Production scheduling affects the cost of production. Hence, it is one of the important problems for operational problems. Especially for productions that require assembly precedencies, an inappropriate production schedule may be the reason for overtime decisions for a finite planning period. An inappropriate production schedule may lead to tardiness in assembly jobs as subassembly parts may not be ready on time. To meet the deadline of products, tardiness must be compensated using overtime. In this study, we considered an assembly job shop scheduling problem for multi-group jobs with sub-assembly precedences from a real-world application. Our aim is to determine the production schedule that minimizes overtime for a finite planning time interval. We developed a mixed integer programming model that minimizes the overtime complying with the delivery dates for the problem.  We conducted a case-study on a construction machinery industry in Thailand. Construction machines have several welded body parts with sub-assembly processes. Welded body parts with sub-assembly processes have cutting, bending, machining and pre-welding processes. The readiness of the welded body parts before the machine assembly is critically important for the continuity of the machine assembly line.