Albert was the grandson of his namesake Albert Heijn (1865–1945), who began the family business with a single grocery store in Oostzaan and after extending to multiple stores laid the foundation of the same named leading Dutch retail chain, which was expanded by Albert into a multinational company. Albert introduced the supermarket store model in the Netherlands and was instrumental behind several innovations in the retail industry such as the passing of an international standard for bar codes in 1974. He was CEO of Ahold until 1989.
In 1989 he was honored with the Sydney R. Rabb Award by the Food Marketing Institute making him the first non-American to win this prestigious award.
Albert Heijn had lived at Pudleston Court in Herefordshire, England for many years when he died, and was in no way formally involved with Ahold at the time of his death, although he at times commented upon the state of the company. In Hereford he founded a new company called Eign Enterprises (named after the English pronunciation of his surname) which established shops, restaurants, hotels and other enterprises in the local region. For this he was named Honorary Freeman of the City of Hereford in 2002.