What is the name of the law that states that there is a long-term relationship between the inventory, throughput, and flow time of a production system in a steady state?单项选择题
A
Holt's law
B
Little's law
C
Murphy's law
D
Throughput's law

Question

What is the name of the law that states that there is a long-term relationship between the inventory, throughput, and flow time of a production system in a steady state?

BlackTom AI · Accepted Answer

Little's Law states the steady-state relationship between average inventory (L), average throughput or arrival rate (λ), and average flow time (W): L = λ × W.

Relevant concepts:
- Inventory (L): average number of items/customers in the system.
- Throughput/arrival rate (λ): average number of items completed (or arriving) per unit time.
- Flow time (W): average time an item spends in the system from entry to exit.
- Steady state: average arrival rate equals average departure rate and averages are taken over a long time.

Step-by-step reasoning and derivation:
1. Let N(T) be the number of items that enter and leave the system during time interval [0, T]. Each item i spends time Wi in the system.
2. Total time spent by all items in the system over [0, T] is Σ_{i=1}^{N(T)} Wi.
3. The time-average number of items in the system over [0, T] equals (1/T) ∫_0^T n(t) dt, which equals (1/T) Σ_{i=1}^{N(T)} Wi (counting each item’s presence over time).
4. Define average inventory L = (1/T) Σ Wi, average flow time W = (1/N) Σ Wi, and arrival rate λ = N/T.
5. Substitute: L = (N/T) × (1/N Σ Wi) = λ × W. Thus L = λW (Little’s Law).

Numerical example:
If throughput λ = 10 units/hour and average flow time W = 2 hours, then L = 10 × 2 = 20 units on average in the system.

Why the correct answer is correct:
John Little proved this universal relation (often called Little’s Law or Little’s Theorem). It directly links inventory, throughput, and flow time in steady state and is widely used in queuing and production analysis.

Why other options are incorrect:
- Holt’s law: not related; Holt’s method is a forecasting technique for time series.
- Murphy’s law: an adage (“anything that can go wrong will go wrong”), not a production law.
- “Throughput’s law”: not a standard or established law in queueing theory.

Conclusion: The correct answer is Little’s law, which matches the provided answer.

What is the name of the law that states that there is a long-term relationship between the inventory, throughput, and flow time of a production system in a steady state?单项选择题

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