[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-239367-105":53,"doc-detail-239367-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","operations-management-part-ii-critical-path-method-cpm","Operations Management Part II - Critical Path Method (CPM)","","Operations Management Part II content introduces the Critical Path Method (CPM) for planning and controlling projects. It explains the critical path and critical activities (bottlenecks), how to identify them by evaluating all start-to-end paths, and how activity delays affect overall project completion time. The lesson includes the meaning of key network concepts such as events, activities, predecessors/successors, and dummy activities, and works through sample problems to compute critical paths and total duration.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/operations-management-part-ii-critical-path-method-cpm/239367/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/operations-management-part-ii-critical-path-method-cpm/239367.png","ImageObject",442,249,{"name":88,"@type":89},"Aditya","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-28","2026-09-11",true,{"@type":98,"interactionType":99,"userInteractionCount":45},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What is the critical path in CPM, and how is it identified?","Question",{"text":108,"@type":109},"The critical path is the path with the largest total execution time from the start event to the end event. It is identified by calculating the time for each possible path and selecting the maximum.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Why are activities on the critical path called critical activities (bottleneck activities)?",{"text":113,"@type":109},"They are critical because they cannot be delayed without delaying the project completion time. Any delay in a critical activity delays the whole project.",{"name":115,"@type":106,"acceptedAnswer":116},"How do dummy activities help in a CPM network diagram?",{"text":117,"@type":109},"Dummy activities are used to retain different nodes as separate while still providing required connectivity in the network. They do not represent real activities but preserve correct precedence relationships.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},239367,1791721984,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":45,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Problem 2  \nDevelop a network diagram for the project specified below:  \n\n| Activity | Immediate Predecessor\u003Cbr>Activity |\n| --- | --- |\n| A | - |\n| B | A |\n| C, D | B |\n| E | C |\n| F | D |\n| G | E, F |\n\nSolution  \nActivity A has no predecessor activity. i.e. , It is the first activity. Let us suppose that activity A takes the project from event 1 to event 2. Then we have the following representation for A:  \nFor activity B, the predecessor activity is A. Let us suppose that B joins nodes 2 and 3. Thus we get  \nA B  \n1  2  3  \nActivities C and D have B as the predecessor activity. Therefore we obtain the following:  \n4  \nC  \nD  \n5  \nActivity E has D as the predecessor activity. So we get  \n C   \n4  \nActivity F has D as the predecessor activity. So we get  \nD F  \n3   6l  \n5  \nActivity G has E and F as predecessor activities. This is possible only if nodes 6 and 6l are one and the same. So, rename node 6l as node 6. Then we get  \nD F  \n3   6 !   \n5  \nand  \n5  \nF  \n4  \nE  \nG is the last activity.  \nPutting all the pieces together, we obtain the following diagram the project network:  \nStart event  \n4  \nEnd event  \nG  \nF  \nC  \nD  \n5  \n1  \nE  \n6  \n7  \nThe diagram is validated by referring to the given data.  \nNote: An important point may be observed for the above diagram. Consider the following parts in the diagram  \nC E  \n3   6  \n4  \nand  \n D   \n F  6l  \n5  \nWe took nodes 6 and 6l as one and the same. Instead, we can retain them as different nodes. Then, in order to provide connectivity to the network, we join nodes 6l and 6 by a dummy activity. Then we arrive atthe following diagram for the project network:  \nStart event  \n7  \nC  \nD  \n5  \n1  \nG  \nEnd event  \nQuestions  \n1. Explain the terms: event, predecessor event, successor event, activity, dummy activity, network.  \n2. Construct the network diagram for the following project:  \n\n| Activity | Immediate Predecessor\u003Cbr>Activity |\n| --- | --- |\n| A | - |\n| B | - |\n| C | A |\n| D | B |\n| E | A |\n| F | C, D |\n| G | E |\n| H | E |\n| I | F, G |\n| J | H, I |\n\n****  \nLesson 4-Critical Path Method (CPM)  \nLesson Outline  \nӹ The concepts of critical path and critical activities  \nӹ Location of the critical path  \nӹ Evaluation of the project completion time  \nLearning Objectives  \nAfter reading this lesson you should be able to  \nӹ understand the definitions of critical path and critical activities ӹ identify critical path and critical activities  \nӹ determine the project completion time  \nIntroduction  \nThe critical path method (CPM) aims at the determination of the time to complete a project and the important activities on which a manager shall focus attention.  \nAssumption For Cpm  \nIn CPM, it is assumed that precise time estimate is available for each activity.  \nProject Completion Time  \nFrom the start event to the end event, the time required to complete all the activities of the project in the specified sequence is known as the project completion time.  \nPath In A Project  \nA continuous sequence, consisting of nodes and activities alternatively, beginning with the start event and stopping at the end event of a network is called a path in the network.  \nCritical Path And Crtical Activities  \nConsider all the paths in a project, beginning with the start event and stopping at the end event. For each path, calculate the time of execution, by adding the time for the individual activities in that path.  \nThe path with the largest time is called the critical path and the activities along this path are called the critical activities or bottleneck activities. The activities are called critical because they cannot be delayed. However, a non-critical activity may be delayed to a certain extent. Any delay in a critical activity will delay the completion of the whole project. However, a certain permissible delay in a non –critical activity will not delay the completion of the whole project. It shall be noted that delay in anon-critical activity beyond a limit would certainly delay the completion t","cbCaionOmZGpXrLI","https://ap.wps.com/l/cbCaionOmZGpXrLI","pdf",771158,178,"English","# Lesson 4 - Critical Path Method (CPM)\n## Lesson Outline\n## Learning Objectives\n## Introduction\n## Assumptions for CPM\n## Project Completion Time\n## Path in a Project\n## Critical Path and Critical Activities\n## Problem 1\n## Solution for Problem 1\n## Problem 2","[{\"question\":\"What is the critical path in CPM, and how is it identified?\",\"answer\":\"The critical path is the path with the largest total execution time from the start event to the end event. It is identified by calculating the time for each possible path and selecting the maximum.\"},{\"question\":\"Why are activities on the critical path called critical activities (bottleneck activities)?\",\"answer\":\"They are critical because they cannot be delayed without delaying the project completion time. Any delay in a critical activity delays the whole project.\"},{\"question\":\"How do dummy activities help in a CPM network diagram?\",\"answer\":\"Dummy activities are used to retain different nodes as separate while still providing required connectivity in the network. They do not represent real activities but preserve correct precedence relationships.\"}]","Operations Management Part II - Critical Path Method (CPM) | PDF",1789147693,62]