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The paper describes an algorithm for finding a quasi-optimal production plan for complex production systems that involve moving products through a chain of linked processes with varying resource sets. The general problem of optimizing a network of manufacturing enterprises is considered: a set of enterprises producing homogeneous products is modeled during a process consisting of a set of sequential operations arranged in a strict sequence. Standard methods for solving production planning problems are considered. According to the analytical review, most planning tasks in such systems are resolved using original techniques. For this reason, a universal heuristic algorithm was proposed. An algorithm with two branches is also proposed for two cases: for the case of a known constraint in the system and for an alternative case. The algorithm is focused on application in production systems in which the acquisition of empirical data is complicated by the large volume, heterogeneity, and limited reliability of data. In such systems, quasi-optimization in accordance with the proposed algorithm will allow for obtaining a satisfactory result with the permissible and required computing power. The algorithm can be classified as a greedy algorithm. It is partly based on local optimization and performs well for production with a long cycle and a small number of products. For this reason, the approach is recommended for heavy industry, shipbuilding, aircraft manufacturing, and other productions with a long cycle.