Theory of Constraints

393. Theory of Constraints

Theory of Constraints (TOC, Goldratt 1984): a management philosophy that says system performance is determined by the bottleneck (the constraint). Identify the bottleneck, exploit it, subordinate everything else.

393.1. The five focusing steps

Identify the constraint — the bottleneck resource limiting system throughput
Exploit — maximize utilization of the bottleneck (no idle time, perfect quality, no setups)
Subordinate — every other resource serves the bottleneck (don’t push more than the bottleneck can absorb)
Elevate — invest to increase bottleneck capacity (add equipment, overtime, etc.)
Return to step 1 — when the bottleneck moves elsewhere, repeat

393.2. Throughput accounting

TOC replaces traditional cost accounting (which over-emphasizes unit costs) with three measures:

Throughput (T): sales revenue minus truly variable costs
Investment / Inventory (I): money tied up in the system
Operating Expense (OE): money to convert inventory into throughput

Net profit: $𝑇 - 𝑂 𝐸$

Return on investment: $\frac{𝑇 - 𝑂 𝐸}{𝐼}$

Goal: increase $𝑇$ first, decrease $𝐼$ second, decrease $𝑂 𝐸$ third. Traditional accounting often prioritizes OE reduction, which can hurt $𝑇$ if you cut the bottleneck.

393.3. Product mix problem (with constraint)

Given multiple products competing for a single bottleneck, maximize total throughput:

max \sum_{𝑖} 𝑇_{𝑖} 𝑥_{𝑖} s.t. \sum_{𝑖} 𝑏_{𝑖} 𝑥_{𝑖} \leq bottleneck capacity

where $𝑏_{𝑖}$ is bottleneck-minutes per unit of product $𝑖$ . Optimal: produce in decreasing order of $\frac{𝑇_{𝑖}}{𝑏_{𝑖}}$ (throughput per bottleneck minute).

This is a single-constraint LP — explicit solution by ratio ranking.

393.4. Drum-Buffer-Rope (DBR) scheduling

A scheduling discipline derived from TOC:

Drum: the bottleneck sets the pace
Buffer: small protective inventory in front of the bottleneck — never let it starve
Rope: communicates bottleneck demand backward to release new work into the system (a “rope” tying the entry point to the bottleneck)

DBR is essentially CONWIP but with the WIP cap chosen to keep just the right amount of buffer in front of the bottleneck.

393.5. Compared to Lean

	TOC	Lean / Toyota
Focus	Bottleneck — what limits throughput	Waste — what doesn’t add value
Inventory at bottleneck	Buffer (protective)	Reduce (Just-in-Time)
Improvement target	Throughput per bottleneck-minute	Cycle time, waste elimination
Best for	Complex job shops, bottleneck-driven systems	Repetitive manufacturing, low variability

Many production systems benefit from both — Lean to reduce variability and waste, TOC to manage the residual bottleneck. The two are complementary, not competing.

393.6. See also

Factory Physics — quantitative bottleneck analysis
CONWIP — DBR’s modern equivalent
Line Balancing
Best/Worst/PWC