Production systems, including flexible and smart manufacturing systems, adhere to a predetermined sequence of machine operations based on the demand criterion. As the number of machines and jobs to sequence grows, the problem’s complexity also increases. To address this issue, which is considered a top priority in the industry today, agile sequencing techniques are necessary. Nonetheless, most of the present sequencing and scheduling algorithms are unable to handle the personalized machine setups found in various factories and educational facilities. Furthermore, these setups frequently have unique precedence orders for processing jobs and other limitations. This paper aims to address this pressing problem by modeling and developing an optimum job sequence for a real-life custom machine setup with precedence constraints. According to the scheduling literature, this is a variant of the permutation flow shop problem. As part of the research, the optimal job sequence is tested and validated in a simulated environment. The Nawaz, Enscore, and Ham (NEH) algorithm and the Campbell Dudek Smith (CDS) algorithm are modified to accommodate the special structure of the problem at hand and to execute the sequencing task. The NEH algorithm’s resulting sequence is compared with that of the CDS algorithm in terms of makespan time for both flow shop and job shop scenarios for this specific case study. Although NEH and CDS performed similarly in the flow-shop problem, as the product variety is consistent, NEH outperformed CDS in the job-shop scenario for combination of different ratios and different categories of product variants. A thorough sensitivity analysis is also conducted to examine the effects of various supplementary parameters on makespan time.