Flexible job shop scheduling problem (FJSP) is an NP-hard combinatorial optimisation problem, which has significant applications in the real world. Due to its complexity and significance, lots of attentions have been paid to tackle this problem. In this study, the existing solution methods for the FJSP in recent literature are classified into exact algorithms, heuristics and meta-heuristics, which are reviewed comprehensively. Moreover, the real-world applications of the FJSP are also introduced. Finally, the development trends of the manufacturing industry are analysed, and the future research opportunities of the FJSP are summarised in detail.

Workflow compositions have been exploited in business process modelling to handle concurrent invocations of modular components. With the emergence of Industry 4.0 warehouse automation, which enable the integration of business processes, mechanised robots, sensor–actuators and human participants, analysis and specification of workflows become crucial. As such environments have dynamic deployments due to varying demand rates and environmental conditions, the workflow compositions are intended to be adaptable to runtime changes. In addition, monitoring the end-to-end latency and optimal runtime binding is critical in industrial deployments such as warehouse automation. The authors provide specifications in the concurrent programming language Orc that supports most commonly used workflow patterns. Complex deployments involving multiple robotic agents and business processes further require analysis of correctness, liveness, and safety properties. In order to verify the workflows, the Orc specifications are translated into workflow net representations, with verification done using the TAPAAL model checker. The advantages of deploying fine grained analysis of workflows are demonstrated over picker/delivery robots involved in warehouse operations. The envisioned set of reusable specifications may be extended and applied to a variety of Industry 4.0 deployments to handle complex workflow interactions.

The vehicle routing problem with time windows (VRPTW) is the most important and widely studied combinational optimisation problem. However, most constructive heuristics create a new path when the customer violates the constraint and cannot insert into any existing path, causing the time window constraint to be tight and generating more paths. Aiming at the above problems, a new constructive heuristic algorithm is proposed. The algorithm firstly uses the convex hull of the customer location to determine the initial seed client and reduces the redundant path; meanwhile, the calculation method of the traditional optimal insertion position is improved, and the calculation efficiency is improved to some extent; in addition, for customers who cannot insert any feasible path, the exchange operator is introduced to give the current solution a disturbance instead of directly creating a new seed client and a new path to further reduce the redundant path. The experimental results show that the algorithm can effectively solve the close time window of VRPTW for evenly distributed customers, and even provide a strict time window for evenly distributed customers and a certain amount of hybrid geographic cluster customers.

Control of hot-steel rolling mills aims at raising the levels of quality of the related industrial production and at minimising the cost of the electric energy consumed by such industrial units. This paper proposes a non-linear optimal control approach for the hot-steel rolling mill system. The non-linear dynamic model of the hot-steel rolling mill undergoes approximate linearisation around a temporary operating point which is recomputed at each iteration of the control method. The linearisation relies on Taylor series expansion and on the calculation of the system's Jacobian matrices. For the approximately linearised model of the hot-steel rolling process, an H-infinity feedback controller is designed. This controller provides the solution of the non-linear optimal control problem for the system under model uncertainty and external perturbations. For the computation of the controller's feedback gain, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a robust state estimator.