Police spent £13 million last year looking for missing people – many of them children in local authority care.
Just 73 under-17s – most of them from city or county council children's homes – triggered more than 1,700 alerts to Leicestershire Police last year.
That is nearly a third of the 5,500 missing people inquiries handled by the force last year. Now, a senior officer has called on councils to tighten up procedures at their children's homes.
Detective Chief Inspector Andy Sharp, head of the force's safeguarding team, said: "We have young people in care who have been reported as missing from home 60, 70 or even 80 times.
"We've analysed the figures and we estimate that 73 children are responsible for 1,796 reports. Not every one of those children is in care, but the vast majority are.
"If every one of those cases involved a genuine safeguarding issue then I'd say 'fine, we are here to prevent people coming to harm'.
"But where I get concerned is the number of cases where people repeatedly go missing."
Leicestershire County Council has said it would work with Leicestershire Police to reduce the number of children in its care who go missing, Det Chief Insp Sharp said.
He now hopes Leicester City Council will follow suit.
Other major sources of missing alerts are mental health units and "vulnerable" patients who walk out of hospital.
Mr Sharp said he had held talks with health officials and they had agreed to try to reduce the number of alerts from their hospitals or residential units.
About 15 people are reported missing from mental health units in the city and county each month.
Det Chief Insp Sharp said a typical, short-term missing case cost the force about £2,400. However, he said: "When you are talking about high-risk missing people you could easily quadruple that average figure, especially when you bring in a search team or the helicopter."
The force, which is facing substantial cuts to its £175 million annual budget, calculated the £13 million bill using research published last August by academics at Portsmouth University. The £13 million is basically officers' time which could be spent on traditional crime fighting or investigation.
A child missing from care is automatically categorised as a medium or high risk, whereas some missing people are deemed to be at little risk of coming to harm.
Police and crime commissioner Sir Clive Loader – elected in November to set the force's budget and to oversee the cuts programme – also recently highlighted missing people inquiries as a major cost to the force which needed to be reduced.
City assistant mayor Vi Dempster, responsible for children, young people and schools, said: "A child in the care of a local authority is already vulnerable.
"When they go missing they are more vulnerable.
"We have very good protocols in place, so as soon as a child who has been reported missing is found they are interviewed because we want to understand why they did it and what can be done to prevent it happening again. We do have a close relationship with the police and, clearly, there is more work to be done."
A city police officer, who asked not to be named, said: "Of course, we're going to treat a case of a child missing from care as an absolute priority.
"In some cases we're aware of concerns about those young people being at risk of getting drawn into prostitution, very unhealthy relationships with adults or crime generally.
"What is annoying is finding a child who's been missing scores of times from a home has, again, been found at his mate's house because he wanted to borrow some DVDs or has just gone for a wander into town.
"In my experience, the bulk of the children missing from home cases probably shouldn't have been reported to the police in the first place."
