Multi-local search-based general variable neighborhood search for distributed flow shop scheduling in heterogeneous multi-factories

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Heterogeneous multi-factories in different regions bring a challenge to managers in distributed production scheduling. This paper studies a distributed flow shop scheduling problem in heterogeneous multi-factories (DHFSP) with different processing capabilities of machines and electricity prices in multi-factories. The mixed-integer linear programming model (MILP) of the DHFSP is established, where different time-of-use electricity prices and states of machines (running and idle) are integrated. The proposed MILP model is based on position and time-indexed variables where the position of a job in the sequence is modeled and the time horizon is discretized into time slots. Every job on a machine corresponds to a series of position and time-indexed decision variables A multi-local search-based general variable neighborhood search (MGVNS) is presented to address the DHFSP. The earliest due date rule and a distributed version of NEH (Nawaz–Enscore–Ham) are combined to generate a promising initial solution. Four efficient greedy local search methods that move jobs between heterogeneous multi-factories and within the critical factory are presented. The properties of DHFSP are used to reduce the computing time of objectives. A right-shifting procedure is presented to save the electricity cost by considering the total electricity cost consumed by the processing of the jobs and the idle state of the machine between two adjacent jobs. The experiments and investigation are provided on large-sized instances to demonstrate the effectiveness and efficiency of MGVNS. The effectiveness of initialization, accelerated methods, right-shifting procedure, and local search methods are also significant. From the managerial insights, the proposed model can be extended to many real scenarios, such as semiconductor or automobile production, by integrating specific production constraints. The proposed model and scheduling methods provide an economical way to generate efficient schedules to balance the production efficiency and cost.