VIRTUAL FACTORY

Optimizing Under Competing Targets

Hit the throughput target at MINIMUM cost — every machine costs money, so add capacity only where it actually buys throughput (the bottleneck), staying within budget.

01Challenge

You need 10 parts/min, but you have a budget of 5 machines. Throwing machines at every station blows the budget; too few misses the rate. Find the cheapest line configuration that still hits 10/min.

02Model

Now two goals pull against each other. Throughput wants more machines; cost wants fewer. The resolution is simple but strict: spend only on the bottleneck. A machine added to a non-bottleneck station is pure waste — cost goes up, throughput doesn't move. So the optimal line is the one where every dollar went to the station that was actually limiting the rate, and not a dollar more.

Hit the throughput target at minimum cost.

03Guided practice

1. Bottleneck only. Drill 8/1 = 8 s is the limit (7.5/min). Cut 4 and Assemble 6 are fine for 10/min (need ≤6 s). 2. Add ONE machine to Drill. 8/2 = 4 s → new max is Assemble 6 → 60/6 = 10/min. 3. Check the budget. Total machines = 4 ≤ 5. Don't touch Cut or Assemble — that would only spend budget for no gain.

04Feedback

PASS WHEN PASS when throughput ≥ 10/min AND total machines ≤ 5. The cheapest line that meets the rate.

Under 10/min — fix the bottleneck (Drill) so the limit becomes the next station (Assemble at 6 s = 10/min).
Throughput is fine but you're over budget — you added machines to a non-bottleneck. Remove them; they bought nothing.
A machine on a station that isn't the bottleneck raises cost and leaves throughput unchanged — spend only where it's limiting.

05Retrieve & space

When two targets compete (throughput vs cost), you add capacity only at the ____ (bottleneck).
Adding a machine to a non-bottleneck changes cost by ____ and throughput by ____ (up; nothing).
To hit 10/min the slowest per-machine cycle must be ≤ ____ s (6).

06Mastery & project

Meet the throughput target at or under the machine budget — optimize under competing constraints.

This cost-aware optimization is exactly the capstone's job, on a bigger line.

← Yield, scrap & process capability Capstone: Run & Optimize a Virtual Factory →

VIRTUAL FACTORY

Optimizing Under Competing Targets

Edit the production line (JSON: each station has a cycle time in seconds and a number of parallel machines), then run it. The twin animates parts flowing and grades the line's throughput.