When Boeing engineers build a 737 airliner, they must acquire components from at least 600 companies before the plane can be put into the air.

Allocating profits to that many manufacturers can induce sky-high headaches among those whose job it is to ensure that profits are distributed fairly based on the cost-benefit analysis. The challenge has taken on increased complexity during the pandemic, as some companies have joined forces to save costs.

Help could be on the way. Relying on game theory, mathematics is used to analyze competitive business relationships.Khalid Bachkar, professor of international business and logistics, is helping to find new ways to make sense of complex business arrangements. Relying on a network of 52 computers, Bachkar and fellow researchers sought to “optimize” solutions through a practice known as distributed computing, along with the design of generated algorithms.

Distributed programming is a time-saving exercise that breaks down tasks into smaller segments. Computers work in unison, but on separate challenges. In the researchers’ solution, they used a university computer network to solve a problem that would require the processing power of about 330 state computers powered by state-of-the-art processors.

“We tested an algorithm solution that resulted in strong competitional results,” Bachkar says. “We had 1,000 players and determined the solution in six minutes and 40 seconds. According to our knowledge of the literature, we’ve never seen a game theory problem solved using distributed programming that gives such strong results.”

Bachkar and a trio of collaborators highlight their findings in “Supply network design with uncertain demand: Computational cooperative game theory approach using distributed parallel programming,” (Computers & Industrial Engineering, 2022).

The paper addresses evolving realities in the way business is done in the 21^st-century global economy, which has made for strange bedfellows.

“Even Samsung and Apple, were locked in many court battles, but they share resources,” Bachkar says. “That’s a reality. During COVID, we have seen many companies cooperating, and sharing and pooling their resources with other companies to produce products.”

Game theory and distributed parallel processing could be a winner for consumers. When companies share resources, prices are likely to drop, while the quality of products can improve, Bachkar notes.

Typically, determining a fair and stable distribution of payoffs among a coalition of manufacturers has been a “very cumbersome problem” he adds. “This is a new era that we’ve entered. Computer algorithms will solve the problems for us, with the help of mathematics, and that’s important. You’re pairing computer science with game theory and mathematical programming. We have the resources to solve problems that couldn’t be solved a couple of years ago in a short amount of time.”