They’re lost.

The city Department of Education paid nearly $9 million for 6,000 school-bus GPS units — but up to 80 percent were never even turned on, according to a blistering new audit of the bungled system.

An 18-month probe by the Special Commissioner of Investigation found such egregious incompetence that it called for the potential sacking of the top DOE administrator in charge of the program, Alexandra Robinson.

The DOE initially contracted with the GPS firm, Navman, in 2015 to document transportation costs for its special education students to qualify for Medicaid reimbursements, according to the report.

The city annually transports about 50,000 special-needs kids, or roughly a third of the students on its public school buses.

But the DOE’s installation, operation and tracking of the system was so comprehensively inept that it failed to collect the required data for reimbursement — and hasn’t managed to recoup a dime from the feds, the report states.

The DOE should have been eligible for up to $1 million in reimbursements annually — or as much as $7 million, the report found.

“From the beginning, the Navman project lacked oversight, accountability, communication, and employees with the technical abilities to oversee a large-scale management project — that ultimately failed when no usable data was retrieved for Medicaid reimbursement,” according to the report.

Despite clear evidence that the system was in crisis since its inception, DOE officials continued to replenish its funding year after year in “the epitome of throwing good money after bad,” the report found.

The probe discovered that the initiative was totally dependent on individual bus drivers activating their GPS systems — and that the vast majority didn’t bother to do so, rendering the units useless.

The DOE has long been plagued by shoddy bus service, and the GPS system was touted as a far-reaching solution for fuming moms and dads. Parents, they promised, would no longer be in the dark about the location of tardy or absent buses.

But with most of the units dormant, parents have derived little to no benefit from the system — while the operation has cost taxpayers millions of dollars.

In addition, the SCI found that Navman routinely billed the DOE for GPS units that were clearly unrelated to the department — with some sitting in vehicles as far away as West Africa and California.

The report recommended stiff punishment for Robinson, chief of the DOE’s Office of Pupil Transportation.

“SCI therefore recommends discipline up to and including termination of Robinson for her consistent, willful neglect of the Navman project’s problems, her mismanagement of the project, and her failure to take corrective action even when advised of significant issues,” the report states.

SCI boss Anastasia Coleman ripped the DOE for the mismanagement.

“The DOE has an obligation to maximize its financial resources to best assist the students and families of the district,” she said in a statement. “It is imperative that the Department use sound management and best practices to ensure every available dollar is used appropriately.”

Schools Chancellor Richard Carranza said in a statement Monday, “Our contract with Navman ends in December and starting this year, we’ll implement new, functional Via GPS technology on every bus so that parents can receive real-time updates on their child’s location on their mobile device.

“While the contract process takes a significant amount of time, we are doing it the right way and not cutting corner.”

The DOE did not comment when asked about the fate of Robinson.