2. Manufacturing Scheduling

The recent development and advances in technology as well as the market demand for highly customized and personalized products have been pushing manufacturing companies to develop new solutions to become more dynamic and flexible to face these emergent trends and the quickly changing markets.

Most of the existing production systems are based on automated systems built to achieve high performances and high delivery rates, coming from the second and third industrial revolutions, but have no capability regarding autonomy, adaptation, and flexibility. Consequently, a group of expert technicians is needed to solve a problem each time a disturbance occurs in the production line. In addition to these restrictions, the emergence of new manufacturing paradigms, the appearance of new technologies and processes, the cheaper development of IT infrastructures, and the emerging possibility of digitization, among other factors, led to a disruption in the industrial scene.

The fourth industrial revolution—under the abbreviation of I4.0 in Europe, industrial internet or smart manufacturing in the USA, smart factory in South Korea, and made in China 2025 in China [1,2,3]^[1][2][3]—is happening now but started with first steps several years ago. It makes use of different emerging technologies and paradigms such as AI, cyber-physical systems, Internet of Things (IoT), cloud computing, digital twin, agent-based systems, among others, and allows the development of more dynamic and agile approaches to improve the efficiency of manufacturing systems [4,5]^[4][5]. The capability to collect, store, and analyze data was hugely improved, which makes it possible for manufacturers to better understand their equipment, their products, their manufacturing processes, their customers, their workers, and even their competitors, which increases the smartness degree in manufacturing systems, and leads to a better interconnection between the different systems.

Smart manufacturing comprises both horizontal and vertical integrations. Horizontal integration connects the different players of the value chain along the entire product lifecycle, which allows the optimization of the production process from suppliers to manufacturers and end users. The digitization of data and processes allow the system to be shared, analyzed, and to dynamically adapt in real-time during the manufacturing process ^[6]. Vertical integration combines different hierarchical levels in the production process within the factory, from working stations and human workers on the shopfloor to software technology, such as manufacturing execution systems and marketing activities ^[1].

However, with all the recent developments in technology, one of the main challenges in production systems continues to be the development of scheduling solutions to deal with all the planning information as well as unpredictable events on distributed production processes ^[7]. These challenges occur not only in the development phase, due to the implementation complexity of the systems, but also in the design phase. Nevertheless, several research articles have discussed and proposed manufacturing scheduling approaches under the smart manufacturing umbrella, such as [5,8,9,10,11,12,13,14]^{[5][8][9][10][11][12][13][14]}.

Scheduling has been largely applied in many different areas such as energy consumption [15^[15][16],16], transportation ^[17], staff distribution ^[18], and manufacturing [19,20]^[19][20], among other areas, to help the industries to plan their activities. For each scheduling solution for different areas of application, specific algorithms and mathematical models should be developed, since it is not achievable to develop a one-fit-all solution ^[18].

In manufacturing, scheduling can be considered as a process of arranging, controlling, and optimizing work on the shopfloor ^[21]. Sometimes, parts need to wait too long on the shopfloor due to limited resources to manage them or due to weak planning of the system. Production scheduling aims to efficiently allocate the available resources and reach a predefined goal since scheduling is a process of optimizing work and time. A scheduling problem may be described as an environment composed of one or more machines, with specific characteristics, and a set of jobs (products with one or more operations that will be processed by the machines). The goal is to optimize an objective or group of objectives by assigning each job to a specific machine in a specific time in order to be processed, while conflicts between operations are avoided ^[22]. Succinctly, scheduling determines what is going to be carried out and where this will happen and with what resources.

Manufacturing processes can be very dynamic. Even in environments where the processes happening on the shopfloor are always the same and known in advance, they can be affected by one or another disturbance that forces all production to stop until the problem is solved. Although some years ago manufacturing systems were not ready for this change and were not efficient enough to deal with these disturbances, nowadays, manufacturing is becoming more adaptive, dynamic, and highly flexible to meet market requirements and adjusts to every change that may improve the process. This is even more important in the era of the emergence of mass individualization, where the disturbances in the production line can be even more significant. In order to minimize the unexpected events and improve the overall production performance, one of the key challenges is to develop reliable and robust scheduling solutions. I4.0 scheduling approaches should be designed to deal with these smart and dynamic manufacturing systems and their new technologies.

Although this has been studied for decades, complex and robust scheduling solutions are frequently disregarded in real manufacturing scenarios, where they are sometimes carried out manually, on data sheets, or on simple or limited software programs. These solutions frequently lead to significant errors since they do not consider the current status of the shopfloor and are not adaptive to different scenarios. Though, more robust solutions are not implemented mainly due to the complexity of implementing them in large-scale systems with real-time constraints, since it is considered to be a non-deterministic polynomial-time hard combinatorial optimization problem which is quite difficult to reach an optimal solution for with traditional optimization techniques ^[23]. However, scheduling optimization has direct impacts on the production efficiency, sustainability, and also on costs of manufacturing systems and must be developed to its full capabilities [5,24]^[5][24].

Most researchers assume some constraints, such as that resources are always available or that the processing time of a job is known in advance and remains constant during the entire process, but in real systems this is not always true.

Disturbances may occur during the production process, which lead to a rescheduling that should be performed as fast as possible. These disturbances can be the arrival of new orders, canceled orders, or machine breakdowns which lead to the machine’s unavailability, or some emergency event [5,25]^[5][25]. Additionally, job processing times may increase over time, which is a situation knowing as deterioration of resources in scheduling problems ^[26], or even decrease when there is a learning factor or the workload can be reinforced ^[27]. Consequently, to adapt to the manufacturing system, it is vital that the scheduling process is dynamic and quick to avoid unnecessary system downtimes and costs.

In flexible and agile manufacturing environments, products can have several different feasible processing plans and most of the time it is very hard to find a good one for all the products. Production scheduling is a very important decision making in a factory and it can be a difficult problem depending on the number of calculations necessary to obtain a schedule that gives an optimal or near-optimal solution for the given objectives ^[19].

The production scheduling optimization problem may be decomposed into several categories, according to the factory type. There are several environments depending on the machine’s layout and the flow of the products, which can mainly be divided into: flow shop, which is composed of a set of machines arranged in series, one after another, where the products follow the same execution order through all the machines ^[28]; job shop, which can be described as a set of machines that should process a set of different jobs, where each job is composed of a group of operations to be processed in a given order, so each product may have a different route ^[29]; open shop, composed of machines that can perform all operations and thus there are no fixed routes for each job, which consist of unordered operations that do not have precedence constraints ^[30]. Usually, the essence of these is that several jobs (products with one or more operations to be processed) are assigned to a set of machines at specific times, satisfying some constraints, while trying to minimize the makespan, i.e., the time between the moment that the first job started until the moment that the last job is finished, or optimize some other objective, such as the production due dates, or the number of finished products, or the load balancing, which refers to assigning the task among different resources equally to provide better quality service, in the case of human workers, and reduce idle times and work-in-process in the case of machines [23,26,31,32,33]^{[23][26][31][32][33]}.

Moreover, to produce an optimized solution, restrictions regarding product parts, material availability, machines or work capacity, start and due dates, costs, distribution requirements, or setup efficiency conditions must be known ^[34].