For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent.As a result of this change in the processing time, the WIP inventory

The correct option is decreases by 30%.

To understand why this is correct, we can apply Little's Law from operations management and queueing theory. Little's Law states that the long-term average number of items in a stationary queueing system, which represents the Work-in-Process (WIP) inventory, is equal to the long-term average effective arrival rate (or production rate) multiplied by the average time that an item spends in the system (processing time).

Mathematically, Little's Law is expressed as:
$$\mathrm{WIP}=R\times T$$
where:
• $\mathrm{WIP}$ is the Work-in-Process inventory.
• $R$ is the production rate (throughput).
• $T$ is the average processing time (flow time).

Let us analyze the initial state of the assembly line:
• Initial production rate, $R_1=4\text{pieces per hour}$
• Initial processing time, $T_1=60\text{minutes}=1\text{hour}$
Using Little's Law, the initial WIP inventory is:
$${\mathrm{WIP}}_1=R_1\times T_1=4\times 1=4\text{pieces}$$

Now, let us analyze the changes made to the assembly line:
• The production rate is kept the same:
$$R_2=R_1=R$$
• The average processing time is brought down by 30%:
$$T_2=T_1-0.30T_1=0.70T_1$$

Using Little's Law, the new WIP inventory is:
$${\mathrm{WIP}}_2=R_2\times T_2=R_1\times \left(0.70T_1\right)=0.70\times (R_1\times T_1)=0.70\times {\mathrm{WIP}}_1$$

Since the new WIP inventory is 70% of the initial WIP inventory, the percentage change in the WIP inventory is:
$$\text{Percentage Change}=\frac{{\mathrm{WIP}}_2-{\mathrm{WIP}}_1}{{\mathrm{WIP}}_1}\times 100\%$$
Substitute ${\mathrm{WIP}}_2=0.70{\mathrm{WIP}}_1$ into the equation:
$$\text{Percentage Change}=\frac{0.70{\mathrm{WIP}}_1-{\mathrm{WIP}}_1}{{\mathrm{WIP}}_1}\times 100\%=-0.30\times 100\%=-30\%$$
The negative sign indicates a decrease. Therefore, the WIP inventory decreases by 30% as a direct result of the 30% reduction in processing time while maintaining a constant production rate.