Normal Processing Times Research Articles

An optimal energy-efficient scheduling with processing speed selection and due date constraint in a single-machine environment

To relive the pressure of electricity grid during the peak period, time-of-use (TOU) pricing strategy has been implemented in industries to encourage manufacturers to transfer some processing tasks from peak periods to non-peak periods, and the due date of each job cannot be violated. Under these contexts, this paper addresses a speed-scaling single machine scheduling problem with due date constraint to minimize the total electricity cost (TEC). More precisely, the main innovative works are described as follows: (1) seven critical problem properties (including four theorems and three lemmas) based on different processing time window forms are formally derived; and (2) a property-based genetic algorithm (PGA) with hybrid initialization method is designed according to the characteristics of the studied problem. In the numerical experiments, the Taguchi method of design-of-experiment is employed to seek the optimal combination of four key parameters in PGA. Subsequently, the effectiveness and superiority of the proposed hybrid initialization method and problem properties are separately demonstrated by randomly generated 20 instances. After that, compared with other two traditional scheduling strategies, the proposed energy-efficient strategy can save at least 16% of TEC on average. Next, a relaxation coefficient (CR) is designed to measure the intrinsic link between TEC and the instance parameters (i.e. the due date and normal processing time). Finally, a real case is presented to verify the benefits of the proposed PGA algorithm and variable processing speeds, and the results show that the newly generated scheduling scheme based on the proposed PGA can reduce up to 46.36% of TEC compared with the existing company’s scheduling scheme.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. Furthermore, we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it. In this approach, the multi-verse optimization is adopted to find favorable solutions from the huge solution domain, while the stochastic simulation method is employed to assess them. By conducting comparison experiments on test problems, it can be verified that the developed approach has better performance in coping with the considered problem, compared to two classic multi-objective evolutionary algorithms.

Two-Agent Single Machine Scheduling with Deteriorating Jobs and Rejection

We consider two two-agent scheduling problems with deteriorating jobs and rejection. Two agents A and B compete for the usage of a single machine. The actual processing time of job J j X is p j X = b j X a + b t , X ∈ A , B , where b j X is the normal processing time of J j X , a ≥ 0 , b ≥ 0 and t denotes the starting time of J j X . A job is either rejected by paying a rejection penalty, or accepted and processed on the machine. The objective is to minimize the sum of the completion time of the accepted A -jobs and total rejection penalty of the rejected A -jobs subject to an upper bound on the sum of the given objective function f B of the accepted B -jobs and total rejection penalty of the rejected B -jobs, where f B ∈ C max B , ∑ C j B . We give dynamic programming algorithms for them, respectively. When f B = C max B , we present a fully polynomial-time approximation scheme (FPTAS) for the case a = 0 and b = 1 . When f B = ∑ C j B , a fully polynomial-time approximation scheme is also presented.

Impact of surface texture on ultrasonic wire bonding process

Due to the complex mechanisms, the ultrasonic (US) wire bonding process is usually optimized in the way of varying the processing parameters including normal force, US power, and processing time. In this study, a new way by creating different surface textures on substrates was used to alter the bonding process and improvements of the bonding process were detected. Three different surface textures including deposited strips, straight ditches at different angles, and elliptic ditches were designed and created on glass substrates. The results showed that the elliptic ditches hardly influence the bonding process while the deposited strips and straight ditches significantly alter the bonding process. The deposited strips help break the oxide scale and facilitate the transportation of oxides to the outside of contact. With the straight ditches, the oxide removal efficiency was significantly enhanced. Especially when the driving current exceeded 0.45 A, long chips from the ditches were clearly observed during the bonding process. The chips were aluminum and aluminum oxide which were continuously cut from the wire, accumulated in the ditches, pressed and squeezed to the outside of the contact. With a different angle of the straight ditches, the shape of the bonding footprint can be changed correspondingly. Compared to the bonding on smooth surfaces, the bonding strength on substrates with deposited strips and straight ditches was a few times higher and had a smaller deviation. The bonding process window was significantly enlarged.

An optimal online algorithm for single-processor scheduling problem with learning effect

This paper deals with the canonical single-processor online scheduling problem with the position-based learning effect. Specially speaking, a round of jobs arriving online over time will be processed on a single processor. Noticeably, in this model, for each job Jk, the actual processing time pkl is defined as a power function of its position l, i.e., pkl=pklβ, where pk indicates its normal processing time and β≤0 is the learning index. Our goal is to make the sum of completion times as small as possible. For this problem, we testify that there is no online algorithm with a competitive ratio of less than 2. Most notably, we design an online algorithm entitled as Delayed Shortest Normal Processing Time (DSNPT), matching the lower bound proposed by us, and hence DSNPT is optimal.

Parallel-Machine Scheduling with Step-Deteriorating Jobs to Minimize the Total (Weighted) Completion Time

In this paper, we consider the parallel-machine scheduling with step-deteriorating jobs. The actual processing time of each job deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on the case of the common job deteriorating date. For the minimization problem of total completion time, we first show that the problem is NP-hard in the strong sense. Then we propose one property of any optimal schedule. Furthermore, we prove that two special cases of common normal processing time or common penalty are polynomially solvable. For the minimization problem of total weighted completion time, we analyze the NP-hardness and present a polynomial time optimal algorithm for the case of common normal processing time and common penalty.

Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

Single batch machine scheduling with dual setup times for autoclave molding manufacturing

Batch scheduling involves a machine that can process several jobs simultaneously. The existing literature mainly focuses on the batch-size-dependent setup time. However, setup time depends not only on the batch size but also on technological characteristics. This paper investigates a single batch scheduling problem with dual quantitative and technological setup times extracted from autoclave molding production. A mixed-integer linear programming model (MILP) is established, in which the objective function is to minimize the makespan. The quantitative setup time is linear with the batch size, whereas the technological setup time is nonlinear with the occupied area of all jobs (jobs are represented by rectangles) in a batch. Three lower bounds are presented for evaluating the proposed algorithms. Then, a two-stage approximate algorithm is designed to solve the problem. The first stage concerns the normal batch processing time. In the second stage, an iterative local search method focuses on all terms in the objective function and improves the current solution’s quality. Finally, different scales of instances are designed to test the effectiveness and efficiency of the algorithms. Statistical analysis shows that the proposed algorithm in this paper can handle the problem well compared to other algorithms.

Parallel-machine scheduling with identical machine resource capacity limits and DeJong’s learning effect

ABSTRACT We consider parallel-machine scheduling with identical machine resource capacity limits and DeJong’s learning effect. Each job has a resource consumption requirement and a normal processing time. The actual processing time of a job is a function of its normal processing time, subject to DeJong’s learning effect, while the resource consumption of a job is a function of its actual processing time. Each machine has the same resource capacity limit. The objective is to maximise the minimum machine load. Considering three resource consumption functions, namely, linear, concave, and convex, we show that all three scheduling models are NP-hard and propose two approximation algorithms for the models and analyse their worst-case ratios.

The single machine scheduling problem with setup times under an extension of the general learning and forgetting effects

This paper addresses the optimization of a single machine scheduling problem with additional constraints which are sequence-independent setup times and time-dependent learning and forgetting effects. The considered objective function is to minimize the maximum completion time (makespan). We define a bivariate general learning and forgetting model consisting of two independent variables which are the sum of normal processing times of previous jobs in the schedule and the setup time of the present job. We demonstrate some global properties of an optimal schedule and prove that the problem is ordinary NP-hard by means of a polynomial transformation from a known decision problem to the decision version of the considered problem. Furthermore, we propose an integer non-linear programming model and a dynamic programming model which can be executed in pseudo-polynomial time.

Two-stage hybrid flow shop scheduling on parallel batching machines considering a job-dependent deteriorating effect and non-identical job sizes

In this paper, we investigate a specialized two-stage hybrid flow shop scheduling problem with parallel batching machines considering a job-dependent deteriorating effect and non-identical job sizes simultaneously. A novel concept of three-dimensional wasted volume based on the job normal processing time, job size, and job deteriorating rate is first proposed. Some structural properties, as well as a heuristic algorithm, are developed to solve the single parallel batching machine scheduling problem. Since the two-stage hybrid flow shop scheduling problem is NP-hard, a hybrid EDA-DE algorithm combining estimation of distribution algorithm (EDA) and differential evolution (DE) algorithm is proposed to tackle the studied problem. In addition, the Taguchi method of design of experiments (DOE) is implemented to tune the parameters of the EDA-DE. Finally, a series of computational experiments are carried out to compare the performance of the proposed hybrid EDA-DE algorithm and some recent existing algorithms from the literature, and the comparative results validate the effectiveness and efficiency of the proposed algorithm.

Scheduling Dual-Objective Stochastic Hybrid Flow Shop With Deteriorating Jobs via Bi-Population Evolutionary Algorithm

Hybrid flow shop scheduling problems have gained an increasing attention in recent years because of its wide applications in real-world production systems. Most of the prior studies assume that the processing time of jobs is deterministic and constant. In practice, jobs’ processing time is usually difficult to be exactly known in advance and can be influenced by many factors, e.g., machines’ abrasion and jobs’ feature, thereby leading to their uncertain and variable processing time. In this paper, a dual-objective stochastic hybrid flow shop deteriorating scheduling problem is presented with the goal to minimize makespan and total tardiness. In the formulated problem, the normal processing time of jobs follows a known stochastic distribution, and their actual processing time is a linear function of their start time. In order to solve it effectively, this paper develops a hybrid multiobjective optimization algorithm that maintains two populations executing the global search in the whole solution space and the local search in promising regions, respectively. An information sharing mechanism and resource allocating method are designed to enhance its exploration and exploitation ability. The simulation experiments are carried out on a set of instances, and several classical algorithms are chosen as its peers for comparison. The results demonstrate that the proposed algorithm has a great advantage in dealing with the investigated problem.

Scheduling parallel machine problem under general effects of deterioration and learning with past-sequence-dependent setup time: heuristic and meta-heuristic approaches

This study investigates an identical parallel machine scheduling problem with past-sequence-dependent setup times and general effects of deteriorating and learning. The actual job processing time on each machine is defined by a two-element function of the normal processing times of the preprocessed jobs and its scheduled position on the same machine. Moreover, the job setup time on each machine is a function of the actual processing times of the preprocessed jobs on the same machine. A novel mixed-integer programming model is developed to satisfy the goal of minimizing total completion time. Due to the NP-hard characteristic and intractability of the problem, three efficient methodologies including a heuristic algorithm (HA), a genetic algorithm (GA) with an enhanced exploration ability and an ant colony optimization (ACO) combined with a new stochastic elitism strategy are designed to find optimal/near-optimal solutions within an appropriate period of time. The effectiveness and efficiency of the presented model and the proposed algorithms are verified by computational experiments. The computational results indicate that the suggested algorithms are effective and executable approaches to generate solutions as good as optimal solution in the small-sized problems. Also, the ACO statistically outperformed the HA and GA in the medium- and large-sized problems.

Two-agent single-machine scheduling with cumulative deterioration

We address cumulative deterioration scheduling in which two agents compete to perform their respective jobs on a single machine. By cumulative deterioration we mean that the actual processing time of any job of the two agents is a linear increasing function of the total normal processing times of already processed jobs. Each agent desires to optimize some scheduling criterion that depends on the completion times of its own jobs only. We study several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. The aim is to find an optimal schedule that minimizes the objective value of one agent while maintaining the objective value of the other agent not exceeding a fixed upper bound. For each problem under study, we design either a polynomial-time or a pseudo-polynomial-time algorithm to solve it.

A further study on two-agent parallel-batch scheduling with release dates and deteriorating jobs to minimize the makespan

We re-visit the two-agent scheduling on a parallel-batch machine to minimize makespan, where jobs have release dates and linear deteriorating processing times. The objective is to minimize the makespan of agent A with the makespan of agent B being bounded. In the paper Tang, Zhao, Liu, and Leung (2017), the authors reported comprehensive research for this scheduling model. Especially, they presented polynomial-time algorithms for the following four problems. In the first, the batch capacity is unbounded and the two agents are compatible. In the second, the batch capacity is bounded, the two agents are incompatible, the A-jobs have a fixed number of normal processing times, and the B-jobs have a common release date. In the third and forth, the batch capacity is bounded, the two agents are compatible, and the release dates and normal processing times are either agreeable or reversely agreeable. But their discussions for the above four problems are logically confusing. In this paper we present a more efficient polynomial-time algorithm for the first problem and show that the other three problems are NP-hard. We also present a pseudo-polynomial-time algorithm for the version where the batch capacity is bounded, the two agents are incompatible, and A-jobs and B-jobs have their common release dates, respectively. We finally present a strongly polynomial-time algorithm for the version where the batch capacity is unbounded and the two agents are incompatible.

An efficient simulation–neural network–genetic algorithm for flexible flow shops with sequence-dependent setup times, job deterioration and learning effects

This study presents an integrated approach based on artificial neural network (ANN), genetic algorithm (GA) and computer simulation to explore all the solution space in stochastic flexible flow shop with sequence-dependent setup times, job deterioration and learning effects. The objective of this study is minimizing total tardiness of jobs in the sequences. In this study, the outputs of ANN are inputted to GA and outputs of simulation model are inputted to ANN. We consider learning effects in this problem which means that workers become more experienced with the passage of time, and thus, the processing duration decreases. Deterioration of job means that processing time is a decreasing function of its execution start time. It is not possible to propose a mathematical optimization model for the stated problem; therefore, a simulation optimization approach based on ANN–GA is introduced for a relatively large problem. Finally, actual experiments are conducted to show the applicability of the proposed novel algorithm in finding near-optimal solutions with normal, uniform and exponential processing and setup times. This is the first study that presents an integrated intelligent approach for optimal solution of stochastic flexible flow shop problem with sequence-dependent setup times, job deterioration and learning effects in a real case study.

Two-agent stochastic flow shop deteriorating scheduling via a hybrid multi-objective evolutionary algorithm

Multi-agent and deteriorating scheduling has gained an increasing concern from academic and industrial communities in recent years. This study addresses a two-agent stochastic flow shop deteriorating scheduling problem with the objectives of minimizing the makespan of the first agent and the total tardiness of the second agent. In the investigated problem, the normal processing time of jobs is a random variable, and the actual processing time of jobs is a linear function of their normal processing time and starting time. To solve this problem efficiently, this study proposes a hybrid multi-objective evolutionary algorithm which is a combination of an evolutionary algorithm and a local search method. It maintains two populations and one archive. The two populations are utilized to execute the global and local searches, where one population employs an evolutionary algorithm to explore the whole solution space, and the other applies a local search method to exploit the promising regions. The archive is used to guide the computation resource allocation in the search process. Some special techniques, i.e., evolutionary methods, local search methods and information exchange strategies between two populations, are designed to enhance the exploration and exploitation ability. Comparing with the classical and popular multi-objective evolutionary algorithms on some test instances, the experimental results show that the proposed algorithm can produce satisfactory solution for the investigated problem.

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.

Single-machine rescheduling problems with learning effect under disruptions

Rescheduling in production planning means to schedule the sequenced jobs again together with a set of new arrived jobs so as to generate a new feasible schedule, which creates disruptions to any job between the original and adjusted position. In this paper, we study rescheduling problems with learning effect under disruption constraints to minimize several classical objectives, where learning effect means that the workers gain experience during the process of operation and make the actual processing time of jobs shorter than their normal processing time. The objectives are to find optimal sequences to minimize the makespan and the total completion time under a limit of the disruptions from the original schedule. For the considered objectives under a single disruption constraint or a disruption cost constraint, we propose polynomial-time algorithms and pseudo-polynomial time algorithms, respectively.

A blocking flow shop deteriorating scheduling problem via a hybrid chemical reaction optimization

This study presents a blocking flow shop deteriorating scheduling problem which has a widespread application in manufacturing and service systems. In the investigated problem, there is no buffer between machines, and the actual processing time of jobs on each machine is described as a linear function of their starting time and normal processing time. In order to deal with this problem more efficiently, this study develops a hybrid chemical reaction optimization algorithm, where some special strategies are developed based on the problem characteristics, for example, solution representation, on-wall ineffective collision, decomposition, inter-molecule ineffective collision, and synthesis reactions. In addition, a variable neighborhood search is designed to strengthen the search ability of the chemical reaction optimization algorithm. Computational simulation experiments on a set of instances and performance comparisons are provided. They show that the proposed algorithm is superior to the standard chemical ...