The tolerance scheduling problem for maximum lateness in Industry 4.0 systems

Abstract

Industry 4.0 is a new production paradigm that promotes the digitalization of currentindustrial systems, in order to improve substantially their productivity andflexibility. This process has been pushed ahead by new technologies that arepoised to change the very concept of production, like cyber-physical systems(CPS) and the Internet of Things (IoT). CPS link the physical aspects of productionprocesses to digital platforms on which they run their virtual twins. Thus,CPS integrate in a single space the physical and digital ones (Lee et al., 2015;Platzer, 2018). The IoT, in turn, facilitates the connection of different CPS, transmittingthe real-time data collected by sensors in the physical space. The CPSwill take care of most decision-making processes, particularly routine ones(Rossit and Tohme´, 2018). All this yields smart manufacturing systems, runningautonomously. In this setting it becomes necessary to reconsider traditional planningmethods, in particular those addressing scheduling problems. The schedulingproblem is the last decision-making phase previous to the execution of productionplans. It involves a very short time horizon, relating work orders (that agree withthe requirements of customers) to physical resources of the organization (Pinedo,2016). It is natural to conclude that these aspects make scheduling decisions susceptibleto be impacted by Industry 4.0 developments (Liu et al., 2019).Scheduling problems require finding solutions to the problem of allocatingwork orders on machines, intending to achieve assignation efficiency according tosome performance metric. Once a solution has been found the schedule is executed.Then, unforeseen events and other real-world contingencies (machinebreakdowns or delays, for instance) may affect the normal implementation of theplan. Then, rescheduling processes have to be run in order to reassign jobs toother machines (Vieira et al., 2003; Ouelhadj and Petrovic, 2009).Traditional approaches do not contemplate systems in which there is a fluidinteraction between the physical and virtual aspects, where the latter can be representedby spaces of decision. The information obtained in the physical spacemodifies, in real time, the parameters of the cyberspace, leading to new decisionsthat affect the execution in the physical space. This loop is a feature of Industry4.0 technologies. But this real-time connection generates an excess of informationthat might trigger a reschedule. The tolerance scheduling problem (Rossit et al.,2019a) consists of taking up the information about unexpected events, evaluatingtheir magnitude according to the schedule being executed at the moment in whichthey arise. Rossit et al. (2019a) formulate this problem in full detail, but in thischapter, we intend to generate mixed-integer models and run numerical experimentshighlighting the virtues of this scheme of tolerances. As a base case wewill consider the single machine scheduling problem in which maximum tardinessis the objective.