Scheduling in a manufacturing shop with sequence-dependent setups

In this paper, the problem of scheduling multiple jobs in a flexible manufacturing cell with multiple machine stations is addressed. Due to the large capital investments that usually characterize flexible manufacturing systems (FMS), an area of control of great interest to system users is that of maximizing the system performance through the minimization of machine idle and setup times. The magnitude of total time spent on machine setups and idle times is influenced by the availability of jobs, job mix, similarities of jobs and job scheduling procedure used. Similar jobs on the same machine require less setup times. Similarly, the use of an adequate scheduling method also reduces total idle and setup times. Such reduction improves the flow times of jobs. In this paper, a heuristic algoritm for scheduling jobs with sequence dependent setup times in a FMS is presented. The measure of performance for evaluating schedule adequacy is the production makespan.     

Two-machine robotic cell scheduling problem with sequence-dependent setup times

In this paper, we introduce a new and practical two-machine robotic cell scheduling problem with sequence-dependent setup times (2RCSDST) along with different loading/unloading times for each part. Our objective is to simultaneously determine the sequence of robot moves and the sequence of parts that minimize the total cycle time. The proposed problem is proven to be strongly NP-hard. Using the Gilmore and Gomory (GnG) algorithm, a polynomial-time computable lower bound is provided.     

Two-machine flowshop scheduling with job class setups to minimize total flowtime

This paper studies the two-machine flowshop scheduling problem with job class setups to minimize the total flowtime. The jobs are classified into classes, and a setup is required on a machine if it switches processing of jobs from one class to another class, but no setup is required if the jobs are from the same class. For some special cases, we derive a number of properties of the optimal solution, based on which we design heuristics and branch-and-bound algorithms to solve these problems. Computational results show that these algorithms are effective in yielding near-optimal or optimal solutions to the tested problems.     

A single machine carryover sequence-dependent group scheduling in PCB manufacturing

This paper considers the problem of minimizing the makespan on a single machine with carryover sequence-dependent setup times. A similar problem with multi-machine flow shop usually arises in the assembly of printed circuit boards (PCBs). This research investigates the possibility of processing all components of PCBs using just one machine. By doing so the operational costs of having multi-machines can be reduced, and as a result, finding an optimal solution might be more plausible. The objective is to minimize the maximum completion time of all board groups, commonly known as makespan. The operational constraints are such that all board types within a board group must be completely kitted, as it is traditionally performed by kitting staff, before that board group begins its assembly operation. We introduce the external setup (kitting) time and require that it be performed solely by the machine operator during the run time of the current board group, and thereby completely eliminating the need for kitting staff. The carryover sequence-dependent setup time, namely the internal (machine) setup time, is realized when a new board group is ready for assembly operation and is dependent on all of the previously scheduled board groups and their sequences. To the best of our knowledge, this is the first time the external and internal setup times are integrated in PCB group scheduling research. We develop a branch-and-bound algorithm and a lower-bounding structure. The lower bound consists of two approaches, which enable the algorithm to simultaneously reduce performing unnecessary exploration. In order to test the efficiency of the algorithm, several problem instances with different board groups have been used. The algorithm developed requires a significantly large computation time to optimally solve very large problems. Thus to speak for the efficiency in terms of solving comparable large industry-size problems, we evaluate the deviation of the algorithm from the lower bound which turns out to be very small, with an average of only 6%, in all of the problem instances considered.     

An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups

In many real-world production systems, it requires an explicit consideration of sequence-dependent setup times when scheduling jobs. As for the scheduling criterion, the weighted tardiness is always regarded as one of the most important criteria in practical systems. While the importance of the weighted tardiness problem with sequence-dependent setup times has been recognized, the problem has received little attention in the scheduling literature. In this paper, we present an ant colony optimization (ACO) algorithm for such a problem in a single-machine environment. The proposed ACO algorithm has several features, including introducing a new parameter for the initial pheromone trail and adjusting the timing of applying local search, among others. The proposed algorithm is experimented on the benchmark problem instances and shows its advantage over existing algorithms. As a further investigation, the algorithm is applied to the unweighted version of the problem. Experimental results show that it is very competitive with the existing best-performing algorithms.     

Capacitated lot-sizing and scheduling with sequence-dependent,period-overlapping and non-triangular setups

In production planning, sequence dependent setup times and costs are often incurred for switchovers from one product to another. When setup times and costs do not respect the triangular inequality, a situation may occur where the optimal solution includes more than one batch of the same product in a single period—in other words, at least one sub tour exists in the production sequence of that period. By allowing setup crossovers, flexibility is increased and better solutions can be found. In tight capacity conditions, or whenever setup times are significant, setup crossovers are needed to assure feasibility. We present the first linear mixed-integer programming extension for the capacitated lot-sizing and scheduling problem incorporating all the necessary features of sequence sub tours and setup crossovers. This formulation is more efficient than other well known lot-sizing and scheduling models.     

A simultaneous and iterative approach for parallel machine scheduling with sequence-dependent family setups

In this paper, we address a parallel machine scheduling problem to minimize the total weighted completion time, where product families are involved. Major setups occur when processing jobs of different families, and sequence dependencies are also taken into account. Considering its high practical relevance, we focus on the special case where all jobs of the same family have identical processing times. In order to avoid redundant setups, batching jobs of the same family can be performed. We first develop a variable neighborhood search algorithm (VNS) to solve the interrelated subproblems in a simultaneous manner. To further reduce computing time, we also propose an iterative scheme which alternates between a specific heuristic to form batches and a VNS scheme to schedule entire batches. Computational experiments are conducted which confirm the benefits of batching. Test results also show that both simultaneous and iterative approach outperform heuristics based on a fixed batch size and list scheduling. Furthermore, the iterative procedure succeeds in balancing solution quality and computing time.     

Intelligent controllers for bi-objective dynamic scheduling on a single machine with sequence-dependent setups

This article addresses the problem of dynamic job scheduling on a single machine with Poisson arrivals, stochastic processing times and due dates, in the presence of sequence-dependent setups. The objectives of minimizing mean earliness and mean tardiness are considered. Two approaches for dynamic scheduling are proposed, a Reinforcement Learning-based and one based on Fuzzy Logic and multi-objective evolutionary optimization. The performance of the two scheduling approaches is tested against the performance of 15 dispatching rules in four simulation scenarios with different workload and due date pressure conditions. The scheduling methods are compared in terms of Pareto optimal-oriented metrics, as well as in terms of minimizing mean earliness and mean tardiness independently. The experimental results demonstrate the merits of the proposed methods.     

Scheduling unrelated parallel machines with sequence-dependent setups

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms based on tabu search are developed to identify the best schedule that gives the minimum weighted tardiness. To enhance both the efficiency and efficacy of the search algorithms, four different initial solution finding mechanisms, based on dispatching rules, are developed. While there is no evidence of identifying solutions of better quality by employing a specific initial solution finding mechanism, the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both. Based on the extensive statistical analysis performed, the search algorithm with short-term memory and fixed tabu list size is recommended for solving small size problems, while that with long-term memory and minimum frequency for solving medium and large size problems, combined with fixed tabu list size for the former and variable tabu list size for the latter.     

Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths.     

Two-machine flow-shop scheduling with rejection

We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+?)R and a makespan value of at most (1+?)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.     

Criteria selection and analysis for single machine dynamic on-line scheduling with multiple objectives and sequence-dependent setups

Fertile opportunities exist for research involving dynamic and stochastic scheduling with multiple conflicting objectives and sequence-dependent setups as little has been reported in the literature to date. This research focuses on understanding and identifying the criteria that could be combined into a single rule using the linear weighted aggregation approach to consider the contradicting needs of cycle time and delivery accuracy. Eight dispatching criteria are compared and evaluated using discrete event simulation. In most studies, the basic concept is to combine different dispatching criterion that performs the best in each objective into a single rule but this may be insufficient. Simulation results show that it is necessary to take into account not only the criterion’s strength in optimizing a performance objective but also the degree of trade-off it has on the other conflicting performance objectives of interest. A correlation analysis of the objectives used is also presented.     

Two-machine flowshop scheduling with bicriteria problem

This paper attempts to solve a two-machine flowshop bicriteria scheduling problem with release dates for the jobs, in which the objective function is to minimize a weighed sum of total flow time and makespan. To tackle this scheduling problem, an integer programming model with N²+3N variables and 5N constraints where N is the number of jobs, is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, a heuristic scheduling algorithm is presented. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. The average solution quality of the heuristic algorithm is above 99% and is much better than that of the SPT rule as a benchmark. A 15-job case requires only 0.018 s, on average, to obtain an ultimate or even optimal solution. The heuristic scheduling algorithm is a more practical approach to real world applications than the integer programming model.     

Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups

This paper considers the problem of scheduling part families and jobs within each part family in a flowshop manufacturing cell with sequence dependent family setups times where it is desired to minimize the makespan while processing parts (jobs) in each family together. Two evolutionary algorithms—a Genetic Algorithm and a Memetic Algorithm with local search—are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The proposed algorithms use a compact representation for the solution and a hierarchically structured population where the number of possible neighborhoods is limited by dividing the population into clusters. In comparison to a Multi-Start procedure, solutions obtained by the proposed evolutionary algorithms were very close to the lower bounds for all problem instances. Moreover, the comparison against the previous best algorithm, a heuristic named CMD, indicated a considerable performance improvement.     

Two-machine open shop scheduling with secondary criteria

This paper considers two-machine open shop problems with secondary criteria where the primary criterion is the minimization of makespan and the secondary criterion is the minimization of the total flow time, total weighted flow time, or total weighted tardiness time. In view of the strongly NP-hard nature of these problems, two polynomially solvable special cases are given and constructive heuristic algorithms based on insertion techniques are developed. A strongly connected neighborhood structure is derived and used to develop effective iterative heuristic algorithms by incorporating iterative improvement, simulated annealing and multi-start procedures. The proposed insertion and iterative heuristic algorithms are empirically evaluated by solving problem instances with up to 80 jobs.     

A simulated annealing algorithm for single machine scheduling problems with family setups

Motivated by the real-life scheduling problem in a steel-wire factory in China, this paper studies the problem of minimizing the maximum lateness on a single machine with family setups. In view of the NP-hard nature of the problem, neighborhood properties of the problem are investigated. It is found that the traditional move-based neighborhood is inefficient to search. Then a new neighborhood, which is based on batch destruction and construction, is developed. A simulated annealing algorithm with the new neighborhood is proposed. Experiments are carried out on the randomly generated problems and the real-life instances from a factory in China. Computational results show that the proposed algorithm can obtain better near optimal solutions than the existing algorithm.     

Stochastic proportionate flowshop scheduling with setups

This paper addresses the problem of scheduling n jobs on a proportionate two-machine flowshop where the machines are subject to random breakdowns and setup times are considered separate from processing times. The considered performance measure is makespan. Sequences that minimize makespan with probability 1 are obtained when the first or the second machine is subject to random breakdowns without making any assumptions about downtime distributions or counting processes. It is assumed that the processing and setup times on one machine dominate the corresponding times on the other machine. In the case that processing and setup times on the first and second machines are proportionate, it is shown that the longest processing time (LPT) rule gives an optimal solution when only the first machine is subject to breakdowns, while the shortest processing time (SPT) rule yields an optimal solution when only the second machine suffers breakdowns.     

Total flow time minimization in a flowshop sequence-dependent group scheduling problem

We have developed a mathematical programming model for minimizing total flow time of the flow shop sequence dependent group scheduling (FSDGS) problem, typically classified as F_m|fmls, S_plk, prmu|∑C_j. As the problem is shown to be strongly NP-hard, a tabu search (TS) algorithm as well as a hybrid ant colony optimization (HACO) algorithm have been developed to heuristically solve the problem. A lower bounding (LB) method based on the Branch-and-Price algorithm is also developed to evaluate the quality of the metaheuristic algorithms. In order to compare the performance of metaheuristic algorithms, random test problems, ranging in size from small, medium, to large are created and solved by both the TS and the HACO algorithms. A comparison shows that the HACO algorithm has a better performance than the TS algorithm. The results of the heuristic algorithms are also compared with the results of the LB method to evaluate the quality of the solutions. The LB method presented in this paper can be generalized to solve the FSDGS problem with other objective functions.     

ABC-based manufacturing scheduling for unrelated parallel machines with machine-dependent and job sequence-dependent setup times

To date, the topic of unrelated parallel machine scheduling problems with machine-dependent and job sequence-dependent setup times has received relatively little research attention. In this study, a hybrid artificial bee colony (HABC) algorithm is presented to solve this problem with the objective of minimizing the makespan. The performance of the proposed HABC algorithm was evaluated by comparing its solutions to state-of-the-art metaheuristic algorithms and a high performing artificial bee colony (ABC)-based algorithm. Extensive computational results indicate that the proposed HABC algorithm significantly outperforms these best-so-far algorithms. Since the problem addressed in this study is a core topic for numerous industrial applications, this article may help to reduce the gap between theoretical progress and industrial practice.