Despite buying for 1.1 million students, custodians at New York City public schools are forced to pay more for supplies than a regular consumer walking into a local hardware store.

Straightjacketed by a city contract that requires them to spend their supply budget with a single merchant, the custodians pay in some cases hundreds of dollars more for paper towels, hand soap, batteries, trash cans, jigsaws, and even snow shovels.

Through the company’s two approved catalogs, a sheet of Plexiglass costs $224.54. But a custodian could buy the same sheet for just $125 at Dunrite Glass & Windows at 106th Street and Lexington Avenue. Even Ace Hardware and a Lower Manhattan Home Depot can beat the catalog, charging, respectively, $12.25 for a snow shovel listed at $16.97 and $169.99 for a jigsaw listed at $187.

Custodians said the company, Strategic Distributors Inc., a so-called integrated supplier based in Bristol, Pa., will locate items not listed in its catalogs, but the legwork can be costly. When a custodian who supplied invoice records to The New York Sun asked SDI last month how much it would cost to replace batteries for a floor scrubber, the company’s quote, $1,663, was nearly $600 higher than the one a local supplier sent, $1,016.

“Quite a lucrative deal they have,” the president and business manager of the city’s custodian union, Robert Troeller, said. Mr. Troeller’s union, Local 891 at the International Union of Operating Engineers, represents custodian engineers, who act as superintendents for each of the city’s 1,200 school buildings, managing the school’s supply and physical plant budgets.

Comparison shopping used to be the norm, but after working with the management consulting firm Accenture, the Department of Education in 2003 switched to a model that business supply experts said is becoming popular at many businesses. Aiming to slash costs and hassles, the integrated supply model winnows hundreds of competitive bidding processes custodians hold with thousands of suppliers to a single effort by the city to find one “integrated supplier.”

Twelve companies wrote proposals to serve in that role, and SDI — whose clients also include the University of Pennsylvania and Siemens — was the “legitimate winner,” the Department of Education’s executive director for contracts and purchasing, David Ross, said.

“We’re going out competitively to assure that we get good value for the taxpayer dollar,” Mr. Ross said. “And I guess the proof is in the pudding, because if somebody were able to offer us better value, they would have.”

Peter Soh, a spokesman for Accenture, the firm that recommended the change, said the city’s new approach to “strategic sourcing” has saved the city tens of millions of dollars.

Mr. Ross said complaints about the catalog are “not uncommon.”

“When you have hundreds, maybe thousands of items in a catalog, there’s no question that you could find some of those items in a catalog at a lower price elsewhere. The question is, at what expense?” he said. “I don’t think custodians or principals or teachers should be wasting their time trying to find 20% off on a $10 item. The time it would take to make a phone call or go out and get something as opposed to just placing an order through the DOE system probably doesn’t merit the savings.”

He said he could not cite a specific dollar amount in savings.

A professor at Columbia Business School who studies supply management, Garrett van Ryzin, said relationships such as SDI’s can have impressive results for efficiency, but only if executed carefully. “The devil is in the details,” he said. “It can be anywhere from a cozy, my-Uncle-Bob-owns-a-company and this is some corrupt relationship that doesn’t do anybody any good, to potentially a kind of state of the art way of dealing with a supplier.”

He said one key is having an “open-book” relationship between the supplier and the client, where each side has access to the other’s books to ensure neither is being gouged. A Department of Education spokeswoman, Marge Feinberg, said the department reviews pricing “up front and throughout the year.”

“Where there’s evidence that pricing is less than favorable, we either get SDI to reduce the catalog price or take a credit,” she said.

Mr. van Ryzin said a close relationship is also useful if it helps the supplier find innovative ways to meet the client’s needs.

Invoices shared with the Sun show that SDI acts as a middleman in a way that can distance interactions between custodians and suppliers, working with firms the custodians once worked with directly rather than letting the custodians arrange pricing and delivery themselves.

Only one portion of a custodian’s budget, the supply allocation, is restricted by the SDI contract. Mr. Troeller said those allocations range from a few thousand dollars to $20,000, depending on the size of the school. The rest of the custodial budget is discretionary. A majority of that money goes to paying salaries for janitors and other cleaning staff, but engineers said they also use some of the money to buy extra supplies after their supply allocations run out.

Purchases of more than $250 from that budget must be competitively bid.

Several items— including a DeWalt drill bit set, a Crescent adjustable wrench, and Rayovac AAA batteries — were priced lower in the SDI catalog than they were at local stores.