This paper considers an unrelated parallel machine scheduling problem with variable maintenance based on machine reliability to minimize the maximum completion time. To obtain the optimal solution of small-scale problems, we firstly establish a mixed integer programming model. To solve the medium and large-scale problems efficiently and effectively, we develop a hybrid discrete spider monkey optimization algorithm (HDSMO), which combines discrete spider monkey optimization (DSMO) with genetic algorithm (GA). A few additional features are embedded in the HDSMO: a three-phase constructive heuristic is proposed to generate better initial solution, and an individual updating method considering the inertia weight is used to balance the exploration and exploitation capabilities. Moreover, a problem-oriented neighborhood search method is designed to improve the search efficiency. Experiments are conducted on a set of randomly generated instances. The performance of the proposed HDSMO algorithm is investigated and compared with that of other existing algorithms. The detailed results show that the proposed HDSMO algorithm can obtain significantly better solutions than the DSMO and GA algorithms.

This paper addresses the permutation flowshop scheduling problem with peak power consumption constraints (PFSPP). The real-time power consumption of the PFSPP cannot exceed a given peak power at any time. First, a mathematical model is established to describe the concerned problem. The sequence of operations is taken as a solution and the characteristics of solutions are analyzed. Based on the problem characteristics, eight heuristics are proposed, including balanced machine-job decoding method, balanced machine-job insert method, balanced job-machine insert method, balanced machine-job group insert method, balanced job-machine group insert method, greedy algorithm, beam search algorithm, and improved beam search algorithm. Similarly, the canonical artificial bee colony algorithm and iterated local search algorithm are modified based on the problem characteristics to solve the PFSPP. A large number of experiments are carried out to evaluate the performance of new proposed heuristics and metaheuristics. The results and discussion show that the proposed heuristics and metaheuristics perform well in solving the PFSPP.

This paper deals with the problem of scheduling jobs in a parallel flow shop environment without buffers between machines and with sequence-dependent setup times in order to minimize the maximum completion time of jobs. The blocking constraint normally leads to an increase in the maximum completion time of jobs due to the blockage of machines, which can increase even more so when setup times are considerable. Hence, the heuristic to solve this problem must take into account these specificities in order to minimize the timeout of machines. Because the procedures designed to solve the parallel flow shop scheduling problem must deal not only with the sequencing of jobs but also with their allocation to the flow shops, 36 heuristics have been tested in this paper, of which 35 combine sequencing rules with allocation methods while the last one takes a different approach that is more related to the nature of this problem. The computational evaluation of the implemented heuristics showed good performance of the heuristic designed especially for the problem (RCP0) when the setup times are considerable. Furthermore, the evaluation has also allowed us to propose a combined heuristic that leads to good solutions in a short CPU time.

Cross-docking is a logistics strategy that consolidates the products of different inbound trucks according to their destinations in order to reduce the inventory, order picking, and transportation costs. It requires a high level of collaboration between inbound trucks, internal operations, and outbound trucks. This article addresses the truck-to-door sequencing problem. Truck-to-door sequencing has been studied by some researchers in different titles such as scheduling and sequencing of inbound and outbound trucks of the cross-dock center. However, previous studies have not considered repeat truck holding pattern. Therefore, it is important to determine the doors and the sequence of the inbound and outbound trucks that should be assigned in a cross-dock center. This paper focuses on optimizing truck-to-door sequencing with consideration of repeat truck holding pattern in inbound trucks in order to minimize makespan. Two methods are considered to solve this problem, including mathematical modeling and a heuristic algorithm. In the first method, a mixed integer-programming model is developed to minimize the makespan. Then, GAMS software is used to solve small-scale problems. In the second approach, a heuristic algorithm is developed to find near-optimal solutions within the shortest time possible and the algorithm is used to solve large-scale problems. The results of the mathematical model and the heuristic algorithm are slightly different and show the good quality of the presented heuristic algorithm.

The literature on flow shop scheduling has extensively analyzed two classes of problems: permutation and non-permutation ones (PFS and NPFS). Most of the papers in this field have been just devoted on comparing the solutions obtained in both approaches. Our contribution consists of analyzing the structure of the critical paths determining the makespan of both kinds of schedules for the case of 2 jobs and m machines. We introduce a new characterization of the critical paths of PFS solutions as well as a decomposition procedure, yielding a representation of NPFS solutions as sequences of partial PFS ones. In structural comparisons we find cases in which NPFS solutions are dominated by PFS solutions. Numerical comparisons indicate that a wider dispersion of processing times improves the chances of obtaining optimal non-permutation schedules, in particular when this dispersion affects only a few machines.

Flow shop scheduling problems with rudimentary criteria of minimum makespan are the most important investigated problems in the field of scheduling. Generally during the process of generating an optimal sequence, multiple partial sequences claiming the optimal value of makespan are observed. In this paper a novel tie-breaking rule to select one of the best optimal sequences out of all possible partial sequences is developed which then applied to Nawaz-Enscore-Ham (NEH) heuristic to solve the scheduling problems in permutation flowshop without increasing the computational complexity. The performance of proposed heuristic is tested with other existing tie-breaking heuristics of similar complexity over Taillard and VRF's instances. Computational results reveal that in terms of solution quality, the proposed heuristic outperforms over the other NEH based heuristics of the same complexity reported in literature.

This paper addresses the minimization of makespan for the permutation flow shop scheduling problem with blocking and sequence and machine dependent setup times, a problem not yet studied in previous studies. The 14 best known heuristics for the permutation flow shop problem with blocking and no setup times are pre-sented and then adapted to the problem in two different ways; resulting in 28 different heuristics. The heuristics are then compared using the Taillard database. As there is no other work that addresses the problem with blocking and sequence and ma-chine dependent setup times, a database for the setup times was created. The setup time value was uniformly distributed between 1% and 10%, 50%, 100% and 125% of the processing time value. Computational tests are then presented for each of the 28 heuristics, comparing the mean relative deviation of the makespan, the computational time and the percentage of successes of each method. Results show that the heuristics were capable of providing interesting results.

This study proposes a simheuristic that hybridizes NSGA-II with Monte Carlo simulation to address a stochastic flexible flow shop problem featuring stochastic machine breakdowns. In real-world scenarios, machine breakdowns frequently occur, resulting in negative impacts such as time loss, late deliveries, decreased productivity, and order accumulation. Therefore, this study considers the times between failures and times to repair as stochastic parameters. Multiple objectives are concurrently addressed, including expected makespan, expected tardy jobs, and the standard deviation of tardy jobs. A mathematical model was formulated for the deterministic version of the problem and separately solved for the minimization of tardy jobs and the minimization of makespan in small instances. Subsequently, the proposed simheuristic was executed for both small and large instances. The results demonstrate that the NSGA-II simheuristic enhances outcomes across all objective functions compared to the simulation of optimal solutions provided by the mathematical models in small instances, yielding average GAPs of -16.64%, -21.87%, and -53.33% for expected tardy jobs, expected makespan, and standard deviation of tardy jobs, respectively. Furthermore, the simheuristic outperforms the simulation of solutions given by seven dispatching rules, showcasing average improvements of 48.01%, 48.18%, and 95.63% for the same objectives, respectively.

The development and assessment of 48 heuristics for the sequence-independent setup time permutation flow shop problem (PFSP-SIST) are presented in this article. This contribution combines four tie-breaking solutions with twelve priority rules for the NEH heuristic fourth and first stage, respectively. Heuristics are evaluated on Ruiz and Allahverdi (2007) benchmark problem instances, that covers small, medium and large-size problems. The popular accelerations of Taillard were used in all tests, which were adapted to the sequence-independent setup time constraint. The aim is to reduce the longest job completion time, which is also referred to as makespan. Computation results show that using different tie-breaking strategies has a greater impact on performance than using different priority rules. The heuristics that presented the best results in relatively low computation time are those that use the FFs tie-breaking strategy procedure to the sequence-independent setup time problem.

Advanced production systems usually are complex in nature and aim to deal with multiple performance measures simultaneously. Therefore, in most cases, the consideration of a single objective function is not sufficient to properly solve scheduling problems. This paper investigates the multi-objective mixed no-idle flowshop scheduling problem. The addressed optimization case is minimizing makespan subject to an upper bound on total completion time. To solve this problem, we proposed a two-stage iterated greedy and a multi-objective constructive heuristic. Moreover, we developed a new multi-objective improvement procedure focusing on increasing the performance of the developed methods in solving the addressed problem. and a new initialization procedure. We performed several computational tests in order to compare our developed methods with the main algorithms from similar scheduling problems in the literature. It was revealed that the proposed approaches give the best results compared with other state-of-the-art performing methods.