How to use this guide
The midterm math is a small set of formulas used over and over. Most lost marks come from doing the right formula in the wrong order (crashing a non-critical activity, dividing by variance instead of standard deviation), so every topic ends with a Traps box.
Topic order. Work the tabs left to right; each one leans on the one before. 01 Process flow introduces bottlenecks and cycle time. 02 Intro OSCM is the vocabulary you'll write out. 03 Projects builds in four steps: draw the network → CPM (critical path, slack) → PERT (probabilities) → crashing (buying time). 04 Inventory goes EOQ → reorder point and safety stock → total cost and discounts. 05 Capacity goes utilization → layout cost → line balancing. The Walkthrough then puts a whole project question together the way an exam would.
Inside each topic: read the idea, do each worked example on paper before opening the solution (they run simplest first), then break the lab by changing numbers. Finish with the generator in Practice until you get several in a row right.
| Level | What it asks | Example |
|---|---|---|
| Beginner | One definition, or one formula in one step | Crash cost per week; utilization vs efficiency; throughput vs cycle time |
| Intermediate | A standard calculation with a few steps | EOQ and the reorder point with safety stock; shift output with warm-up |
| Exam level | A full exam-style question with several parts | PERT probability from a, m, b; total cost with a quantity discount |
| Hard | Twists: combining ideas, working backwards, traps | Which path's probability to report; what service level a given reorder point buys |
The problem generator starts at Beginner and steps up a level after three correct answers in a row; you can also pick a level yourself. The written questions, quick checks and flashcards are ordered easy → hard, so flipping through builds each idea from the ground up.
The core formulas
- EF = ES + t, LS = LF − t, slack = LS − ES = LF − EF
- ET = (a + 4m + b) ÷ 6, σ² = ((b − a) ÷ 6)², Z = (D − ETp) ÷ σp, ETp = ΣET, σp² = Σσ²
- Crash cost per week = (CC − NC) ÷ (NT − CT)
- TC = DC + (D/Q)S + (Q/2)H, EOQ = √(2DS ÷ H), H = iC, R = dL + SS = dL + Z√L·σd
- Utilization, efficiency, load-distance C = ΣΣ L·D·K, C = available ÷ demand, Nt = T ÷ C, e = T ÷ (NaC)
Rules people forget: memorize
- ES = largest predecessor EF; LF = smallest successor LS
- D = ET + Zσ (rearrange Z yourself), and Z for 90/95/99% = 1.28 / 1.645 / 2.33 (or read the table backwards)
- "Longer than D" = 1 − table value; negative Z = 1 − value for +Z
- Crash rule: net benefit = indirect + penalty saved − crash cost; stop at ≤ 0
- TAC with safety stock: holding = (Q/2 + SS)H. The plain TC formula has no SS
- Orders per year D/Q, days between orders Q/d, average inventory Q/2 + SS
- Throughput time, cycle time = bottleneck, capacity with warm-up 1 + ⌊(time − throughput) ÷ CT⌋, carriers ⌈busy ÷ CT⌉
- Idle % = 1 − e; always round Nt up
Formula sheets differ between sections and terms. Check what your own exam provides, and memorize anything it leaves out.
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This is the first section. The full guide has every topic, the labs and the practice questions.
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