The Detroit auto makers lost out on as much as $144 in operating income on every vehicle they produced last year due to strained relationships with their parts suppliers, according to an annual study.

Ford Motor Co., General Motors Co. and Fiat Chrysler Automobiles NV chalked up some of the lowest scores in the annual supplier relations survey published by Planning Perspectives Inc., an independent auto maker-supplier consultancy based in Birmingham, Mich. Toyota Motor Corp. and Honda Motor Co. led the pack based on data collected from 435 participating suppliers.

The study highlights how strained relationships with parts makers can financially sting an auto maker as each is trying to wring costs from operations while securing the latest technologies to increase competitiveness. Suppliers traditionally will take their latest developments to auto makers where they have the best working relationships.

"We think that top management is working their butts off to improve these relationships, but it isn't getting down to the front lines within their organizations—the buyers," John Henke Jr., chief executive of Planning Perspectives, said. "They have to be motivated to improve their behavior toward the suppliers. Calling a supplier up on the phone and demanding they lower their prices is not what we call good relationships."

FCA and GM both scored 224 out of a possible 500 points, costing them an estimated $144 per vehicle, In total, GM lost out on $750 million, while FCA missed a $661 million increase.

Nissan Motor Co., with a score of 244, left $131 per vehicle on the table, while Ford scored 261 and missed out on $116 per vehicle.

Both auto makers could have bumped their total operating income by $261 million and $354 million, respectively.

As a group, the four auto makers lost out on a $2.03 billion boost to their operating income.

"While there is more work to do, we have set clear objectives and implemented tools to achieve mutual business goals while building strong relationships between GM and our supplier partners," GM purchasing chief Steve Kiefer said in a statement.

FCA purchasing chief Tom Finelli said the company recently has reorganized to focus on supplier relations globally.

It should "help us drive consistent behaviors across the regions as well as throughout all the levels of the organization," he said.

Ford and Nissan weren't immediately available to comment.

Toyota scored 336, while Honda was close behind at 330. Both companies implemented new measures in 2013 after their scores had dropped.

Write to Jeff Bennett at jeff.bennett@wsj.com

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