Unrelated Parallel Machines Scheduling Problem (U-PMSP) is a category of discrete optimization problems in which various manufacturing jobs are assigned to identical parallel machines at particular times. In this paper, a specific production scheduling task the U-PMSP with Machine and Job Dependent Setup Times, Availability Constraint, Time Windows and Maintenance Times is introduced. Machines with different capacity limits and maintenance times are available to perform the tasks. After that our problem, the U-PMSP with Machine and Job Dependent Setup Times, Availability Constraints, Time Windows and Maintenance Times is detailed. After that, the applied optimization algorithm and their operators are introduced. The proposed algorithm is the genetic algorithm (GA), and proposed operators are the order crossover, partially matched crossover, cycle crossover and the 2-opt as a mutation operator. Then we prove the efficiency of our algorithm with test results. We also prove the efficiency of the algorithm on our own data set and benchmark data set. The authors conclude that this GA is effective for solving high complexity parallel machine problems.

This issue is a typical NP-hard problem for an unrelated parallel machine scheduling problem with makespan minimization as the goal and no sequence-related preparation time. Based on the idea of tabu search (TS), this paper improves the iterative greedy algorithm (IG) and proposes an IG-TS algorithm with deconstruction, reconstruction, and neighborhood search operations as the main optimization process. This algorithm has the characteristics of the strong capability of global search and fast speed of convergence. The warp knitting workshop scheduling problem in the textile industry, which has the complex characteristics of a large scale, nonlinearity, uncertainty, and strong coupling, is a typical unrelated parallel machine scheduling problem. The IG-TS algorithm is applied to solve it, and three commonly used scheduling algorithms are set as a comparison, namely the GA-TS algorithm, ABC-TS algorithm, and PSO-TS algorithm. The outcome shows that the scheduling results of the IG-TS algorithm have the shortest manufacturing time and good robustness. In addition, the production comparison between the IG-TS algorithm scheduling scheme and the artificial experience scheduling scheme for the small-scale example problem shows that the IG-TS algorithm scheduling is slightly superior to the artificial experience scheduling in both planning and actual production. Experiments show that the IG-TS algorithm is feasible in warp knitting workshop scheduling problems, effectively realizing the reduction of energy and the increase in efficiency of a digital workshop in the textile industry.

This paper aims to develop new highly efficient PSC-algorithms (algorithms that contain a polynomial-time sub-algorithm with sufficient conditions for the optimality of the solutions obtained) for several interrelated problems involving identical parallel machine scheduling. These problems share common basic theoretical positions and common principles of their solving. Two main intractable scheduling problems are considered: (“Minimization of the total tardiness of jobs on parallel machines with machine release times and a common due date” (TTPR) and “Minimising the total tardiness of parallel machines completion times with respect to the common due date with machine release times” (TTCR)) and an auxiliary one (“Minimising the difference between the maximal and the minimal completion times of the machines” (MDMM)). The latter is used to efficiently solve the first two ones. For the TTPR problem and its generalisation in the case when there are machines with release times that extend past the common due date (TTPRE problem), new theoretical properties are given, which were obtained on the basis of the previously published ones. Based on the new theoretical results and computational experiments the PSC-algorithm solving these two problems is modified (sub-algorithms A1, A2). Then the auxiliary problem MDMM is considered and Algorithm A0 is proposed for its solving. Based on the analysis of computational experiments, A0 is included in the PSC-algorithm for solving the problems TTPR, TTPRE as its polynomial component for constructing a schedule with zero tardiness of jobs if such a schedule exists (a new third sufficient condition of optimality). Next, the second intractable combinatorial optimization problem TTCR is considered, deducing its sufficient conditions of optimality, and it is shown that Algorithm A0 is also an efficient polynomial component of the PSC-algorithm solving the TTCR problem. Next, the case of a schedule structure is analysed (partially tardy), in which the functionals of the TTPR and TTCR problems become identical. This facilitates the use of Algorithm A1 for the TTPR problem in this case of the TTCR problem. For Algorithm A1, in addition to the possibility of obtaining a better solution, there exists a theoretically proven estimate of the deviation of the solution from the optimum. Thus, the second PSC-algorithm solving the TTCR problem finds an exact solution or an approximate solution with a strict upper bound for its deviation from the optimum. The practicability of solving the problems under consideration is substantiated.

We consider the real-life problem of planning tasks for teams in a corporation, in conditions of some restrictions. The problem takes into account various constraints, such as for instance flexible working hours, common meeting periods, time set aside for self-learning, lunchtimes and periodic performance of tasks. Additionally, only a part of the team may participate in meetings, and each team member may have their own periodic tasks such as self-development. We propose an algorithm that is an extension of the algorithm dedicated for scheduling on parallel unrelated processors with the makespan criterion. Our approach assumes that each task can be defined by a subset of employees or an entire team. However, each worker is of a different efficiency, so task completion times may differ. Moreover, the tasks are prioritized. The problem is NP-hard. Numerical experiments cover benchmarks with 10 instances of 100 tasks assigned to a 5-person team. For all instances, various algorithms such as branch-and-bound, genetic and tabu search have been tested.

This paper uses a Genetic Algorithm (GA) to reduce total tardiness in an identical parallel machine scheduling problem. The proposed GA is a crossover-free (vegetative reproduction) GA but used for four types of mutations (Two Genes Exchange mutation, Number of Jobs mutation, Flip Ends mutation, and Flip Middle mutation) to make the required balance between the exploration and exploitation functions of the crossover and mutation operators. The results showed that use of these strategies positively affects the accuracy and robustness of the proposed GA in minimizing the total tardiness. The results of the proposed GA are compared to the mathematical model in terms of the time required to tackle the proposed problem. The findings illustrate the ability of the propounded GA to acquire the results in a short time compared to the mathematical model. On the other hand, increasing the number of machines degraded the performance of the proposed GA.