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464 Lecture 09 CPM Revision

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Scheduling Techniques r The scheduling techniques are î To plan, schedule, budget and control the many activities associated the projects; î Focusing on customers desired completion date; î Converting project plans into an operating timetable and î Providing direction for managing the day-to-day activities of projects r Critical Path Method (CPM) î Deterministic r Project Evaluation Review Technique (PERT) î Probabilistic

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Critical Path r Critical Path Method (CPM) is a very widely used technique. Applications include: î Building/construction; î Production planning; î Maintenance planning; î Computer system development; î Launching a new product; î Auditing; î Mobilisation/military planning; î Planning generally. r Critical path methods are a vital tool in all project based activities

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Representing a Project as a Network r A project involves several activities (or tasks) e.g. to build a house design, get planning permission, find a builder, lay foundations, order materials, build, select paint, select carpet and finish. r We can represent the relationship between the tasks as a network r In the network, nodes represent events (usually the start or completion of a task) and arcs represent activities (usually the tasks to be done) r The arrows on the arcs indicate that an event must be completed before the next i.e. Design Planning Permission

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Representing a Project as a Network We can add times to the arcs, showing how long each activity takes: Design Planning Permission 6 weeks13 weeks More than one event can occur at the same time (concurrent activities) Design Planning Permission 6 13 Find Builder 4 123 1 2 3 4

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Representing a Project as a Network In the network, 2 or more activities are not allowed to have the same starting and ending node To model this, we add an extra Dummy Activity of duration 0 when one of the 2 activities are finished: Design Planning Permission 6 13 Find Builder 4 1 2 3 4 Dummy 0 Foundations 2 Order Materials 4 5 6

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Critical Path Characteristics r There is one and only one starting and one completion (terminal) node r Critical Path networks are directional. Hence we talk about arcs rather than links r There is only one arc between each pair of nodes r There are no circuits r There are no loops r There must be at least one path from start node to completion node r There may be multiple paths from start to completion r There may be more than one critical path r There may be activities with zero duration

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Critical Path Objectives r There may be more than one Critical Path Objective. r Objectives may include: î Minimise total project time; î Minimise total project cost; î Minimise cost for a given time; î Minimise time for a given cost; î Minimise idle resources; î Straightforward project management; î Budget control. r CPM methods are used as both î planning tools and î control tools

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Critical Path Methods There are three stages. r First we go through the network from the start working out the earliest possible completion time of each task. r This is known as the forward pass. This will give you a total time for the project. r Then, starting at the final node, we work backwards calculating the latest completion time necessary to complete the preceding task for each activity. r This is known as the backward pass. r Where the forward earliest completion time equals the backward latest completion at a node, that node lies on the critical path.

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The Critical Path r There are several paths from start to finish of the project r The longest path is called the critical path r It represents the shortest time that the project can be completed r We can find the critical path by asking the following questions: î What is the earliest time that activities can be completed (or, in other words, each node is reached)? î What is the latest time that we could start the activities from a node and still complete the project in the shortest time?

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A Critical Path Problem 165432 3 r What is the critical path through this network? r How would we set about computing it? 0 2 3 7 2 2 5 6 3 Finish Start 0 2

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Forward Pass 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF)

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Forward Pass 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 3

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Forward Pass 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 3 5?

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 2 3

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 2 3 6 =max(3+3, 4)

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 2 3 6 6 =max(3+2, 6+0)

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 2 3 6 6 13 =max(6+7, 6+3)

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 Calculating the Earliest Finishing/completion time (EF) 2 3 6 6 13 19 =max(13+6, 11)

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Forward Pass (Cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 2 2 3 6 6 13 19 EF LF

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Backward Pass 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 Calculating the latest finishing/completion time (LF)

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 14? Calculating the latest finishing/completion time (LF)

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 Calculating the latest finishing/completion time (LF) 13

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 Calculating the latest finishing/completion time (LF) =min(13-7, 19-5)

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 Calculating the latest finishing/completion time (LF) 6 =min(6-0, 13-3, 19-2)

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 Calculating the latest finishing/completion time (LF) 6 =min(6-2, 6-3) 3

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 Calculating the latest finishing/completion time (LF) 6 3 4

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Backward Pass (cont.) 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 Calculating the latest finishing/completion time (LF) 6 3 4 0 =min(3-3, 4-2)

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Critical Path 165432 3 0 2 3 7 2 2 5 6 3 Finish Start 0 0 3 2 6 2 6 13 19 13 6 6 3 4 0 Critical Path

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Building the Network from a list of the activities r Well look at this by example – see handout r The basic ideas are: î Start with the first activity î Subsequent activities start from the completion node of one of its predecessors î If an activity has more than one predecessor, you put indummy arcs from the other predecessors to the starting node of the activity

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