Driving Path Drag overcomes project crashing challenges associated with manual assessments else linear programming.

It is not unusual for project managers to be instructed to shorten the project’s duration. This requires, the normal times of critical path activities to be reduced, which requires cost/time trade-offs consideration.

# Project Crashing: Manual Process

Since the normal time and cost estimate of each activity is known, the crash time estimate considers what the shortest time the activity could achieve if all effort (*at a reasonable cost*) were made to reduce the activity time, i.e. overtime, more workers, better equipment, etc. Naturally, this results in higher activity costs.

While critical activities can be reduced up to their crash limit, it does not guarantee the project duration will also be reduced by the same amount, since any new reduction may lead to a new critical path. To check whether a new critical path may occur, it is necessary to check whether a positive free float of any non-critical activity becomes zero.

By reducing the duration of the critical activity by one-time unit, compute the new free floats of the non-critical activities; check which ones have reduced their old positive free float by one unit and of these, the one with the smallest old positive free float gives the positive free float limit. That is, for a critical activity,

Reduction limit = min {crash limit, positive free float limit}

Continue to proceed in this fashion until all critical activities in the latest critical path are at their crash limits.

This approach is impractical for complex schedules due to the likelihood of human error. Instead, linear programming, which is a mathematical model whose requirements are represented by linear relationships finds an optimal solution to achieve the best outcome, i.e. minimum duration for least amount of cost.

# Project Crashing: Linear Programming

The time/cost trade-off scheduling problem (Elmaghraby 1977) is formulated as,

The variable *ti* denotes the realisation time of event (node) *i* and the variable *yij* denotes the duration of activity (i,j). The parameter *cij* represents the marginal cost of crashing activity i with one-time unit. The parameters *cdij* and *ndij* denote the crash and normal duration of activity (i,j). The set *E* refers to the set of project activities, while *delta n* represents the project deadline.

Naturally, while this approach eliminates human error associated with the manual process, it is none the less time consuming to set up the model. Fortunately, **pm***insight* has a tool that eliminates the above challenges.

# Driving Path Drag

Critical Path Drag was introduced in 1999 and represents the amount of time that each task contributes to the project’s Critical Path. That is, it asks, “How much could the Critical Path by compressed by eliminating this task?” By providing a visual display, project organisations and professionals can evaluate and prioritise potential schedule accelerations or recovery.

For the example above, activities a, b, c, d and e are on the critical path ie they have zero float. Activity e has a driving path drag of 15 meaning the critical path can be reduced by this amount, while activity c has a driving path drag of 3 before it starts to compete with activity i as they have then will have the same critical path. Based on this current assessment, activities f, g, h and I have zero driving path drag, which is to be expected since they each have positive float.

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# Learn More

If you would like to know more about leveraging data-driven actionable insights for your project schedule, then feel free to contact me on itierney@pminsight.com.au

**About Ian:** I have more than 20-years IT Project Portfolio experience spanning vendor, solutions integrator and customer side both for private and government organisations. I have worked for Motorola, Ericsson, Vodafone, Dimension Data and Fujitsu amongst others. I am the principal of **pm***insight*, a boutique consultancy specialising in empowering project organisations and professionals with project data-driven insights.