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Applied operatons research cpm1

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Simran Chhina

This document defines key terms related to critical path method (CPM) for project scheduling. It defines a project, activities, events, dummy activities, networks, critical paths, and provides examples. It also lists 3 sample problems to draw networks from activity information and identify the critical paths and project durations.

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Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com Applied Operations Research MB301 Handout-1 Critical Path Method-1 Definitions- 1. Project A project is a temporary endeavor with a defined beginning and end (usually time constrained, and often constrained by funding or deliverables), undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value. Checklist (project definition checklist) Endeavor Temporary Endeavor Defined Beginning Define d End Undertake n to meet unique goals and objectives Leads to value addition Project / Not Construction of House (for its owner) Yes (non-repetitive, a home can be build only once) Yes (Buying of Plot) Yes (White- wash and Floorin g) Yes (To create a place of residence) Yes (benefit of shelter) Project Preparation of Maggi Yes (a single packet can be made only once Yes (Starting to boil the water) Yes (Servin g it) Yes (To satisfy hunger) Yes (hunger satisfied) Project Every project can be sub-divided into smaller parts for various reasons Specialization Planning and Management Economies of Scale 2. Activity (or a task or a job) any portion of the project which consumes time or resources, and has a definable beginning and end Example- Preparation of Maggi can be divided into many smaller steps/portions i. Boil water ii. Break the noodle cakes and put them in boiling water iii. Add tastemaker, once the noodles are soft iv. Mix well and wait for it to evenly dissolve v. Serve hot
Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com Each step has well definable beginning and end, and No Activity can start until all previous activities in the same chain a re complete i.e. activity (ii) cannot start before activity (i) is complete. Types of Activities- Predecessor Activities the activities which immediately come before another activity without any intervening activities Successor Activities activities which follow another activity without any intervening activities Activities Predecessor Activities (immediately before) Successor Activities (immediately after) Boil water - Break the noodle cakes and put them in boiling water Break the noodle cakes and put them in boiling water Boil water Add tastemaker, once the noodles are soft Add tastemaker, once the noodles are soft Break the noodle cakes and put them in boiling water Mix well and wait for it to evenly dissolve Mix well and wait for it to evenly dissolve Add tastemaker, once the noodles are soft Serve hot Serve hot Mix well and wait for it to evenly dissolve - 3. Event- the starting and finishing point of an activity or a group of activities Types of Events- Head Event marks the beginning of the activity Tail Event marks the end of the activity Merge Event an event which represents the joint completion of more than one activity Burst Event- an event which represents the joint starting of more than one activity 4. Dummy Activities- A hypothetical activity which requires zero effort and zero resources for completion 5. Network it is a graphical representation of a project, depicting the flow as well as the sequence of well defined activities and events.
Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com 6. Network Path- it consists of a set of activities that connects the networking beginning event to the network terminal event 7. Critical Path the longest path through the network is called critical path, it determines the minimum duration in which the said project can be finished. Problems to be discussed in class- 1. Draw the network form the following and find the critical path (and project duration) Activity Duration (days) 1-2 2 1-3 4 1-4 3 2-5 1 3-5 6 4-6 5 5-6 7 2. Draw the network form the following and find the critical path (and project duration) Activity Duration (days) Activity Duration (days) 1-2 5 5-9 3 1-3 8 6-10 5 2-4 6 7-10 4 2-5 4 8-11 9 2-6 4 9-12 2 3-7 5 10-12 4 3-8 3 11-13 1 4-9 1 12-13 1 3. Draw the network form the following and find the critical path (and project duration) Activity Immediate Predecessor Duration (Days) A - 10 B - 9 C A 9 D A 8 E B 7 F B 11 G D,E 5

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Applied operatons research cpm1

  • 1. Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com Applied Operations Research MB301 Handout-1 Critical Path Method-1 Definitions- 1. Project A project is a temporary endeavor with a defined beginning and end (usually time constrained, and often constrained by funding or deliverables), undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value. Checklist (project definition checklist) Endeavor Temporary Endeavor Defined Beginning Define d End Undertake n to meet unique goals and objectives Leads to value addition Project / Not Construction of House (for its owner) Yes (non-repetitive, a home can be build only once) Yes (Buying of Plot) Yes (White- wash and Floorin g) Yes (To create a place of residence) Yes (benefit of shelter) Project Preparation of Maggi Yes (a single packet can be made only once Yes (Starting to boil the water) Yes (Servin g it) Yes (To satisfy hunger) Yes (hunger satisfied) Project Every project can be sub-divided into smaller parts for various reasons Specialization Planning and Management Economies of Scale 2. Activity (or a task or a job) any portion of the project which consumes time or resources, and has a definable beginning and end Example- Preparation of Maggi can be divided into many smaller steps/portions i. Boil water ii. Break the noodle cakes and put them in boiling water iii. Add tastemaker, once the noodles are soft iv. Mix well and wait for it to evenly dissolve v. Serve hot
  • 2. Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com Each step has well definable beginning and end, and No Activity can start until all previous activities in the same chain a re complete i.e. activity (ii) cannot start before activity (i) is complete. Types of Activities- Predecessor Activities the activities which immediately come before another activity without any intervening activities Successor Activities activities which follow another activity without any intervening activities Activities Predecessor Activities (immediately before) Successor Activities (immediately after) Boil water - Break the noodle cakes and put them in boiling water Break the noodle cakes and put them in boiling water Boil water Add tastemaker, once the noodles are soft Add tastemaker, once the noodles are soft Break the noodle cakes and put them in boiling water Mix well and wait for it to evenly dissolve Mix well and wait for it to evenly dissolve Add tastemaker, once the noodles are soft Serve hot Serve hot Mix well and wait for it to evenly dissolve - 3. Event- the starting and finishing point of an activity or a group of activities Types of Events- Head Event marks the beginning of the activity Tail Event marks the end of the activity Merge Event an event which represents the joint completion of more than one activity Burst Event- an event which represents the joint starting of more than one activity 4. Dummy Activities- A hypothetical activity which requires zero effort and zero resources for completion 5. Network it is a graphical representation of a project, depicting the flow as well as the sequence of well defined activities and events.
  • 3. Hemant Sharma (Applied Operation Research-MB301) Can be reached at sharma.hemant@ymail.com 6. Network Path- it consists of a set of activities that connects the networking beginning event to the network terminal event 7. Critical Path the longest path through the network is called critical path, it determines the minimum duration in which the said project can be finished. Problems to be discussed in class- 1. Draw the network form the following and find the critical path (and project duration) Activity Duration (days) 1-2 2 1-3 4 1-4 3 2-5 1 3-5 6 4-6 5 5-6 7 2. Draw the network form the following and find the critical path (and project duration) Activity Duration (days) Activity Duration (days) 1-2 5 5-9 3 1-3 8 6-10 5 2-4 6 7-10 4 2-5 4 8-11 9 2-6 4 9-12 2 3-7 5 10-12 4 3-8 3 11-13 1 4-9 1 12-13 1 3. Draw the network form the following and find the critical path (and project duration) Activity Immediate Predecessor Duration (Days) A - 10 B - 9 C A 9 D A 8 E B 7 F B 11 G D,E 5