Abstract
Manufacturing industry reflects a country’s productivity level and occupies an important share in the national economy of developed countries in the world. Jobshop scheduling (JSS) model originates from modern manufacturing, in which a number of tasks are executed individually on a series of processors following their preset processing routes. This study addresses a JSS problem with the criterion of minimizing total quadratic completion time (TQCT), where each task is available at its own release date. Constructive heuristic and meta-heuristic algorithms are introduced to handle different scale instances as the problem is NP-hard. Given that the shortest-processing-time (SPT)-based heuristic and dense scheduling rule are effective for the TQCT criterion and the JSS problem, respectively, an innovative heuristic combining SPT and dense scheduling rule is put forward to provide feasible solutions for large-scale instances. A preemptive single-machine-based lower bound is designed to estimate the optimal schedule and reveal the performance of the heuristic. Differential evolution algorithm is a global search algorithm on the basis of population, which has the advantages of simple structure, strong robustness, fast convergence, and easy implementation. Therefore, a hybrid discrete differential evolution (HDDE) algorithm is presented to obtain near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions. The superiority of the HDDE algorithm is highlighted by contrast experiments with population-based meta-heuristics, i.e., ant colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). Average gaps 45.62, 63.38 and 188.46 between HDDE with ACO, PSO and GA, respectively, are demonstrated by the numerical results with benchmark data, which reveals the domination of the proposed HDDE algorithm.
Highlights
Smart manufacturing has become a new competitive advantage in many countries
A hybrid discrete differential evolution (HDDE) algorithm is provided to achieve near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions
Given that no extra job is released after the completion of job J3, the remaining parts of jobs J1 and J2 are scheduled with the shortest remaining processing time (SRPT) rule
Summary
Smart manufacturing has become a new competitive advantage in many countries. governments have issued smart-manufacturing-related strategies, such as ‘Made in China 2025’ in China and ‘Industrial 4.0’ in Germany. The manufacturing process of gears can be abstracted as a jobshop scheduling (JSS) model where each job has its own release date. The optimal objectives of the JSS model are makespan that can minimize maximum machine loads, or total completion time (TCT) that can minimize work-in-process inventory. These criteria are linearized with designated weight factors for substituting bi-objective optimization. The shortest processing time, dense schedule (SPT-DS) heuristic, is proposed to achieve feasible solutions for large-scale instances. A JSS model with the TQCT criterion is established, where each job is available at its own release date This scheduling model simulates the production environment in which jobs arrive to the system over time.
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