Chapter 7: Cost of Time

Definition and Components of Cost of Time

The timing of a project can affect both its benefits and its costs.

We owe thanks to Donald Reinertsen for the powerful concept of the Cost of Delay in lean product development. We extended this concept to that of the Cost of Time (CoT) in project management by:

1. Differentiating the delay from the postponement (or the project delay from the delayed product use).
2.  Establishing reference values for the delay and postponement.
3.  Defining various time-related cost components.

We express the Cost of Time in monetary units per unit of time, for example, $/week or $/month.

Shortening the optimal cycle time generates acceleration costs and extending it generates delay costs. A project is delayed when its execution takes more than the optimal cycle time. The theoretical optimal cycle time assumes no resource constraints and no workflow queues, while the adjusted optimal cycle time takes into account the resource constraints and the ability to manage queues. Work in Progress, batch sizes and capacity utilization affect the flow of work and they are delay factors. And in all cases, we are talking about an expected cycle time with attached probability.

As we discussed, the cost of project delay is a combination of incremental direct and indirect costs. It cannot be generated if the project hasn’t started. But even if it hasn’t started, the project may incur other time-related costs. To understand what these costs are, we need to answer the following question: When is the best time to start and finish a project?

Let’s use a case study to calculate the answer. We will apply the Just-in-Time concept to project management.

Project Case Study

Let's say that the ideal point in time to complete a project to develop a new summer soft drink is the 15th of April in year N. This will allow us to start selling the new product from the 1st of May. If we complete the project before April 15th, we will incur costs of holding finished project deliverables of $2,200 per week. Completion of the project after April 15 will cause loss of sales.

When is the best time to start this project? As soon as possible, so that we have enough time to finish it on time? No, the best time depends on the optimal project cycle time. If it's 6 months, the estimated ideal point in time to start the project is October 15 in year N-1.

Let’s assume that the cost of acceleration is $7,000 per week and the cost of delay is $2,000 per week. In addition, we have to account for the cost of lost opportunity and the cost of deferred use of project deliverables.

The new drink will be on sale from May to September for 4 years (for 85 weeks).

Any delay in this project will lead to loss of sales. The sales won’t simply shift over time. Lost sales in May won’t be offset by sales in October. If that were the case, we would have had costs related to deferred sales. But in this case, the sales will be completely lost and we will incur 100% lost opportunity cost for each day of unrealized sales, that is, for each day of project delay. Our actual cost will equal the lost profits for the days of missed sales.

If our lost opportunity cost is $9,000 per week, we can do the math.

Assuming the project starts on October 15 in year N-1 and that the optimum cycle time is 6 months, the best-case scenario is to finish it on April 15th in year N with zero CoT. The CoT for a week of acceleration, that shifts completion to a date before April 15, is $9,200 ($7,000 cost of acceleration + $2,200 cost of holding) and the CoT for a week of delay is $11,000 ($2,000 cost of delay + $9,000 lost opportunity cost). 

Also, we can see that our cost of acceleration is lower than the sum of the cost of lost opportunity and the cost of delay (or the CoT for a week of delay). If the project was already delayed, saving a week of cycle time will result in $4,000 of net benefit ($11,000 - $7,000) though the investment costs will increase. 

If the optimal start date for the project was missed and the earliest possible start date is the 11th of December in year N-1, we can buy 8 weeks of cycle time for $56,000 (8 weeks x $7,000 cost of acceleration per week), but we need to check if with the increased costs the project still has an acceptable return on investment. 

We can use the costs of holding to assess the benefit of starting the project early, to reduce the likelihood of missing out on the ideal completion date. Here, we may decide that it’s better to start several weeks earlier than the optimum time and to absorb the cost of $2,200 per week for premature project delivery (Cost of Premature Delivery).

There are some special cases of the Cost of Time. For example, if we develop a prototype of a product to present at a trade show on a certain date and if we cannot use the prototype in any other way, missing the deadline will cause a 100% waste of project investment and a 100% loss of opportunity. Our loss will be the sum of the investment costs and the unrealized profit from using the product.

Other special cases are the projects that have a very high social Cost of Time. Delaying the use of a new vaccine, for example, can lead to loss of life (high deferred use cost).

Unlike the two examples above, most times we have both lost opportunity and deferred use costs. This occurs when the project delay or postponement leads to a partial loss of opportunity.

Let’s look at another project example.

Project Case Study

Suppose that each one-month delay results in a 1% reduction in the total project's life cycle profit. If the expected monthly profit is a constant $20,000 when the project is not delayed and the expected revenue-generating period is 36 months, the cost of lost opportunity will be $7,200 for each month of delay ($20,000 x 36 x 1% = $7,200). The reason may be that we have missed the opportunity to become a market leader and to gain a significant market share. Project revenue decreases as the delay increases. 

In addition, we incur costs for deferred use of project products. If revenue and profit simply shift over time, a one-month delay does not lead to a total loss of the profit for that month, but to a cost of one-month profit shifting - so, we have to account for the time value of money.

Let’s assume that the opportunity cost of our capital is 0.6 percent per month. Here, we need to apply a 0.6 percent discount rate on the shifted monthly profits to calculate the cost of deferred use. Since the entire revenue generation period is shifted by one month, we need to calculate the discounted values for each month.

However, the easiest way to perform the calculation is to take into account the shift of income from month 1 to month 37, changing nothing else. We have to estimate the present value of the profit for month 37 at the time of month 1. Based on constant monthly profit of $20,000 (for simplicity of calculation), this present value is $16,125 - please use a present value calculator to reproduce the calculation. Hence, the lost profit from shifting revenue by one month is $3,875 ($20,000 - $16,125).

Assuming that the cost of delay is $8,000 per month plus an additional cost of perishable information component that increases by $3,000 per month ($11,000 in total for month 1, $14,000 for month 2, $17,000 for month 3, etc.), we show the calculation of the cost of time in the following table:

Table 7.1: Calculation of Cost of Time

In this example, the impact of the cost of deferred use is moderate. However, when comparing the CoT for different projects, the revenue profile plays a big role. If we expect Project A to generate revenue for 24 months and Project B for 24 years, with similar investment costs and expected rate of return, the monthly profits and the costs of deferred use of the two projects will differ significantly. It’s likely that the difference in the monthly lost opportunity costs will also be significant.

Figure 7.1: Cost of Time

However, what happens when we’ve missed the best time to start the project? The opportunity window is already open and the ideal start date is "yesterday" or "six months ago". In this case, we must accept that the reference point for the lost opportunity and the deferred use is the present moment, "today". The Cost of Time for the past is a sunk cost. The methods for calculating the components of the Cost of Time remain the same.

What should we use the Cost of Time for? For at least three things:

• to evaluate the effect of the Cost of Time on project success measures
• to improve our trade-off decisions
• to prioritize projects and tasks (see Projects Sequencing/Schedule Prioritization)

The Cost of Time is a variable that affects the project’s performance. We need to know how incremental change in the Cost of Time (adding costs for a unit of time, such as one week) affects the profitability. We can do this by analyzing the sensitivity of the project, which can answer questions such as:

• How does the variation of the cycle time or the period of project implementation affect project profitability?
• What are the switching values of the delay or postponement that offset the project benefits and costs, or that reduce the return to the minimum acceptable level?

In the project example above, if a Cost of Time of $152,000 reduces the return to the minimum acceptable level, the maximum delay we can accept is five months (provided the costs don’t increase for another reason).

Failure to account for the Cost of Time can lead to waste, even more so given that the CoT is not static. For example, changing market conditions can lead to a higher CoT that makes the project unviable. To limit the waste, we would have to stop the project.

To summarize, the Cost of Time is caused by project delay (or acceleration) or postponed (or premature) execution which may induce a cost of project delay or acceleration, a cost of perishable information, a cost of regulatory and contractual penalties, a cost of lost opportunity, a cost of premature delivery and a cost of deferred use of project assets. In addition, it may be useful to consider the cost of customer dissatisfaction with late delivery. For dependent projects, we have to take into account the Cost of Time of the delayed downstream projects. 

Figure 7.2: Cost of Time Components

The Cost of Time is a cost and/or benefit deviation (relative to a project's baseline scenario) that we should consider when optimizing the project's net benefit.

Best Time to Decide: Last Responsible Moment vs. Most Responsible Moment

The moments when we make decisions or commitments induce time-related costs. If we decide before the best moment, we incur the cost of premature decision. When we miss the best moment, we incur the cost of delaying the decision.

One of the most popular rules in Lean and Lean-Agile states that decisions and commitments should be deferred until the last responsible moment. The rationale is that this way we avoid decisions based on assumptions, incomplete information, and lack of knowledge.

"Slow decisions" refers to keeping options open and taking more time to explore them. This warrants decision-making based on good understanding, as the genchi genbutsu principle requires.

The defer decisions/commitments rule lives its own life and is interpreted in different ways. It’s most often associated with the concept of the “last responsible moment”, but also with its variations, such as the “last possible moment” or “decide as late as possible”.

The true purpose of this rule is to decide at the best time. What is missing is a definition of the best time. This definition is precisely what the Last Responsible Moment seeks to provide.

There may be some justification for the second rule in this definition, but the crucial rule is the first one, which is about comparing the costs and benefits of delaying a decision. Technically, this rule guarantees the negative effect of the decision, as the cost outweighs the benefit. It would be an improvement to say that the Last Responsible Moment is the instant when, if a decision isn’t taken, the cost of the delay of a decision will surpass the benefit of delay. But this is not the major problem. Does this rule at all correctly define what’s the best point in time to decide?

Let's look at an example to answer this question. It’s about a project where investments in design options made in $100,000 increments increase the probability of realizing the benefits.

Table 7.2: Last Responsible Moment vs. Most Responsible Moment

Moment N is the First Possible Moment to make a decision to choose a design option, as there are no options available to choose from before that. Therefore, N is our reference point in time for delaying the decision.

The costs and benefits of delaying a decision are measured by the additional expected life cycle costs and the additional expected life cycle benefits (compared to the baseline scenario), resulting from the decision being made at a later point in time.

In this example, the cost of delaying the decision from moment N to moment N+6 is $1,800,000 - $1,200,000 = $600,000 and the benefit is $1,753,320 - $1,153,500 = $599,820. The net effect of making the decision in moment N+6 is close to zero: $599,820 - $600,000 = -$180.

N+7 is the Last Possible Moment, because failing to make a decision at this moment eliminates all alternatives. Looking at the net effect of the decision, it’s also the most irresponsible moment.

According to the original definition above, N+6 is the Last Responsible Moment because it’s “the instant in which the cost of the delay of a decision surpasses the benefit of delay”. However, as we can see, N+6 is far from the best decision-making point in time, because it results in a significant expected loss (-$46,680). To be precise, N+6 is the first irresponsible moment to take a decision. This is not surprising, because the Last Responsible Moment violates the principles of marginal economics.

When applying the revised definition, N+5 becomes the Last Responsible Moment – the instant when, if a decision isn’t made, the cost of the delay of the decision will surpass the benefit of delay. This improves the expected net benefit, but it’s clear that this is also not the best moment. At best, N+5 is the Last Acceptable Moment.

The best decision-making point in time is the one that maximizes the project’s expected net benefit. This is also when the net effect of the decision is greatest. In our case, this is moment N+3, which we’ll call the Most Responsible Moment.

Sometimes the last possible moment is the best moment, which makes the concept of the last (responsible) moment look natural. And using "responsible" implies that the decision won’t be made at the wrong time.

But as we’ve seen, the Last Responsible Moment isn’t the best moment to decide. When it’s applied blindly, it can easily lead to negative results. Instead, we suggest using the Most Responsible Moment, which is based on solid economic principles.

Most Responsible Moment is the instant of making a decision that maximizes the net benefit of the project.

Thus, our recommendation is to defer decisions and commitments until the most responsible moment.

• The Cost of Time is an actual cost that influences the project life cycle costs.
• Cost of Time is caused by varying the project cycle time or shifting the project implementation period.
• The Cost of Time components may include Cost of Project Delay, Cost of Project Acceleration, Cost of Perishable Information, Cost of Regulatory and Contractual Penalties, Cost of Lost Opportunity, Cost of Premature Delivery, Cost of Deferred Use, Cost of Customer Dissatisfaction and Cost of Delaying Dependent Projects.
• The reference value for project delay or acceleration is the optimal project cycle time.
• The reference point for the lost opportunity, premature delivery and deferred use is the ideal point in time to complete the project. If this ideal point is already missed, the reference point is the present moment.
• We should use the Cost of Time to evaluate its effect on project success measures, to improve the trade-off decisions and to prioritize projects and tasks.
• The moment when we make decisions and commitments induces time-related costs.
• The rationale for deferring decisions and commitments until the last responsible moment is to avoid actions based on assumptions, incomplete information, and lack of knowledge.
• However, the concept of the Last Responsible Moment doesn’t define the best decision-making moment.  We recommend using the concept of the Most Responsible Moment instead – which is the instant of making a decision that maximizes the net benefit of the project.

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[1] Liker, Jeffrey K. (2004). The Toyota Way: 14 Management Principles from the World's Greatest Manufacturer. McGraw-Hill 

[2] Lean Construction Institute, Glossary: https://leanconstruction.org/pages/learning/education/glossary/#l (last accessed 2022-10-20)