Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Single machine scheduling with past-sequence-dependent setup times and learning effects

This paper studies a single machine scheduling problem with setup times and learning considerations. The setup times are proportional to the length of the already scheduled jobs. That is, the setup times are past-sequence-dependent. It is assumed that the learning process reflects a decrease in the process time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. The following objectives are considered: the makespan, the total completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalty. Polynomial time algorithms are proposed to optimally solve the above objective functions.     

Scheduling with multi-attribute setup times

In this paper we address a scheduling problem with multi-attribute setup times originated from the manufacturing plant of a company producing PVC sheets. In the considered scheduling problem, each job has a number of attributes and each attribute has one or more levels. Because there is at least one different level of attribute between two adjacent jobs, it is necessary to make a setup adjustment whenever there is a switch to a different job. The objective of the problem is to determine a processing sequence so as to minimize the total setup time on a single machine.     

Heuristics for minimizing maximum lateness on a single machine with family-dependent set-up times

We address the problem of scheduling a single machine subject to family-dependent set-up times in order to minimize maximum lateness. We present a number of local improvement heuristics based on the work of previous researchers, a rolling horizon heuristic, and an incomplete dynamic programming heuristic. Extensive computational experiments on randomly generated test problems compare the performance of these heuristics. The rolling horizon procedures perform particularly well but require their parameters to be set based on problem characteristics to obtain their best performance.     

An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan

This paper considers a two-stage assembly scheduling problem of N products with setup times to minimize the makespan. In this problem, there is a machining machine which produces components in the first stage. When the required components are available, a single assembly machine can assemble these components into products in the second stage. A setup time is needed whenever the machining machine starts processing components, or the item of component is switched on the machine. The problem is formulated as a mixed integer programming model, and several properties for finding optimal solutions are developed. Moreover, an efficient heuristic based on these optimal properties is proposed. A lower bound is derived to evaluate the performance of the proposed heuristic. Computational results show that the proposed heuristic can obtain a near optimal solution in almost zero time and the average percentage deviation is only 0.478.     

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.     

Single machine scheduling problem with interval processing times to minimize mean weighted completion time

The single resource scheduling problem is commonly applicable in practice not only when there is a single resource but also in some multiple-resource production systems where only one of the resources is bottle neck. Thus, the single resource (machine) scheduling problem has been widely addressed in the scheduling literature. In this paper, the single machine scheduling problem with uncertain and interval processing times is addressed. The objective is to minimize mean weighted completion time. The problem has been addressed in the literature and efficient heuristics have been presented. In this paper, some new polynomial time heuristics, utilizing the bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive computational experiments. The conducted experiments include a generalized simulation environment and several additional representative distributions in addition to the restricted experiments used in the literature. The results indicate that the proposed heuristics perform significantly better than the existing heuristics. Specifically, the best performing proposed heuristic reduces the error of the best existing heuristic in the literature by more than 75% while the computational time of the best performing proposed heuristic is less than that of the best existing heuristic. Moreover, the absolute error of the best performing heuristic is only about 1% of the optimal solution. Having a very small absolute error along with a negligible computational time indicates the superiority of the proposed heuristics.     

A study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times

We present a systematic comparison of hybrid evolutionary algorithms (HEAs), which independently use six combinations of three crossover operators and two population updating strategies, for solving the single machine scheduling problem with sequence-dependent setup times. Experiments show the competitive performance of the combination of the linear order crossover operator and the similarity-and-quality based population updating strategy. Applying the selected HEA to solve 120 public benchmark instances of the single machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness widely used in the literature, we achieve highly competitive results compared with the exact algorithm and other state-of-the-art metaheuristic algorithms in the literature. Meanwhile, we apply the selected HEA in its original form to deal with the unweighted 64 public benchmark instances. Our HEA is able to improve the previous best known results for one instance and match the optimal or the best known results for the remaining 63 instances in a reasonable time.     

Single machine scheduling problems with resource dependent release times

We consider two single machine scheduling problems with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. In the first problem, the objective is to minimize the total resource consumption with a constraint on the sum of job completion times. We show that a recognition version of the problem is NP-complete. In the second problem, the objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. We provide some optimality conditions and show that the problem is polynomially solvable.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

Multi-agent based approach for single machine scheduling with sequence-dependent setup times and machine maintenance

Scheduling of single machine in manufacturing systems is especially complex when the order arrivals are dynamic. The complexity of the problem increases by considering the sequence-dependent setup times and machine maintenance in dynamic manufacturing environment. Computational experiments in literature showed that even solving the static single machine scheduling problem without considering regular maintenance activities is NP-hard. Multi-agent systems, a branch of artificial intelligence provide a new alternative way for solving dynamic and complex problems. In this paper a collaborative multi-agent based optimization method is proposed for single machine scheduling problem with sequence-dependent setup times and maintenance constraints. The problem is solved under the condition of both regular and irregular maintenance activities. The solutions of multi-agent based approach are compared with some static single machine scheduling problem sets which are available in the literature. The method is also tested under real-time manufacturing environment where computational time plays a critical role during decision making process.     

Single machine batch scheduling problem with family setup times and release dates to minimize makespan

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an time dynamic programming algorithm and an time dynamic programming algorithm for the problem, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the setup times of all the families and the processing times of all the jobs. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme (PTAS) for the problem.     

Minimizing worst-case regret of makespan on a single machine with uncertain processing and setup times

This research addresses a single machine scheduling problem with uncertain processing times and sequence-dependent setup times represented by intervals. Our objective is to obtain a robust schedule with the minimum absolute deviation from the optimal makespan in the worst-case scenario. The problem is reformulated as a robust traveling salesman problem (RTSP), whereby a property is utilized to efficiently identify worst-case scenarios. A local search-based heuristic that incorporates this property is proposed to solve the RTSP, along with a simulated annealing-based implementation. The effectiveness and efficiency of the proposed heuristic are compared to those of an exact solution method in the literature.     

Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times

We consider a single machine scheduling problem with simple linear deterioration. Job processing times are assumed to be a simple linear function of a job-dependent growth rate and the job's starting time. We seek an optimal schedule, so as to minimize the total absolute deviation of completion times (TADC). We prove several interesting properties of an optimal schedule, and introduce two efficient heuristics which are tested against a lower bound.     

A beam search heuristic for scheduling a single machine with release dates and sequence dependent setup times to minimize the makespan

This paper considers the problem of scheduling a set of jobs subject to arbitrary release dates and sequence-dependent setup times on a single machine with the objective of minimizing the maximum completion of all the jobs, or makespan. This problem is often found in manufacturing processes such as painting and metalworking. A new mixed integer linear program (MILP) is firstly proposed. Because the problem is known to be NP-hard, a beam search heuristic is developed. Computational experiments are carried out using a well-known set of instances from the literature. Our results show that the proposed heuristic is effective in finding high quality solutions at low computational cost.     

Single machine common flow allowance scheduling with a rate-modifying activity

In this paper we consider single machine SLK due date assignment scheduling problem with a rate-modifying activity. In this model, the machine has a rate-modifying activity that can change the processing rate of machine under consideration. Hence the actual processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. We need to make a decision on when to schedule the rate-modifying activity, the optimal common flow allowance and the sequence of jobs to minimize total earliness, tardiness and common flow allowance cost. We introduce an efficient (polynomial time) solution for this problem.     

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

A note on “Single machine scheduling with time-dependent deterioration and exponential learning effect”

result in a recent paper Huang, Wang, Wang, Gao, and Wang (2010) (Computers & Industrial Engineering 58 (2010) 58–63) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect.