Week 2 exercises
Capacity, bottleneck and process choice for Test 2 · Heizer Ch. 7 + S7
Test 2 (Week 4, 22 October) covers Chapter 7, Supplement 7 and Supplement 5; Chapter 5 itself is not tested. Its calculation items are of the kinds below and on the Week 2 bonus sheet, with changed numbers (what Test 2 asks). Work on paper, with a calculator; write the unit next to every result.
The formulas in words. Capacity of a step = 60 min ÷ minutes per unit × parallel workers or machines. A batch machine makes units per load × 60 ÷ minutes per load. The line makes what its bottleneck makes, the step with the lowest capacity. Throughput time = sum of all step times of one unit; bottleneck time = minutes between two finished units. Utilization = actual output ÷ design capacity; efficiency = actual output ÷ effective capacity. Break-even volume = fixed cost ÷ (price − variable cost per unit). Crossover volume = difference in fixed cost ÷ difference in variable cost.
Formula sheet to download: Week 2 formula sheet: capacity, bottleneck, crossover (PDF, 1 page) — the one-page sheet handed out with the bonus sheet; print it and keep it next to you while you practise.
Start here: the Week 2 key content (party pizza line, chain of three firms), then the Solved Problems at the end of Chapter 7 and Supplement 7.
Part A · Problems from the textbook
Solve problems on these topics from Chapter 7 and Supplement 7 of Heizer et al. (2023); the problem texts are in the book. ● = warm-up, ●● = test level, ●●● = stretch. Do at least the ● and ●● topics.
| Topic | Level | What it trains |
|---|---|---|
| Design capacity, effective capacity, actual output | ● | the three capacity levels and their units |
| Utilization and efficiency | ● | which capacity goes into the denominator |
| Bottleneck of a line | ●● | capacity per step, the minimum, parallel resources |
| Throughput time and bottleneck time | ●● | one unit through all steps vs. time between two units |
| Break-even volume | ●● | fixed cost, price, variable cost per unit |
| Crossover of two or three processes | ●● | which process is cheapest at which volume |
| Capacity planning when demand grows | ●●● | how many machines, people or shifts are needed |
Part B · The same ideas in new settings
Eight problems of our own, with answers, appear here after Thursday’s class: from a laundry evening to a frame line with two bottlenecks.
The cases
Look again at the two processes from Thursday morning, Frito-Lay and Arnold Palmer Hospital. For each, be ready to say which process strategy it follows (volume and variety), where the bottleneck is likely to sit, and why a fixed flow suits one and a variable flow suits the other. The case Backhaus Kaya trains the same ideas with numbers.
The in-class bonus
The Week 2 bonus sheet was not written on 8 October; you write it in class on Thursday, 15 October. It counts toward Test 2. Bonus sheets are handed out in class only and are never on this site; the exercises on this page are the training for them and for the test. Rules: Assessment.
Sources
Heizer et al. (2023), Chapter 7 and Supplement 7 (Part A topics and definitions). Part B: own material, R. Bartnik (2026).