11/1/2018. Overview PERT / CPM. Network representation. Network representation. Project Scheduling. What is a path?

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1 PERT / CPM BSD Dave Novak Fall Overview Introduce Discuss what a critical path is Discuss critical path algorithm Example Source: nderson et al., 1 Quantitative Methods for Business 1 th edition some slides are directly from 1 J. Loucks 1 Cengage Learning Network representation Depending on the network being modeled, a node can represent many different things (abstract or real, at different scales) People in a social network Transfer stations and holding facilities in a supply network Buildings, entire organizations, countries etc. Units within an organization Cultural or performance attributes Network representation rcs or links connecting nodes also represent many different things (abstract or real, different scales) Some type of connection (ability to get from one node to another) Physical links in a communications network Roadways in a transportation network Strength of relationships between people or organizations Measures of organizational knowledge, etc. 4 What is a path? In network analysis (most any network transportation, telecommunication, social, etc.) a PTH is a sequence of nodes connected by arcs or links i.e., the specific set and sequence of links and nodes that are followed to get from the start to the finish Project Scheduling Projects often consist of many different tasks that are performed by a number of different individuals and departments Not possible for managers to remember and account for all information related to project planning and scheduling PERT and CPM are two well-known quantitative techniques to help managers with the planning process 1

2 PERT Program Evaluation and Review Technique Developed by U.S. Navy for Polaris missile project to handle uncertainty associated with activity times CPM Critical Path Method Developed by DuPont & Remington Rand Developed for industrial projects for which activity times generally were known 8 Modern project management software combines features from both approaches PERT and CPM techniques are used to plan, schedule, and control a wide variety of projects such as: R&D of new products and processes Construction of buildings and highways Maintenance of equipment Design and installation of new systems Used to plan the scheduling of individual activities or tasks that make up a specific project Large projects have many activities complicating factor in scheduling and carrying out all the activities in a project is that some activities depend on the completion of other activities before they can be started 1 Used to answer questions such as: What is the total time to complete the project? What are the scheduled start and finish dates for each specific activity? Which activities are critical and must be completed exactly as scheduled to keep the project on schedule? How long can noncritical activities be delayed before they cause an increase in completion time for the entire project? CPM CPM assumes that activity times are known with certainty (variation in the time it takes to complete a particular activity is very small and is not a concern) ctivity times can be reduced by adding more resources to the activity Identifies trade-offs between time and cost for the activities of the project CPM Reduce activity time at an increased cost when is it worthwhile, and for which activities? critical path is a path consisting of activities with zero slack 11 1

3 1 PERT PERT builds upon CPM by allowing you to add information concerning minimum, average, and maximum completion time estimates for each task or activity Incorporates uncertainty into the process How are these used in practice? Many project scheduling tools used in business employ these approaches i.e., Microsoft Project However: does not scale particularly well and is less effective as project size and complexity increases Break project into smaller pieces Manage each piece as a separate project using 14 Multi-level, nested schedules How are these used in practice? Some organizations prefer coarser milestone scheduling Establish milestones for key objectives or deliverables Project team has flexibility wrt how responsibilities are divided and achieved Combinations Milestone scheduling for overall project for subprojects Network model We begin with CPM Construct a model of the project network to observe sequencing of activities Nodes of the network represent the activities The arcs or links between the nodes of the network reflect the precedence (or timebased, pre-requisite sequencing) of the relationships of the activities Float building example Frank s Floats is in the business of building elaborate parade floats. Frank s crew has a new float to build and want to use to help them manage the project. The table on the next slide shows the activities that comprise the project as well as each activity s estimated completion time (in days) and each activities immediate predecessors (previous activities). Frank wants to know: 1) the total time to complete the project, ) which activities are critical, and ) the earliest and latest start and finish dates for each activity. Steps to critical path algorithm 1) List all activities ) ID immediate predecessors for each activity ) Estimate completion time for each activity 4) Draw project network ) Forward pass ) Backward pass ) Calculate slack for each activity 8) Find activities with ZERO slack ) ID critical path

4 Step 4. Initial Paperwork B. Build Body D. Body F. Final Paperwork G. Mount Body on Frame What is a path in our example? Sequence of activity or task nodes that connects the entire project from to the Some path examples for our project network: Build Frame E. Frame H. Install Skirt on Frame 1 What is a critical path? In the project management case, all activities must be completed in the proper sequence for the project to be completed The path that takes the MOST time represents the total time to complete the project Essentially represents a binding time constraint if all other paths take less time, then those paths are not the ones that are most critical to completing the project 1 What is a critical path? If activities along the longest path are delayed, then entire project is delayed If there is slack (excess time) in other paths, those paths can be delayed (up to some point = value of slack) before the entire project is delayed CPM: the longest path = the critical path Steps 1 presented together Immediate Completion ctivity Description Predecessors Time (days) Initial Paperwork --- B Build Body C Build Frame D Body B E Frame C F Final Paperwork B,C G Mount Body to Frame D,E H Install Skirt on Frame C 4 Node / activity notation Node / ctivity Time required to complete activity t ES EF 4

5 Node / activity notation Node / activity notation Node / ctivity Earliest feasible time activity can start (ES) Node / ctivity STRT times go first ES EF Earliest feasible time activity can finish (EF) ES EF ERLY start and finish times go on top t t LTE start and finish times go on bottom Latest time activity can start to stay on critical path () Latest time activity can finish to stay on critical path () FINISH times go last Step 4 add completion time. B. D. F. G. E. H. Step forward pass ID earliest start and finish times In our project network, we have 8 activities (i =, B, C, ) Beginning at the node compute: Earliest Time = the maximum of the earliest finish times of all activities immediately preceding activity i This is for an activity with no predecessors 8 Step forward pass Beginning at the node compute: Earliest Time = (Earliest Time) + (Time to complete activity i ) This is for an activity with no predecessors The project completion time is the maximum of the Earliest Times at the node Step forward pass EF i = ES i + t i where EF i = earliest finish for activity (i) ES i = earliest start for activity (i) t i = time to complete activity (i)

6 The forward pass operations Objective is to calculate ES and EF Time required to complete activity t Earliest feasible time activity can start (ES) ES EF Earliest feasible time activity can finish (EF) Step forward pass ES EF ctivity 1 Logically, if the activity begins at ES, then the earliest the activity can possibly finish is EF because the activity requires t time to complete EF = ES + t Step forward pass Step forward pass ctivity B ES EF ctivity D ES EF B D 4 Step forward pass Step forward pass. B. D. F. G. 1 E. 1 H. What do you do, when there is more than one preceding activity? Logically, the ERLIEST start time, has to be the latest finish time of the preceding activities (i.e. F can t start until B is finished and G can t start until E is finished The expected completion time of project is the largest of the earliest finish time values for the nodes directly connected to the F, G, and H are last they are directly connected to the node days for F days for H days for G Expected completion time for the project is days

7 Step backward pass ID latest start and finish times Beginning at the node work backwards through network: Set Latest time for LL of the nodes that are directly linked to the finish (F, G, H) equal to the expected project completion time and work backwards Set for all nodes connected to finish = Step backward pass ID latest start and finish times Beginning at the node work backwards through network: For the node this is the project completion time Latest Time = (Latest Time) - (Time to complete activity i) 8 Step backward pass i = i - t i where i = latest finish for activity (i) i = latest start for activity (i) t i = time to complete activity (i) 4 The backwards pass operations Objective is to calculate and Time required to complete activity t ES EF Latest time activity can be finished if we want to stay on critical path and not delay the project completion time () Latest time activity can start to stay on critical path (). If activity starts after, we know that increases, and all activities following activity are impacted If the activity must be finished at, then the latest the activity can start without impacting the project completion time is because the activity requires t time to complete = t Step backward pass Step backward pass ctivity G. B. D. F. G. 1 G 1 E. 1 H. Set for all activities connected to FINISH = project completion time 41 4

8 Step backward pass ctivity H Step backward pass ctivity D H D Step backward pass. B. D. 1 F. 1 G. 1 1 E. 1 H. 1 1 What do you do, when there is more than one following activity? Set C = minimum of the three activities following H = 1, E =, and F = 1. The smallest of these values is E =. C = E = 4 Step backward pass ctivity C C C precedes E, F, and H So, C is the minimum of the values for E, F, and H E =, F = 1, H = 1 C = Step Calculate slack Step calculate slack The slack of an activity is the amount of time the activity can be delayed without increasing the project completion time For each activity i, calculate: Slack = (Latest ) - (Earliest ), or (Latest ) - (Earliest ) Slack i = i - ES i = i - EF i ctivity. ES EF B. D. 1 G. 1 F. 1 1 E. 1 H t 8

9 Step Calculate slack Steps 8 & ID critical path ctivity B Earliest Earliest Latest Latest Slack Critical (?) Y N Critical path is a path of activities from to node, with ZERO slack times What is the critical path here? C Y D 1 N E F G H Y N Y N Project completion time = the maximum of the earliest finish times for all the activities included in the critical path What is the project completion time? 4 Step critical path Example: D.. B. D. 1 G. 1 F. 1 1 E. 1 H B. 4 E. F. 1 G. I. 8 H. Critical Path: C E G 1 Summary Introduce Define nodes, links, path Discuss what a critical path is Discuss critical path algorithm Example