Kelly Springfield Tire Co., Cumberland, won first place yesterday in an international management science competition that honors achievements in productivity.

Third place in the contest, sponsored by the Operations Research Society and Institute of Management Sciences, was awarded to a U.S. Army manpower planning program developed by General Research Corp., of McLean.

The Maryland tire firm, a subsidiary of Goodyear Tire & Rubber Co., was one of six finalists for the top award. Presentations by the six firms were made to a panel of judges here over the past two days.

Robert King and Robert Love Jr., representing a team of Kelly Springfield scientists, were awarded a $6,000 cash prize for developing and implementing a system coordinating sales forecasting, production schedules, inventory control and distribution that boosted the tire manufacturer's profits by between 7 and 18 percent.

After the new system was installed in 1976, customer service improved while the average inventory required to meet demands decreased by 19 percent. In addition, the Cumberland firm's share of the auto and truck tire replacement market increased at a time of slow tire industry expansion.

The other award to a local firm went to Betty Holz and retired Army Brig. Gen. James Wroth, of General Research, who developed and implemented an Army computer-based program to improve combat readiness by 23 percent. They were awarded $1,500.

Using the General Research computer system, 5,000 fewer persons are required to maintain specified combat readiness and this translates into annual savings of some $50 million, because of reduced training requirements.

Second prize yesterday was awarded to the Ingalls Shipbuilding subsidiary of Litton Industries, for use of a contract negotiation and litigation planning model developed by Kenneth Cooper of Pugh-Roberts Associates. Cooper was awarded $1,500 for his work, which enabled Ingalls to avert near bankruptcy in achieving a negotiated settlement on a disputed contract with the U.S. Navy, which also should reduce future shipbuilding costs.