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 use Little's Law, which is a fundamental relation in operations management. Little's Law states that the average Work-in-Process (WIP) inventory in a stationary system is equal to the long-term average effective production rate (throughput) multiplied by the average processing time (flow time) that a unit spends in the system.

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), and
• $T$ is the average processing time (flow time).

Step 1: Calculate the initial WIP inventory (WIP₁)
Initially, we have:
• Production rate, $R_1=4$ pieces per hour
• Processing time, $T_1=60$ minutes = 1 hour

Using Little's Law, the initial WIP inventory is:
$${\mathrm{WIP}}_1=R_1\times T_1=4\times 1=4\text{pieces}$$

Step 2: Calculate the new WIP inventory (WIP₂) after the change
According to the problem:
• The production rate is kept the same: $R_2=R_1=4$ pieces per hour
• The average processing time is reduced by 30%:
$$T_2=T_1\times (1-0.30)=60\times 0.70=42\text{minutes}=0.7\text{hours}$$

Using Little's Law to find the new WIP inventory:
$${\mathrm{WIP}}_2=R_2\times T_2=4\times 0.7=2.8\text{pieces}$$

Step 3: Determine the percentage change in WIP inventory
The percentage change in WIP inventory is calculated as:
$$\text{Percentage Change}=\frac{{\mathrm{WIP}}_2-{\mathrm{WIP}}_1}{{\mathrm{WIP}}_1}\times 100\%$$
Substituting the values:
$$\text{Percentage Change}=\frac{2.8-4}{4}\times 100\%=\frac{-1.2}{4}\times 100\%=-30\%$$
The negative sign indicates a decrease. Since the WIP inventory is directly proportional to the processing time when the production rate is held constant, reducing the processing time by 30% directly decreases the WIP inventory by exactly 30%.