The long-term relationship between inventory, throughput, and flow time is mathematically related using
's law.

Question

The long-term relationship between inventory, throughput, and flow time is mathematically related using 
's law.

BlackTom AI · Accepted Answer

Little's Law states the long-term relationship between average inventory (I), average throughput or arrival rate (T), and average flow time (F): I = T × F.

1. Relevant knowledge points and concepts
- Inventory (I): the average number of items in the system (work-in-process, customers, jobs).
- Throughput (T): the average rate at which items exit (or arrive at) the system, e.g., items per hour.
- Flow time (F): the average time an item spends in the system (time units).
- Little's Law applies to a stable system in steady state and relates time-average quantities; it is fundamental in queuing theory and operations management.

2. Complete reasoning process step by step
- Define variables: let I be the time-average number in the system, T be the long-run average throughput (items/time), and F be the average time an item spends in the system (time).
- Consider a long observation period of length H. If N items complete the system during this period, average throughput T ≈ N/H.
- Total time spent by all items in the system ≈ N × F (each item spends on average F time units).
- Time-average number in the system I equals (total time spent by all items in system) divided by observation length H: I ≈ (N × F)/H.
- Substitute N/H = T to get I = T × F.

3. Calculation example (intermediate steps)
- Suppose throughput T = 5 units/hour and average flow time F = 2 hours.
- Compute I = T × F = 5 × 2 = 10 units (average inventory/work-in-process).

4. Why the correct answer is correct
- The blank asks for the name of the law that mathematically links inventory, throughput, and flow time; this exact relationship is Little's Law (also called Little’s theorem). It is the standard, proven identity connecting those three measures under steady-state conditions.

5. Why other options would be incorrect (brief)
- Kingman’s formula approximates waiting time in a G/G/1 queue and does not state I = T × F.
- Other named relations from physics or chemistry (e.g., Reynolds, Ohm) are unrelated to queuing/flow relationships.
- No alternative provides the exact long-term identity among inventory, throughput, and flow time the way Little’s Law does.

6. Conclusion
- Therefore, the correct fill-in is Little's (Little’s Law), which matches the provided answer.

The long-term relationship between inventory, throughput, and flow time is mathematically related using 's law.未知题型

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