2nd/10_Wiki/Topic_Programming/AI_and_ML/Theory of Constraints (TOC).md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-theory-of-constraints-toc	Theory of Constraints (TOC)	10_Wiki/Topics	verified	self	TOC Bottleneck Theory Goldratt	none	A	0.9	applied	management optimization systems-thinking ops		2026-05-10	pending	language framework N/A TOC methodology

Theory of Constraints (TOC)

매 한 줄

"매 system throughput 매 single bottleneck 의 결정". Goldratt 의 1984 The Goal 에서 정립. 매 system 의 weakest link (constraint) 가 전체 throughput 의 제한 → 매 다른 모든 부분의 optimization 매 wasted. 매 manufacturing 에서 시작, 매 software (DevOps, ML pipeline, LLM agent throughput) 까지 broad applicable.

매 핵심

매 5-step focusing process

1. Identify the constraint.
2. Exploit it (maximize utilization without extra investment).
3. Subordinate everything else to the constraint.
4. Elevate the constraint (invest to expand capacity).
5. Repeat — 매 constraint 매 moves elsewhere.

매 핵심 metrics (Throughput Accounting)

• Throughput (T) — 매 sales rate of new revenue.
• Inventory / Investment (I) — 매 money tied in the system.
• Operating Expense (OE) — 매 money spent to convert I → T.
• 매 priority: maximize T, minimize I, control OE.

매 modern applications (2026)

• DevOps — 매 The Phoenix Project (Kim 2013) 매 TOC + Lean 매 IT ops 에 적용.
• ML pipeline — 매 GPU bottleneck (training), tokenizer (inference batch), vector store (RAG retrieval).
• LLM agent — 매 sequential tool call 의 dominant latency contributor 의 identify → parallel.
• Org / Team — 매 single approval bottleneck → workflow change.

매 응용

1. Factory floor scheduling (DBR — Drum-Buffer-Rope).
2. Software delivery (CI bottleneck, code review queue).
3. ML inference cost (which stage 매 dominant?).

💻 패턴

매 inference pipeline profiling

import time
def profile_pipeline(stages, inp):
    timings = {}
    out = inp
    for name, fn in stages:
        t0 = time.perf_counter()
        out = fn(out)
        timings[name] = time.perf_counter() - t0
    bottleneck = max(timings, key=timings.get)
    return out, timings, bottleneck

# 매 result: {"tokenize": 0.001, "embed": 0.04, "vector_search": 0.32, "rerank": 0.18}
# 매 bottleneck: vector_search → 매 elevate (HNSW tune, GPU index, shard).

매 LLM agent: serialize → parallelize

# 매 BEFORE (serial — bottleneck = sum)
ctx = await fetch_user(uid)
weather = await get_weather(ctx.city)
calendar = await fetch_calendar(uid)

# 매 AFTER (parallel — bottleneck = max)
ctx, weather, calendar = await asyncio.gather(
    fetch_user(uid), get_weather_for_user(uid), fetch_calendar(uid),
)

매 DBR (Drum-Buffer-Rope) for queue

# 매 Drum: bottleneck stage paces the system
# 매 Buffer: small queue before bottleneck (의 starvation 방지)
# 매 Rope: feedback to release new work only when buffer drains

import asyncio
buffer = asyncio.Queue(maxsize=8)  # 매 Buffer

async def producer():
    while True:
        item = next_work()
        await buffer.put(item)        # 매 Rope (blocks when full)

async def bottleneck_consumer():     # 매 Drum
    while True:
        item = await buffer.get()
        await expensive_step(item)

매 throughput accounting (simple)

def evaluate_change(before, after):
    delta_T = after["throughput"] - before["throughput"]
    delta_I = after["inventory"] - before["inventory"]
    delta_OE = after["op_expense"] - before["op_expense"]
    net = delta_T - delta_OE
    return {"net_value": net, "OK": net > 0 and delta_I <= 0}

매 5-step driver (pseudocode)

def toc_loop(system, n_iterations=5):
    for _ in range(n_iterations):
        c = identify_constraint(system)        # 1
        exploit(c)                             # 2
        subordinate_others_to(c, system)       # 3
        if not enough_capacity(c, target=system.target):
            elevate(c)                         # 4
        # 5: repeat — 매 constraint 매 shift

매 결정 기준

상황	Approach
Multi-stage pipeline	Profile → identify slowest → optimize that
LLM agent latency	Parallel tool calls + cache hot path
Batch ML training	GPU util check (nvidia-smi) — 매 if low, IO bottleneck
Software delivery	Value stream map → find single bottleneck
Cost optimization	Throughput accounting (T - OE), not unit cost

기본값: 매 measure 먼저, 매 single biggest bottleneck 의 fix, 매 repeat — 매 premature optimization 의 X.

🔗 Graph

• 부모: Systems_Thinking
• 변형: Lean · DevOps

🤖 LLM 활용

언제: 매 multi-stage pipeline 의 latency / cost 의 분석, ML / agent system optimization, team workflow bottleneck. 언제 X: 매 single-step task — 매 TOC framing 매 overhead.

❌ 안티패턴

• Local optimization: 매 non-bottleneck 의 optimize 매 system throughput 의 0% 변화.
• Multiple "bottlenecks": 매 일반적으로 single dominant — 매 measure 안 하고 guess 매 wrong.
• Ignoring the shift: 매 bottleneck fix 후 다른 stage 가 새 constraint — 매 repeat 안 하면 stuck.
• Capacity addition without exploit: 매 step 4 (elevate) 의 step 2 (exploit) 전에 — 매 expensive 하게 hardware buy 후 underutilized.

🧪 검증 / 중복

• Verified (Goldratt 1984 The Goal, Kim Phoenix Project 2013, Beyond the Phoenix Project 2018).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — TOC + DevOps/ML pipeline modern application