A government watchdog this week criticized the nearly bankrupt United States Postal Services for overproducing 2 billion stamps that led to $4 million in waste over a two-year period.

The most over-produced stamp was a commemorative line released in 2009 featuring the cartoon family “The Simpsons,” according to a report released by the United States Postal Service Office of Inspector General.

About 682 million out of a run of 1 billion Simpsons stamps went unsold in 2009 and 2010. Coming in second was a series called “Flags of Our Nation” — the Postal Service printed 500 million of these stamps, but only sold about 120 million. Both series were 44-cent stamps. The price of postage has since gone up 1 cent, which means the Postal Service destroyed the leftover stock.

The OIG reviewed 37 stamp lines and found no examples of the USPS underestimating demand. The Postal Service could save $2 million a year by ending the overproduction, the inspector general said.

The OIG recommended improving the system used to decide how many stamps to produce. It also recommended releasing commemorative stamps in limited runs to test demand, and to develop better marketing strategies.

“If the Postal Service can’t address a simple matter such as determining how many commemorative stamps to produce, it shows they can’t address the larger problems,” said Tom Schatz, president of Washington, D.C.-based Citizens Against Government Waste. “Unfortunately, even a small item can create larger problems.”

John Meyers, a stamp collecting enthusiast who was reached Thursday at Dixie Coin and Stamps in Moraine, said the Simpsons and especially the flags series are nice stamps, but have very little collecting value because of how many were produced.

Meyers, 65, said he sells both sets online below face value as part of a variety pack.

“It’s as simple as you print too much of something, you’re not going to sell them all. Especially when postage costs change,” Meyers said.

Responding to the OIG report, the Postal Service said it has increased the production of forever stamps, which cuts down on wasted stamps, and that it is working to fine-tune its production forecasting. The Postal Service also responded that it has transferred responsibility for Stamp Services from its government relations department to its marketing department.

Due to decreased demand and unfunded retirement liabilities for employees, the Postal Service last May announced the closure of 140 mail processing centers across the U.S., including one in Dayton and a dozen others in Ohio.

The closure of the Dayton plant will save an estimated $7.5 million in its first year, and $7.9 million annually after that.

The Postal Service earlier this month said it posted a loss of $5.2 billion in its third quarter and may lose $15 billion in the year ending Sept. 30. It has asked for Congress’ help in cutting costs by eliminating a requirement to pre-pay for future retirees’ health care and letting it stop Saturday mail delivery.

Contact this reporter at (937) 225-2494 or andrew.tobias@coxinc.com

Bloomberg News contributed to this report