## 1 Introduction  
In today's competitive manufacturing industry, there is a constantly increasing demand for customized products, especially within advanced, capital intensive, large-equipment industries [1]. In order to respond to this demand, companies must manufacture and assemble based on specific customer requirements. This type of manufacturing strategy is called engineer-to-order (ETO). ETO products are manufactured and assembled in low volumes to satisfy individual customer's specifications [2]. Typical products include steam turbines and boilers for the power generation industry [3]. A typical ETO product can take months to years to complete and it has strict, complex ordered assembly relationships between components [4]. The customers of ETO products are very strict with delivery time, and late delivery can result in huge penalties. ETO companies need to ensure that products are delivered in a timely manner [5]. In ETO companies, the most important phase is assembly [6]. Assembly accounts for almost 50% of the total production time, for 20% of the total production cost, and for 30% to 50% of the labor cost [7]. Due to the complexity of assembly, the assembly process of each product is treated as a unique engineering project with necessary lead-time [8]. That is the reason why we use the project scheduling methodology in this study [9]. One company performs not just one project, but two or more projects in parallel. Some projects may have to be simultaneously executed in a certain time period. The projects are independent of each other, but they are located at different work centers, competing for workers with different qualifications, working space, equipment, and tools. The layout of a typical ETO product assembly shop is shown in Figure 1. For a large company, multiple projects planned on the same timeline may have thousands of tasks, and frequent conflicts are inevitable. The high level of customization and long task duration of ETO products requires the production plan to be defined and the details disclosed. It is necessary to schedule and balance the utilization of resources under the guarantee of meeting the delivery deadline of all products [4]. In order to react to the high complexity and the large amount of customization in ETO products, the assembly of ETO products is mainly performed by a group of workers. The working situation of the typical ETO product assembly shop is shown in Figure 2. The workers have a lot of experience and are familiar with the assembly process. The task duration is not defined in advance, but depends on the number and the skill level of the workers assigned to the task. There is a downward substitutability in the hierarchical nature of the workforce such that a higher qualified worker type can substitute for a lower qualified one with a higher cost, but not vice-versa [10]. As tasks in the ETO assembly process are manual ones assisted by hand tools or light-weight equipment, the workforce resource has replaced capital, facilities, raw material, and other kinds of manufacturing resources to become the most important resource in the ETO assembly process. If workforce resources can be utilized efficiently, the idle time and production cost can be reduced. The importance of the workforce has been widely recognized, especially in labor-intensive industries. Usually, companies that manufacture ETO products have some kind of estimates of the work content of the assembly tasks based on historical data or the analysis of the work content, and the work content estimate is chosen as the basis in our study [11]. Figure 1: The layout of a typical engineer-to-order (ETO) product assembly shop. Project scheduling is well-known as the project sequencing problem and one of the most important areas in the manufacturing process [12]. The scheduling of ETO products is much more difficult than that of mass production, because different ETO products have different processing routes, different structures, and different due dates, and multiple products need to be produced in parallel.