Cost Time Trade offs and Project Crashing BA 341 Lean Operations Dr Bogdan Bichescu 1 Introduction Recall the project objectives Performance scope Cost Time Project manager often forced to make trade offs between project objectives e g A delayed project must be expedited in order to be completed by deadline Resource constraints lead to changes in Time Cost Trade offs We will focus next on time cost models where the goal is to find either the most cost effective approach to reducing the duration of a project or the project duration corresponding to minimum cost Is there a link between activity duration and activity cost Direct costs e g overtime costs hiring costs leasing buying resource costs etc Indirect costs e g overhead various fixed Reducing Project Duration Usually done by adding manpower and or resources to the project or working overtime Note that doubling manpower does not reduce activity durations in half e g Brook s Law IBM Adding manpower to a late software project makes it even later Fast tracking Rearrange the logic of project activities such that some critical ones can be done in parallel rather than sequentially Some Time Cost Models Goal finding the most cost effective approach to reduce project duration by x days Steps 1 Determine the project inputs List of project activities and activity sequence Activity durations and costs Normal Cost NC the lowest expected activity cost Normal Time NT duration associated with NC Crash Time CT the shortest possible activity time Crash Cost CC the cost associated with CT Some Time Cost Models Steps 2 Find the cost per period slope to expedite each activity crash cost normal cost CC NC slope normal time crash time NT CT Some Time Cost Models Steps 3 Identify the critical path using normal activity times 4 Start crashing reducing the activities on the critical path one activity at a time one period e g day at a time in increasing order of their slopes the lower the slope the cheaper the crashing 5 Reevaluate the critical path after each one period crash if new duration is satisfactory stop otherwise go back to step 4 Consider the following example Project precedence table and crashing info Want to shorten project by 2 days Activity Predecessor Days NT CT Cost NC CC Slope Day A 3 2 40 80 40 B A 2 1 20 80 60 C A 2 2 20 20 D A 4 1 30 120 30 E B 3 2 10 45 35 Finding the Critical Path Using Normal Times 3 5 Earliest Start Time ES C 2 0 0 Start 0 0 0 0 3 A 3 0 3 6 8 3 5 B 2 3 3 5 7 5 8 8 E 3 5 End 0 8 8 Slack LS ES LF EF 8 8 Latest Start Time LS D 4 4 8 Activity Name Duration Finding the Critical Path A B E 3 5 Earliest Start Time ES C 2 0 0 Start 0 0 0 0 3 A 3 0 3 6 8 3 5 B 2 3 3 5 7 5 8 8 E 3 5 End 0 8 8 Slack LS ES LF EF 8 8 Latest Start Time LS D 4 4 8 Activity Name Duration Shortening the Project 1 day Identify the critical activity that is cheapest to crash A slope 40 day Activity E has the lowest B slope 60 day slope let s crash E 1 day a cost of 35 E slope 35 day Project duration is now 7 days but is critical path the same Reevaluate the Critical Path 3 5 Earliest Start Time ES Earliest Finish Time EF C 2 0 0 Start 0 0 0 0 3 A 3 0 3 5 7 3 5 B 2 3 3 5 7 5 7 7 E 2 5 End 0 7 7 Slack LS ES LF EF 7 7 Latest Start Time LS D 4 3 7 Activity Name Duration Shortening the Project by an Additional Day Identify the critical activities that are cheapest to crash Now choose between A slope 40 day A 40 and B slope 60 day B D 90 E cannot be crashed further D slope 30 day The cheapest alternative to further reduce project duration by 1 day is to crash A 1 day a cost of 40 In summary The most cost effective alternative to reduce the project duration by 2 days is Crash E 1 day 35 Crash A 1 day 40 Final Cost 75 Can the project duration be further reduced Yes minimum project duration is 5 days Crash B D 1 day each at a cost of 60 30 90 Critical Path for Crashed Schedule 2 4 Earliest Start Time ES C 2 0 0 Start 0 0 0 0 2 A 2 0 2 4 6 2 4 B 2 2 2 4 6 4 6 6 E 2 4 End 0 6 6 Slack LS ES LF EF 6 6 Latest Start Time LS Latest Finish Time LF D 4 2 6 Activity Name Duration Minimum Cost of Crashing Project to Minimum Duration Step 1 Replace all activity normal durations with their crashed 2 4 durations C 2 0 0 Start 0 0 0 0 2 A 2 0 2 3 5 2 3 B 1 2 3 2 3 D 1 4 5 3 5 E 2 3 5 5 5 End 0 5 5 Minimum Cost of Crashing Project to Minimum Duration Step 2 Identify the critical path 2 4 C 2 0 0 Start 0 0 0 0 2 A 2 0 2 3 5 2 3 B 1 2 3 2 3 D 1 4 5 3 5 E 2 3 5 5 5 End 0 5 5 Minimum Cost of Crashing Project to Minimum Duration Step 3 Relax non critical activities in decreasing order of their slopes 2 4 i e what is the point of fully crashing non critical activities C 2 0 0 Start 0 0 0 0 2 A 2 0 2 3 5 2 3 B 1 2 3 2 3 D 3 4 5 3 5 E 2 3 5 5 5 End 0 5 5 Minimum Cost of Crashing Project to Minimum Duration Finally the minimum cost is the sum of the Cost of crashing the critical activities down to their minimum durations Cost of crashing activity D 1 day from 4 to 3 days 40 A 60 B 35 E 135 30 135 30 165