Adding up: cost, working hours and elapsed time

Working hours and costs sum: every hour worked and every cost incurred counts, whether the steps run one after another or side by side. Elapsed time does not. Steps in a sequence add, steps side by side take as long as the longest one, and waiting time sits on the clock without costing any work. This part explains the difference with two small examples and a lens you can use to read your own map. It gives no advice. What to do with the picture is up to you.

What adds up: working hours and cost

A working hour is an hour someone spends working. A cost is an amount spent: wages, materials, a supplier's invoice, a carrier's fee. Both are things you give up when a step happens.

Both sum, whatever the shape of the process. Order does not matter, and neither does what runs at the same time. Three people working in parallel for 2 hours each is 6 working hours. Those same three people working one after another is also 6 working hours. The cost of 6 hours is the same in both cases.

This is why working hours and costs follow the work, not the calendar. If a step happens, its hours and its costs count. If a step is skipped, they do not. How the steps are arranged does not change them.

Two cautions. First, working hours are not the same as the time a step takes on the clock. A step where two people work for 3 hours takes 3 hours of elapsed time and uses 6 working hours. Second, the amounts are only as good as the figures you enter. They are plan figures, directional estimates, not an accounting record. Wages, a carrier's fee and a guess about materials can sit in the same sum, but that sum is a rough size, not a ledger.

What does not add up: elapsed time

Elapsed time is the time on the clock from the start of a job to its finish. Three rules cover most of it.

• Steps in sequence add. If step B starts when step A ends, the elapsed time is A plus B.
• Steps in parallel take the longest. If two steps run side by side, the clock moves at the pace of the slower one. The faster one finishes and waits.
• A join waits for the slowest arrival. Where branches come back together, for example when welding needs both the cut steel and the hinges, the next step cannot start until the last of them arrives.

Put together, the overall time of a chain is the length of the longest path through it. Some people call this the critical path. The name does not matter. What matters is that a short branch beside a long one adds nothing to the clock. It can be cheap, expensive, busy or idle. The clock follows the long one.

Waiting is on the clock but not in the hours

Part 5 described two clocks: working time and waiting time. Here is how they behave when you add things up.

A delay is time that passes while nobody is working on the job. Paint curing, a carrier carrying, a customer thinking, a supplier's lead time, an approval sitting in someone's inbox. A delay belongs on the path, because the job cannot move on until it is over. But it costs no working hours. Nobody is working.

So a path has two parts: time spent working and time spent waiting. Their sum is the elapsed time. Only the first part shows up in working hours. A path can be mostly waiting and still use very little work.

Why the difference matters

Here is one way to read it. You might read a map as holding two different questions, and the answers do not always point to the same place.

• If you shorten a step that is not on the longest path, working hours or cost may change, but the clock does not. The long branch is still setting the pace.
• If you shorten something on the longest path, the clock moves. It moves until another branch becomes the longest, and then that one sets the pace.

That is a lens, not a recommendation. Whether a faster clock is worth anything, or whether a lower cost is, is for you to decide. Some waiting is built in and some is welcome. A map only lets you see which question you are asking: where does the money and work go, or where does the time go?

Worked examples

Northline Fabrication and Maple Street Bakery are invented for illustration. The figures are not data.

A gate at Northline Fabrication

Northline makes custom steel gates. One gate goes through six steps. Cutting and prepping the steel runs at the same time as ordering the hinges. Welding needs both. Labour is counted at 40 per hour, an assumed figure. Other costs are the steel, the hinges, powder coating and the carrier.

Nothing in this table cares about order. Cut and prep could run before or after ordering hinges, and the totals would be the same: 24 working hours and about 1,380.

The clock is different. Say a working day is 8 hours, so 2 hours of work is a quarter of a day. Delay is waiting time in days.

Cut and prep and order hinges both begin at day 1.25. Cutting is done by day 1.75, but the hinges arrive at day 4.5, so welding starts at 4.5. The cutting branch has 2.75 days of slack, in the sense that it could take that much longer without changing the finish date.

The gate is ready to leave on day 9. On the longest path, work is 2 days (0.25 + 0.25 + 0.75 + 0.5 + 0.25) and delay is 7 days (1 + 3 + 1 + 2). Work and waiting together make 9 days.

You might read this in several ways. The 8 hours of cutting are the largest single block of working hours, yet they sit on the short branch. If cutting took a full day instead of half a day, its hours and cost would probably rise, and the ship date would not move. The hinge branch, which is 2 hours of work and 3 days of waiting, is what sets the pace. If the hinges were already on the shelf, that branch would shrink to almost nothing, and the cutting branch would take over as the longest. Whether any of that matters is for the people at Northline to say.

A special-order cake at Maple Street Bakery

A customer orders a birthday cake. Baking and decorating run in sequence. The box supplier delivers in parallel. Both feed the final boxing step. Times here are in hours.

Working hours sum to 7 (0.5 + 2 + 3 + 0.5 + 1). That includes the half hour spent ordering boxes, even though that branch is not on the clock's longest path.

The clock is 9.5 hours. The bake, cool and decorate branch takes 8 hours from the order. The box branch takes 6.5. Boxing begins when the slower of the two is done. The supplier's 6-hour wait is a long delay, but it sits beside an even longer one, so it adds nothing to the finish time. On the longest path, work is 6.5 hours and delay is 3 hours (the cooling).

Flour, eggs and the cash in the till are stocks here as well, and the baker knows them well. They are not part of this table.