Differences in Production Rates

Introduction

When you compare a robot method with a manual method, the two methods often make a different number of parts each day. The robot method usually makes more. Even if a robot is slower than a human, the company can run it for two or three shifts. You must include this difference in the analysis.

How it works

There are two cases.

Case 1: the value added per unit is known

Use the value added to find the annual revenue of each method:

$$R=(\text{units per day})\times (\text{days per year})\times (\text{value added per unit})$$

Then use the Payback Method and the ROI method on each method, and compare them.

Case 2: the value added per unit is not known

This is common, because one operation is only one step in a sequence of steps that make the product. You may know the final price of the product, but not the value of each step.

In this case:

1. Write the EUAC of each method without revenue, at $i=MARR$
2. Divide the EUAC by the number of units made each year to get the unit cost
3. Select the method with the lowest unit cost

Example 5 (value added is known)

	$IC$	$C$ per year	Salvage value	Units per day
Robot	\100{,}000$	\20{,}000$	\50{,}000$	300
Manual	\29{,}000$	\36{,}000$	none	200

Other data: value added is \1.00$perunit,$MARR=25%$, service life is 3 years, and there are 250 days of operation each year.

Manual method

$$R=200\times 250\times 1=\$50,000\text{ per year}$$ $$n=\frac{29,000}{50,000-36,000}=2.07\text{ years}$$ $$EUAC=-29,000\left(\frac{A}{P},i,3\right)+(50,000-36,000)=0\Rightarrow \left(\frac{A}{P},i,3\right)=0.48276$$

This gives $i=21.07\%$, which is less than the MARR of $25\%$.

Robot method

$$R=300\times 250\times 1=\$75,000\text{ per year}$$ $$n=\frac{100,000}{75,000-20,000}=1.82\text{ years}$$ $$EUAC=-100,000\left(\frac{A}{P},i,3\right)+(75,000-20,000)+50,000\left(\frac{A}{F},i,3\right)=0$$

By trial and error, $i=43.91\%$.

The robot method is better for both payback period and rate of return. The salvage value has a large effect on the rate of return, but the payback method ignores it.

Example 6 (value added is not known)

Use the same data as Example 5, but do not use the \1.00$ value added.

Manual method

$$EUAC=-29,000\left(\frac{A}{P},25\%,3\right)-36,000=-14,857-36,000=-\$50,857\text{ per year}$$ $$\text{Units per year}=200\times 250=50,000$$ $$\text{Unit cost}=\frac{50,857}{50,000}=\$1.017$$

Robot method (includes the salvage value)

$$EUAC=-100,000\left(\frac{A}{P},25\%,3\right)-20,000+50,000\left(\frac{A}{F},25\%,3\right)$$ $$EUAC=-51,230-20,000+13,115=-\$58,115\text{ per year}$$ $$\text{Units per year}=300\times 250=75,000$$ $$\text{Unit cost}=\frac{58,115}{75,000}=\$0.775$$

The robot method has the lower unit cost, so the company selects the robot method.