The scheduling of jobs in functional production systems (job shop scheduling) is a frequently researched area of the literature. However, the management of material handling in functional production systems receives little attention. Publications in connection with that can scarcely be found, even though in the case of small- and medium-sized companies the problem is definitely topical. For them, solving this problem can mean an opportunity for improvement. This paper presents an expert knowledge-based method that contains novelties and uses fuzzy signatures to solve this problem. The performance of the proposed method is compared with the performance of other methods which are common in the industry or in the literature (mixed-integer linear programming, priority dispatch rules, human decisions). We present the construction of the fuzzy signature-based method and the aggregations used. As a novelty, the method of selecting the proper weights for state-dependent dynamic weighting is presented.