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.

▶ Live · scrub & hover — one speed, three competing objectives — throughput up, tool life down, cost U-shaped

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.

If your run fails, check:

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.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you