (σ) (Sum of variance of tasks on CPM) 1/2

(0.25 0.45) ½ 0.87The probability that the project can be completed in 12 days, within the expected projectduration (µ) is 50%. PERT analysis answers questions such as – what would be the probability ofproject completion on time, or conversely, and what the project completion time would be,given a certain probability.The probability distribution used is normal distribution as represented below:In the above example, theprobabilitythattheproject can be completedbetween 9.39 days to14.61 days is 99.7%, 10.26days to 13.74 days is 95% &11.13 days to 12.87 days is68%.This method of schedulingfocuses on generating arealisticschedulebytaking into considerationthe risk factors that mayhave a positive or negativeimpact on the project. Ittries to capture risks anduncertainties associatedwith the project tasks9.3910.2611.1312 days 12.8713.7414.61and the overall project.daysdaysdaysdaysdaysdaysThe schedule is created with some buffer time to deal with risks and uncertainties.ConclusionThe most widely used scheduling technique is deterministic scheduling. In deterministicscheduling the risks are handled as static entities. The task and project duration are fixedvalues. This type of scheduling is mostly used where the projects done are similar in nature andthe project manager has an end to end visibility of the projects. The better visibility lets theproject manager do a confident risk assessment. While developing the schedule, he/she takesinto account all those factors, which give him/her the confidence over the project plan.In probabilistic schedule, risks are stochastic processes having probabilistic outcomes. Theproject duration is not a fixed value, but a value determined from the probability distributionwith some confidence level associated. This type of scheduling is used where there is moreuncertainty in the project. While developing the project plan, the project manager has toconsider various factors, which are uncertain in themselves. Probabilistic scheduling gives arealistic view of the project plan, helping project managers predict the uncertainty and itseffect on the plan.

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chances of successfully completing the project, as per the schedule, greatly depend on the estimations that are deterministic in nature. The number of critical activities may be less than or equal to the total number of project activities. Consider an example of developing a project schedule with three tasks – design, procurement and development.