Solving Project Crash Cost Optimization Problems: Step-by-step Calculations

What Is Project Crash Cost Optimization?

Project crashing is the name given to schedule compression techniques that are used to shorten the duration of a project without changing the scope. This powerful project management methodology involves taking special costly measures to reduce the duration of an activity below its normal value by strategically allocating additional resources to critical activities.

The fundamental goal of crash cost optimization is to find the most economical way to compress project timelines while minimizing the additional expenses incurred. In 1957 the Critical Path Method (CPM) was developed as a network model for project management. Since then, it has become an essential tool for analyzing time-cost trade-offs in project scheduling.

Crashing of the project means to reduce the project completion time by adding extra resources to it. The project can be crashed by reducing the normal completion time of critical activities which is called crashing of activities. This technique is particularly valuable when projects face tight deadlines, potential penalties for late delivery, or opportunities for early completion bonuses.

Understanding the relationship between time and cost is crucial for effective project management. There is a relationship between a project’s time to completion and its cost. For some types of costs, the relationship is in direct proportion; for other types, there is a direct trade-off. Because of these two types of costs, there is an optimal project pace for minimal cost.

Understanding Direct and Indirect Costs in Project Crashing

Before diving into crash cost calculations, it’s essential to understand the two primary cost categories that influence project economics.

Direct Costs

Direct costs are those directly associated with project activities, such as salaries, travel, and direct project materials and equipment. If the pace of activities is increased in order to decrease project completion time, the direct costs generally increase since more resources must be allocated to accelerate the pace.

Examples of direct costs include:

• Labor wages and overtime pay
• Materials and equipment
• Subcontractor fees
• Specialized tools or machinery rentals
• Expedited shipping charges

Indirect Costs

Indirect costs are those overhead costs that are not directly associated with specific project activities such as office space, administrative staff, and taxes. Unlike direct costs, indirect costs typically decrease as project duration shortens because these overhead expenses accumulate over time.

Common indirect costs include:

• Administrative overhead
• Facility rental or lease payments
• Utilities and insurance
• Supervision and management salaries
• Interest on project financing

Direct costs generally increase as activity times decrease, while indirect costs decrease as the overall project duration decreases. The optimal project duration is the point of minimum total cost, found by balancing increased direct costs from crashing activities against decreased indirect costs from a shorter schedule.

Key Terminology and Concepts

To effectively solve crash cost optimization problems, you must understand several fundamental concepts and terms.

Normal Time and Normal Cost

Normal duration is the maximum duration of the activity. Normal cost is the cost associated with the normal duration. The normal duration is equal to the minimal expected duration when the activity is performed with the lowest possible amount of resources, leading to the lowest total activity cost (normal cost).

Crash Time and Crash Cost

Crash duration is the minimum duration of the activity. Crash cost is the cost associated with the crash duration. The crash duration is the shortest activity duration, when the maximum amount of resources has been assigned to the activity, leading to the highest activity cost (crash cost).

Cost Slope (Crash Cost per Unit Time)

The Cost Slope formula is defined as the ratio of an increase in cost to a decrease in time. This metric is crucial for determining which activities should be crashed first to achieve the most cost-effective schedule compression.

The formula for calculating cost slope is:

Cost Slope = (Crash Cost – Normal Cost) / (Normal Time – Crash Time)

The activities having the lowest cost per unit of time reduction should be shortened first. This principle forms the foundation of the crash cost optimization methodology.

Critical Path

The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. The critical path determines the total calendar time required for the project. Crashing only works for critical path activities where it is possible to shorten schedules.

If activities outside the critical path speed up or slow down (within limits), the total project time does not change. This is why identifying the critical path is essential before attempting any crashing activities.

Step-by-Step Process for Solving Crash Cost Optimization Problems

Now let’s walk through a comprehensive, systematic approach to solving project crash cost optimization problems.

Step 1: Gather Complete Activity Data

Begin by collecting all necessary information for each project activity. You’ll need the following data points:

• Activity identification: Unique identifier or name for each activity
• Predecessor activities: Which activities must be completed before this one can start
• Normal duration: The standard time required to complete the activity
• Normal cost: The cost associated with completing the activity in normal time
• Crash duration: The minimum possible time to complete the activity
• Crash cost: The cost associated with completing the activity in crash time
• Maximum crash time: The difference between normal and crash duration (how much the activity can be reduced)

Organize this information in a table format for easy reference throughout the optimization process. Additionally, identify any indirect costs associated with the project, typically expressed as a cost per time unit (e.g., $500 per day).

Step 2: Construct the Project Network Diagram

Create a visual representation of your project using a network diagram. This diagram shows the sequence and dependencies of all project activities. You can use either Activity-on-Node (AON) or Activity-on-Arrow (AOA) notation, though AON is more commonly used in modern project management.

The network diagram helps you visualize the flow of activities and makes it easier to identify potential critical paths.

Step 3: Identify the Critical Path and Calculate Normal Project Duration

Find the critical path, normal project completion time using the normal execution time for each activity. Also find the normal total cost as per the given data.

To identify the critical path:

1. Calculate the earliest start (ES) and earliest finish (EF) times for each activity using a forward pass through the network
2. Calculate the latest start (LS) and latest finish (LF) times for each activity using a backward pass through the network
3. Determine the slack (or float) for each activity: Slack = LS – ES or LF – EF
4. Identify activities with zero slack—these form the critical path

The normal project duration equals the sum of activity durations along the critical path. Calculate the normal total project cost by summing all normal activity costs plus any indirect costs for the normal duration.

Step 4: Calculate Cost Slope for All Activities

For each activity in your project, calculate the cost slope using the formula:

Cost Slope = (Crash Cost – Normal Cost) / (Normal Time – Crash Time)

This calculation tells you how much it costs to reduce each activity by one time unit. Find the crash cost slope for each critical activity and select the activity of least crash cost slope to crash it first.

Create a table ranking all critical path activities by their cost slope, from lowest to highest. Activities with lower cost slopes are more economical to crash.

Step 5: Select Activities to Crash

Crashing analyzes and categorizes activities based on the lowest crash cost per unit time. Crashing only works for critical path activities where it is possible to shorten schedules.

Follow these guidelines when selecting activities to crash:

• Focus on critical path activities: Only crash activities on the critical path, as reducing non-critical activities won’t shorten the overall project duration
• Choose the lowest cost slope: Start with the critical activity that has the lowest cost slope
• Consider crash limits: Don’t exceed the maximum amount each activity can be crashed
• Watch for multiple critical paths: When crashing creates new critical paths, you may need to crash activities on multiple paths simultaneously

If two or more critical activities found have the lowest but equal costs then select the activity as: (i) Where another path in network may become critical by reducing its total time.

Step 6: Crash Selected Activities Incrementally

Crash activities one time unit at a time (or in small increments), recalculating the critical path after each iteration. This iterative approach is important because:

• The critical path may change as you crash activities
• New critical paths may emerge
• You can stop when you reach your target duration or when further crashing becomes uneconomical

After crashing the critical activities according to rule II, check whether there are new critical path(s) or not. If there are, identify all critical activities and crash them according to rule II.

Step 7: Calculate Total Project Cost for Each Duration

After each crashing iteration, calculate the total project cost:

Total Project Cost = Sum of All Activity Costs + (Project Duration × Indirect Cost per Time Unit)

Remember that as you crash activities:

• Direct costs increase (due to crashing costs)
• Indirect costs decrease (due to shorter project duration)
• Total cost may initially decrease, reach an optimal minimum, then increase again

Step 8: Determine the Optimal Project Duration

After crashing all critical activities up-to their lowest possible time, stop the procedure and determine total project cost for all durations like normal duration and crashed durations. Select the project duration as optimum for which total cost is observed minimum.

The optimal project duration is the point where total project cost is minimized. This represents the best balance between direct crashing costs and indirect overhead costs.

Crashing of an activity is economical only if its crashing cost slope is less than the indirect cost per unit time. So only those activities having less crash cost slope should be crashed.

Detailed Worked Example: Construction Project Crashing

Let’s work through a comprehensive example to illustrate the crash cost optimization process in action.

Project Overview

A construction company has been contracted to complete a building project. The project has the following characteristics:

• Normal project duration: 50 weeks
• Desired completion time: 44 weeks
• Indirect costs: $2,000 per week
• Contract includes a penalty of $5,000 per week for late completion
• Bonus of $3,000 per week for early completion (up to 6 weeks early)

Activity Data Table

Here’s the activity information for our project:

Activity	Predecessors	Normal Time (weeks)	Normal Cost ($)	Crash Time (weeks)	Crash Cost ($)	Max Crash (weeks)
A	–	8	10,000	6	14,000	2
B	–	12	18,000	9	24,000	3
C	A	10	15,000	8	19,000	2
D	A	14	21,000	11	27,000	3
E	B, C	9	12,000	7	16,000	2
F	D	11	16,500	9	20,500	2
G	E, F	7	10,500	6	12,500	1

Step-by-Step Solution

Step 1: Calculate Cost Slopes

For each activity, we calculate the cost slope:

• Activity A: (14,000 – 10,000) / (8 – 6) = $2,000 per week
• Activity B: (24,000 – 18,000) / (12 – 9) = $2,000 per week
• Activity C: (19,000 – 15,000) / (10 – 8) = $2,000 per week
• Activity D: (27,000 – 21,000) / (14 – 11) = $2,000 per week
• Activity E: (16,000 – 12,000) / (9 – 7) = $2,000 per week
• Activity F: (20,500 – 16,500) / (11 – 9) = $2,000 per week
• Activity G: (12,500 – 10,500) / (7 – 6) = $2,000 per week

In this example, all activities have the same cost slope, which simplifies our decision-making process.

Step 2: Identify the Critical Path

After constructing the network diagram and performing forward and backward passes, we identify the critical path:

Critical Path: A → D → F → G

Normal project duration: 8 + 14 + 11 + 7 = 40 weeks

Wait—our initial assumption was 50 weeks, but the actual critical path gives us 40 weeks. Let’s recalculate with the correct duration.

Normal total direct cost: $10,000 + $18,000 + $15,000 + $21,000 + $12,000 + $16,500 + $10,500 = $103,000

Normal indirect cost: 40 weeks × $2,000/week = $80,000

Normal total project cost: $103,000 + $80,000 = $183,000

Step 3: Crash Activities Systematically

Iteration 1: Crash Activity A by 1 week (lowest on critical path)

• New duration: 39 weeks
• Additional direct cost: $2,000
• New direct cost: $105,000
• New indirect cost: 39 × $2,000 = $78,000
• Total cost: $183,000 (no change because savings in indirect cost offset the crashing cost)

Iteration 2: Crash Activity A by 1 more week (now at crash limit)

• New duration: 38 weeks
• Additional direct cost: $2,000
• New direct cost: $107,000
• New indirect cost: 38 × $2,000 = $76,000
• Total cost: $183,000

Iteration 3: Crash Activity D by 1 week

• New duration: 37 weeks
• Additional direct cost: $2,000
• New direct cost: $109,000
• New indirect cost: 37 × $2,000 = $74,000
• Total cost: $183,000

Continue this process, checking for new critical paths after each iteration, until you reach the desired duration or until the total cost begins to increase.

Analysis and Interpretation

In this example, because the cost slope ($2,000 per week) equals the indirect cost savings ($2,000 per week), the total project cost remains constant as we crash activities. In real-world scenarios, you’ll typically see the total cost decrease initially, reach an optimal minimum point, and then increase as you continue crashing.

The optimal project duration is the point where total cost is minimized. Project managers should also consider other factors such as early completion bonuses, late penalties, and resource availability when making final decisions.

Advanced Considerations in Crash Cost Optimization

Handling Multiple Critical Paths

Once there is more than one critical path the situation becomes more complicated. When multiple critical paths exist, you must crash activities on all critical paths simultaneously to reduce the overall project duration.

When this occurs:

• Identify all critical paths in the network
• Calculate the combined cost slope for crashing one activity on each critical path
• Select the combination with the lowest total cost slope
• Crash all selected activities by the same amount

Choosing to crash the critical activity with the lowest incremental cost is guaranteed to be an optimal approach (i.e. we crash in the best possible way) provided we have only a single critical path. However once we encounter two or more critical paths we cannot guarantee that we can still crash the project in an optimal way.

Using Linear Programming for Complex Projects

For large, complex projects with many activities, the package calculates the optimal (minimum cost) way to crash the project using linear programming. The advantage of using linear programming to crash a project is that we can automatically guarantee that, for any particular project completion time, we have achieved that time by crashing in a minimum cost fashion.

This article outlines such a strategy, one that uses a linear programming model adaptable for use on most computers with a linear programming package. In doing so, it describes the strategy’s variables and defines its formulas for calculating crashing both costs and network prerequisites.

Linear programming is particularly useful when:

• The project has hundreds or thousands of activities
• Multiple critical paths exist
• You need to guarantee optimal solutions
• Resource constraints are complex

Considering Resource Constraints

It has been expanded to allow for the inclusion of resources related to each activity, through processes called activity-based resource assignments and resource optimization techniques such as Resource Leveling and Resource smoothing. A resource-leveled schedule may include delays due to resource bottlenecks (i.e., unavailability of a resource at the required time), and may cause a previously shorter path to become the longest or most “resource critical” path.

When resources are limited, you may not be able to crash certain activities even if it would be economically beneficial. Always verify that:

• Additional resources are actually available
• Resources can be reallocated from non-critical activities
• The quality of work won’t suffer from resource overallocation
• Team members won’t experience burnout from increased workload

Accounting for Uncertainty with PERT

CPM is a deterministic method that uses a fixed time estimate for each activity. While CPM is easy to understand and use, it does not consider the time variations that can have a great impact on the completion time of a complex project.

For projects with significant uncertainty, consider using PERT (Program Evaluation and Review Technique) in conjunction with CPM. PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average: Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6

Common Mistakes to Avoid

When solving crash cost optimization problems, be aware of these common pitfalls:

Crashing Non-Critical Activities

One of the most frequent errors is attempting to crash activities that are not on the critical path. Not all tasks in a project can be crashed. Only those tasks that are on the critical path and capable of being accelerated can be crashed. Crashing non-critical activities wastes resources without reducing project duration.

Ignoring the Critical Path Changes

You’ll notice how crashing an activity will change the project’s critical path. After each crash, confirm which activities remain on the critical path before further crashing the project. Failing to recalculate the critical path after each iteration can lead to suboptimal decisions and wasted resources.

Exceeding Crash Limits

Every activity has a maximum amount it can be crashed. The activity duration cannot be less than the crash duration. Attempting to crash beyond these limits is impossible and indicates a calculation error or unrealistic expectations.

Overlooking Indirect Cost Savings

Some practitioners focus solely on the increased direct costs of crashing without properly accounting for the reduced indirect costs from shorter project duration. Always calculate total project cost (direct + indirect) to make informed decisions.

Assuming Linear Cost Relationships

Crash duration is typically modeled as a linear relationship between cost and activity duration, but in many cases, a convex function or a step function is more applicable. In real projects, the cost-time relationship may not always be perfectly linear, so use judgment when applying these formulas.

Practical Applications and When to Use Crashing

Project crashing is not appropriate for every situation. Understanding when to apply this technique is crucial for project success.

Ideal Scenarios for Project Crashing

Consider crashing your project when:

• Facing contractual deadlines: When missing a deadline would result in penalties or contract violations
• Pursuing early completion bonuses: When financial incentives exist for finishing ahead of schedule
• Responding to market pressures: When competitive advantage depends on early product launch
• Recovering from delays: When unexpected setbacks have put the project behind schedule
• Freeing resources for other projects: When other high-priority projects need the same resources
• Avoiding adverse conditions: When seasonal factors (weather, holidays, etc.) could impact later work

Finish the project in a predefined deadline date. Recover early delays. Avoid liquidated damages. Free key resources early for other projects. Receive an early completion-bonus.

When NOT to Crash a Project

Avoid crashing when:

• The project is already on schedule or ahead
• Budget constraints make additional costs prohibitive
• Quality would be significantly compromised
• Resources are not available or cannot be reallocated
• Team burnout is already a concern
• Activities have inherent time constraints that cannot be overcome

Not all projects can be efficiently crashed. Some projects have tasks with inherent time constraints or dependencies that cannot be expedited. In such cases, Crashing may not be a feasible option.

Benefits and Risks of Project Crashing

Key Benefits

Project crashing serves the purpose of effective time management. The primary advantages include:

• Reduced project duration: Meet tight deadlines and accelerate time-to-market
• Penalty avoidance: Prevent costly late-delivery penalties
• Bonus opportunities: Capture early completion incentives
• Competitive advantage: Launch products or services before competitors
• Resource optimization: Free up resources for other strategic initiatives
• Risk mitigation: Reduce exposure to time-related risks
• Stakeholder satisfaction: Demonstrate responsiveness to changing requirements

Significant Risks and Limitations

As powerful a tool as ‘crashing’ may be in project management, it’s important to recognize the inherent risks and limitations that come with it. Irrespective of context, making a decision to crash a project calls for a careful risk-benefit analysis. For instance, crashing can lead to a significant increase in project costs, as resources are allocated at an increased rate to fast-track tasks. There are also chances of quality being compromised, as the emphasis on speed may take away focus from crucial details.

Major risks include:

• Increased costs: The primary disadvantage of project crashing is increased costs. Your project was conceived to fit into a budget. Project crashing will take you over your project budget, and, for some people, that’ll mean the project failed.
• Quality concerns: Rushing work can lead to errors, rework, and reduced deliverable quality
• Team burnout: In some cases, crashing may lead to over-exhaustion of resources and result in team burnout.
• Diminishing returns: Extra manpower or resources may not necessarily shorten your project timeline due to the principle of diminishing returns.
• Relationship strain: It can jeopardize the relationship between team members and the project manager. If you want to apply this method, you need a high level of flexibility among all the involved parties of a project.
• Limited applicability: Crashing may not be suitable for all projects. Some projects have inherent limitations, such as dependencies on external factors or constraints that cannot be easily overcome by adding resources or increasing work intensity.

Alternative Schedule Compression Techniques

While crashing is a powerful technique, it’s not the only method for compressing project schedules. Understanding alternatives helps you choose the most appropriate strategy for your situation.

Fast-Tracking

In those situations, you can use two schedule compression techniques: fast tracking and crashing. Fast-tracking: Examine the critical path to identify activities that can be performed simultaneously. Running parallel processes will reduce overall execution time. Crashing: This process involves allocating more resources to speed up activities.

Project crashing is often mixed up with fast-tracking, but important differences exist. Where crashing is about adding resources to maintain schedule, fast-tracking is about using your existing resources. But you’d split or reschedule critical tasks so they could run simultaneously instead of sequentially.

Fast-tracking advantages:

• No additional resource costs
• Can be implemented quickly
• Utilizes existing team capabilities

Fast-tracking disadvantages:

• Increases project risk due to overlapping activities
• May require rework if dependencies are violated
• Can spread resources too thin

Combining Crashing and Fast-Tracking

There’s a third way. You could use both techniques together. In other words, you can bring in additional resources to avoid breaking up an existing team, and use crashing there. And you could also reschedule critical tasks to run in parallel and allocate some activities to the extra resources you’ve added to the project.

This hybrid approach can maximize schedule compression while balancing costs and risks, though it requires careful coordination and monitoring.

Software Tools for Crash Cost Analysis

Modern project management software can significantly simplify crash cost optimization calculations. Currently, there are several software solutions available in industry which use the CPM method of scheduling.

Popular tools include:

• Microsoft Project: Offers built-in CPM calculations and resource leveling
• Primavera P6: Industry-standard for large, complex projects with advanced crashing features
• Smartsheet: Cloud-based solution with critical path templates and collaboration features
• ProjectManager: Provides automated critical path calculations and Gantt chart visualization
• Specialized calculators: Online tools specifically designed for PERT/CPM and crashing calculations

These tools can automatically:

• Calculate critical paths
• Compute cost slopes
• Identify optimal crashing sequences
• Generate time-cost trade-off curves
• Update calculations as project conditions change

Best Practices for Implementing Project Crashing

To maximize the effectiveness of crash cost optimization while minimizing risks, follow these proven best practices:

1. Conduct Thorough Planning

Developing a comprehensive plan before deciding to crash a project is crucial. This includes effectively communicating with your team about the changes, ensuring there are no ambiguities.

• Document all assumptions and constraints
• Verify resource availability before committing
• Create contingency plans for potential issues
• Establish clear success criteria

2. Maintain Quality Standards

While the focus is on speeding up, quality should not be ignored. Implement quality control measures throughout the crashed schedule:

• Build in quality checkpoints
• Allocate time for reviews and testing
• Don’t compromise on critical quality standards
• Monitor deliverable quality metrics closely

3. Communicate with Stakeholders

Keep all stakeholders informed about crashing decisions and their implications:

• Explain the rationale for crashing
• Present cost-benefit analysis clearly
• Set realistic expectations about outcomes
• Obtain approval before implementing changes
• Provide regular progress updates

4. Monitor and Adjust Continuously

Continuous monitoring is essential. Track the progress of the crashed tasks and ensure that they are on schedule. Effective Project Management Software can be invaluable for real-time tracking and reporting. Be prepared to make adjustments as needed. If a task is not responding well to additional resources, consider reallocating those resources to other critical tasks.

5. Consider Team Welfare

Protect your team from burnout and maintain morale:

• Distribute workload fairly
• Provide adequate breaks and recovery time
• Recognize and reward extra effort
• Watch for signs of stress or fatigue
• Plan for post-project recovery periods

6. Document Lessons Learned

After completing a crashed project, capture insights for future reference:

• What worked well and what didn’t
• Actual costs versus estimates
• Impact on quality and team morale
• Recommendations for future crashing decisions
• Updated cost slope data for similar activities

Real-World Industry Applications

Project crashing techniques are applied across numerous industries with varying objectives and constraints.

Construction Industry

Construction projects frequently use crashing to:

• Meet contractual completion dates
• Avoid weather-related delays
• Minimize disruption to building occupants
• Capture seasonal market opportunities

Common crashing methods include adding work shifts, increasing crew sizes, using prefabricated components, and deploying additional equipment.

Software Development

Technology companies crash projects to:

• Beat competitors to market
• Meet product launch windows
• Address critical security vulnerabilities
• Capitalize on market opportunities

Crashing strategies include adding developers, implementing parallel development tracks, using automated testing tools, and leveraging cloud infrastructure for faster deployment.

Manufacturing

Manufacturing projects crash to:

• Meet customer delivery commitments
• Respond to urgent orders
• Minimize production downtime
• Launch new products on schedule

Techniques include overtime shifts, expedited material procurement, additional production lines, and outsourcing to subcontractors.

Event Planning

Event projects crash when:

• Venue availability changes
• VIP schedules shift
• Competing events emerge
• Sponsor requirements change

Crashing approaches include hiring additional staff, using premium vendors, expediting permits and approvals, and increasing marketing spend.

Conclusion

Project crash cost optimization is a sophisticated yet practical technique that enables project managers to make informed decisions about schedule compression. By systematically analyzing the relationship between time and cost, identifying critical paths, calculating cost slopes, and strategically selecting activities to crash, you can achieve optimal project outcomes even under tight deadline constraints.

The concept of Crashing in Project Management serves as a vital tool for Project Managers aiming to expedite project schedules and meet critical deadlines. It empowers project teams to optimise resources, control costs, and mitigate risks. However, the decision to crash a project should be approached with careful consideration, as it comes with both advantages, such as time savings and enhanced client satisfaction, and disadvantages, including increased costs and potential quality compromises.

Success with crash cost optimization requires:

• Thorough understanding of critical path methodology
• Accurate data collection and cost estimation
• Systematic analysis and calculation
• Careful consideration of risks and trade-offs
• Effective communication with stakeholders
• Continuous monitoring and adjustment
• Balance between speed, cost, and quality

Whether you’re managing construction projects, software development initiatives, manufacturing operations, or any other type of project, mastering crash cost optimization techniques will enhance your ability to deliver results on time and within budget. By following the step-by-step approach outlined in this guide and applying best practices, you’ll be well-equipped to tackle even the most challenging schedule compression scenarios.

Remember that crashing is just one tool in the project manager’s toolkit. Use it judiciously, always considering the broader project context, organizational objectives, and long-term implications of your decisions. With practice and experience, you’ll develop the judgment needed to determine when crashing is appropriate and how to implement it most effectively.

Additional Resources

To deepen your understanding of project crash cost optimization and related topics, consider exploring these valuable resources:

• Project Management Institute (PMI) – Professional organization offering certifications, standards, and resources for project managers
• Smartsheet – Provides templates and tools for critical path analysis and project crashing
• Asana’s Guide to Critical Path Method – Comprehensive overview of CPM concepts and applications
• ProjectManager.com – Software and educational resources for project management professionals
• NetMBA Time-Cost Trade-offs – Academic perspective on project time-cost relationships

By combining theoretical knowledge with practical application, you’ll master the art and science of project crash cost optimization, enabling you to deliver successful projects even under the most demanding circumstances.