## 1 Introduction
The literature for project scheduling in ETO companies is scarce [13]. To the best of our knowledge, there is only one earlier work; [PERSON] et al., studied single-project scheduling in an ETO environment [8]. The project scheduling problem and the hierarchical workforce allocation problem are interrelated as the task durations depend on the hierarchical workers assigned to each task. In order to solve these problems, decisions about both multi-project scheduling and hierarchical workforce allocation need to be dealt with together. In real production, the integrated problem is considered by the experienced project manager. The project manager makes the project plan and allocates the workers based on experience. The plan is suboptimal because the project manager can't take global information into account. There is some previous work focusing on the integrated project scheduling and worker allocation issues. [PERSON] et al. used discrete event simulation to optimize workforce allocation in assembly lines for highly customized and low-volume products [11]. [PERSON] and [PERSON] presented the mixed-integer linear program with a tight Linear Programming bound (LP-bound) to solve the problem of simultaneously scheduling IT projects and assigning multi-skilled human resources [14]. [PERSON] et al. used the genetic algorithms for single-project scheduling with multi-skilled operators [15]. [PERSON] et al. presented the mixed integer linear program to solve the integrated single-project scheduling and multi-skilled workforce allocation issue [16]. [PERSON] and [PERSON] used the bees algorithm for multi-mode, resource constrained project scheduling in the molding industry [9]. [PERSON] et al. presented the non-dominated sorting genetic algorithm II (NSGA-II) to solve hierarchical worker allocation and task assignment in a seru production system [17]. Most of the literature treats the problem as a special class of the project scheduling problem, called the multi-mode resource-constrained project scheduling problem (MRCPSP), which is a complex non-deterministic polynomial-time hard (NP-hard) problem [18]. The previous works concentrate on single-project scheduling and hierarchical workforce allocation which is not suitable for ETO assembly. As the ETO projects are assembled in parallel,  
Figure 2: Working situation of the typical engineer-to-order (ETO) product assembly shop. we extend the problem as the multi-mode resource-constrained multi-project scheduling problem (MRCMPSP). The MRCMPSP has considerable practical relevance, especially in the manufacturing industry. It is a large combinational optimization problem, but it had not received much attention until [PERSON] et al., [19] choose the subject of the Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA) Challenge 2013. A large international audience was reached: 21 teams from 14 countries and three continents participated in the competition [20; 21; 22]. The characteristics of the specified problem are defined as follows: the predecessor and successor relationships of each task in the projects are known, the due date and release time of each project are known, the total number of workers is constrained, and the task duration of each execution mode (worker team) is known. We also consider some features in the ETO assembly process to which the necessary attention has not been devoted in the research up until now, such as that floor space limits the number of concurrently-executed tasks, since the maximum number of workers that can be assigned to each task is limited by work-space. The decision problem is to determine the sequence of tasks and allocate the workers to each task in a multi-project environment in order to minimize the maximum completion time, i.e., the makespan. The scheduling problems are computationally complex and it is difficult to find an optimal solution in a reasonable amount of time. The exact methods can only be used to solve small projects which usually have less than 60 tasks [23].