Robots Replacing Labor

DCL Logistics in Fremont, California, is installing robots on e-commerce fulfillment lines. In 2021, U.S. companies spent more than $2 billion on almost 40,000 robots. Brian Tu, chief revenue officer for DCL, says robots are dependably fast and do not take breaks.—reuters.com

In this post, we use a numerical example to compare the production schedules of a worker-operated system and a robot system.

 Assumptions

 Worker-operated system

• An e-commerce fulfillment center with no robots employs workers at $20 an hour.
• The fixed cost of operating a fulfillment center is $30 per hour.
• The total product schedule (orders fulfilled per hour) for this center is

Robot system

• The robot system costs $250,000.
• With a life of 5 years and operating for 10 hours a day, the robot has an implicit rental rate of $20 an hour.
• Workers can still be hired for $20 an hour.
• Other fixed costs remain at $30 an hour.
• The total product schedule for the center with a robot is

Which system has the lower average total cost (ATC)?

Start with the worker-operated system. Fixed cost is $30 per hour and variable cost is $20 per worker, and total cost (TC) is the sum of these costs. Calculate average total cost (ATC) as TC divided by output (number of orders fulfilled).

The TC and ATC schedules for the worker-operated system are

Now do similar calculations for the robot system. Fixed cost is the sum of the implicit rental rate and other fixed costs, which is $50 per hour. Variable cost is $20 per worker hour.

The TC and ATC schedules for the robot system are

Figure 1 compares the ATC of the two systems.

Because the robot system has a higher fixed cost and lower variable costs than the worker-operated system, the ATC of the robot system is higher at small output rates and lower at output rates between 11 and 18 orders per hour.

Which system has the lower marginal cost (MC)?

Start with the worker-operated system. Continue with the TC schedule from before.

When no workers are hired, no orders are fulfilled, and TC equals fixed cost, which is $30 per hour.

Calculate MC as the change in TC divided by the change in output. Place MC values at the midpoints of the output rates.

The MC schedule for the worker-operated system is

Now do similar calculations for the robot system. In the added column, 0 workers fulfill 0 orders per hour with a total cost of $50.

The MC schedule for the robot system is

Figure 2 compares the MC of the two systems.

Because the robot system has a high fixed cost and low variable costs, the MC of the robot system quickly falls to $0 per hour. And because the worker-operated system experiences diminishing marginal returns and a constant variable cost, the MC of the worker-operated system rises as output increases.

Work these questions to check your understanding and get instant feedback.

Answer the following questions to check your understanding of the story.

In the post, how does the ATC schedule of the robot system compare to that of the worker-operated system?

The ATC of the robot system is ______________.

a) lower at small output rates and higher at output rates between 11 and 18 orders per hour

b) lower at all output rates

c) higher at small output rates and lower at output rates between 11 and 18 orders per hour

d) higher at all output rates

The robot system has a higher fixed cost and lower variable costs. What happens at small output rates when the fixed cost dominates? What happens at larger output rates?

At larger output rates, the variable costs dominate the fixed cost. Which system has the lower variable costs?

At smaller output rates, the fixed cost dominates the variable costs. Which system has the greater fixed cost?

Because the robot system has a higher fixed cost and lower variable costs, the ATC is higher at small output rates and lower at output rates between 11 and 18 orders per hour.

Consider the following production schedule.

The wage of a worker is $15 per hour and the fixed cost of operation is $25 per hour. Complete the following statements about costs.

The ATC when output is 28 widgets per hour is ______________ per widget. The MC when output increases from 28 to 30 widgets per hour is ______________ per widget.

a) $3.04; $15

b) $85; $15

c) $3.04; $3.75

d) $85; $3.75

$85 is the TC, not the ATC. Use this information to calculate ATC.

$15 is the change in TC, not the MC. Use this information to calculate MC.

When 28 widgets per hour are produced, TC is $85. When 30 widgets per hour are produced, TC is $100. Use this information to calculate the desired values.

When output is 28 widgets per hour, TC is $85, so ATC is $85 ÷ 28, which is $3.04. When output is 30 widgets per hour, TC is $100. When output increases from 28 to 30 widget per hour, MC is ($100 – $85) ÷ (30 – 28), which is $3.75.

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