Question

In a stable process, increasing average inventory, while keeping average flow rate the same, has the following effect:

a. Average flow time decreases
b. Average flow time increases
c. Average flow time does not change

Answer 1

Increasing average inventory while keeping average flow rate the same results in an increase in the average flow time because items remain in the process longer.

Step-by-step explanation:

In a stable process, increasing the average inventory while keeping the average flow rate the same increases the average flow time. This is because flow time is essentially the amount of time an item spends within the process from entry to exit. If inventory levels are raised without a corresponding increase in flow rate, then individual items will, on average, remain in the system longer before being sold or used.

A simple analogy is a queue in a grocery store: if more people are in line (inventory) but cashiers are checking out customers at the same constant rate (flow rate), it will take longer for any individual in line to get through (flow time).

Answer 2

Increasing average inventory in a stable process with an unchanged average flow rate results in an increase in average flow time, as per Little's Law, which states that inventory and flow time are directly proportional when the flow rate is constant.

Step-by-step explanation:

In a stable process, increasing average inventory while keeping the average flow rate the same leads to an increase in the average flow time. The average flow time is defined as the average time that a unit spends in the system from beginning to end. This includes the time spent both in processing and as inventory. When the average inventory increases, there are more units in the system on average, which means it will take longer for an average unit to get through the system if the flow rate remains unchanged. Little's Law (L = λW), which relates the number of items in a queuing system (L) to the long-term average effective arrival rate (λ) and the long-term average time a unit spends in the system (W), supports this as L and W are directly proportional when λ is constant. Therefore, as inventory increases, flow time also increases.