Little's Law

Conceptual Overview: Explore how Little's Law relates average Works$-$in$-$process $($WIP$)$ to Throughput $($R$)$ and Flow time $($T$).$

Suppose that a voting facility processes an average of $50$ people per hour $($throughput $R=50)$ and that, on average, it takes $12$ minutes for each person to complete the voting process $($Flow time $T=12$ minutes$/60$ minutes$/$hour $=0\mathrm{.}2).$ In the graph we can see that WIP $=50*0\mathrm{.}2=10\mathrm{.}0,$ so we would expect to find about $10$ voters inside the facility.

You may move the sliders to change $R$ and $T$ to produce other values of WIP. Note that, in this graph, changing Throughput R changes the slope of the line and that changing Flow time $T$ changes the location on the line.

At the voting facility, if the throughput doubles, and each voter completes the process twice as fast as before, what would we expect to happen to the work in progress?

a$.$ WIP would stay the same

b$.$ WIP would double

c$.$ WIP would quadruple

d$.$ WIP would decrease by $50\%$

At the voting facility, suppose we discover that the cycle time in the afternoon is twice what it was in the morning. Which of the following is the least likely outcome for the afternoon?

a$.$ WIP doubles and the throughout stays the same.

b$.$ Throughput increase by $20\%$ and WIP increases by $20\%.$

c$.$ Throughput decreases by $50\%$ and WIP stays the same.

d$.$ WIP quadruples and throughput doubles.

Given the original scenario of throughput of $R=50$ and cycle time $T=0\mathrm{.}2,$ what new throughput value would be required to reduce WIP by $50\%$ without changing the cycle time?

a$.100$

b$.25$

c$.0\mathrm{.}4$

d$.0\mathrm{.}1$