A multi-objective mathematical model and evolutionary algorithm for the dual-resource flexible job-shop scheduling problem with sequencing flexibility

In industry, skilled workers typically operate a specific set of machines; therefore, managers need to decide on the most efficient assignments for machines and workers. However, they also need to balance the workload among workers while meeting deadlines. In this research, the dual resource-constraint flexible job-shop scheduling problem with sequencing flexibility (DR-FJSPS) is formulated. The DR-FJSPS deals with decisions made regarding machines, worker assignments, and sequencing flexibility simultaneously in a flexible job-shop environment. Sequencing flexibility is studied in this paper, and precedence relationships of the operations are defined by a directed acyclic graph instead of the traditional linear order. The DR-FJSPS is modelled as a multi-objective problem to minimize conflicting objectives as makespan, maximal worker workload, and weighted tardiness. Due to the intractability of the DR-FJSPS, an elitist non-dominated sorting genetic algorithm (NSGA-II) with an innovative operator is developed to solve this problem efficiently. The algorithm provides a set of Pareto-optimal solutions that decision-makers can use to evaluate trade-offs between conflicting objectives. Tailor-made instances are introduced to demonstrate the applicability of the model and algorithm. A multi-random-start local search algorithm is developed to assess the effectiveness of the adapted NSGA-II. In addition to that, the multi-objective model is solved using the weighted sum approach. A comparison of the solutions demonstrates that the modified NSGA-II provides a non-dominated efficient set in a reasonable length of time. The benefits of the proposed solution methods, such as defining their everyday schedules, adapting schedules according to management needs, prioritization of makespan, on-time deliveries, and workers’ workload simultaneously, are highlighted.