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A single machine scheduling and due-window assignment problem is studied. The objective function is of a minmax type, i.e., the goal is to minimize the maximum cost among all processed jobs. In the classical setting of due-window assignment problems, there are four cost components: for job-earliness, job-tardiness, due-window starting-time and due-window size. We consider in this note a general cost structure which contains in addition to the standard linear earliness and tardiness cost components, a fixed penalty. Thus, early and tardy jobs are penalized also by a fixed cost which is independent of their actual earliness and tardiness values. We show that there are six candidates for the optimal starting time and size of the due-window. Consequently, an efficient, polynomial-time solution algorithm is introduced. [ABSTRACT FROM AUTHOR]

This paper considers a single-machine scheduling problem where jobs have multiple slack due-date assignments, i.e., some jobs have a common flow allowance and all jobs have m (m > 0 is a given constant) common flow allowances. The objective is to determine the multiple common flow allowances and optimal job sequence that minimizes the weighted sum of earliness-tardiness penalty and slack due-date assignment cost, where the weights only depend on their positions in a sequence, i.e., the position-dependent weights. Optimal properties are given for this problem, and then the problem is shown to be polynomially solvable when the number of multiple slack due-date assignments is a given constant. The model with multiple slack due-date assignments can also be extended to position (time)-dependent scheduling. [ABSTRACT FROM AUTHOR]

In this paper we consider single-machine scheduling problems with group technology, where the group setup times are general linear functions of their starting times and the jobs in the same group have general truncated learning effects. The objective is to minimize the makespan and total completion time, respectively. We show that the makespan minimization remains polynomially solvable. For the total completion time minimization, optimal properties are presented and then we introduce some heuristic algorithms and a branch-and-bound algorithm. [ABSTRACT FROM AUTHOR]

This paper discusses the single-machine scheduling problems with deteriorating jobs and past-sequence-dependent delivery times. Under the general deterioration function, the objective is to determine an optimal schedule for the job that minimizes the makespan, and the total weighted completion time. We demonstrate that the makespan minimization is polynomially solvable. For the total weighted completion time, this problem is NP-hard, to solve this problem, we provide the branch-and-bound algorithm and some heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study scheduling with step-learning, i.e., a setting where the processing times of the jobs started after their job-dependent learning-dates are reduced. The goal is to minimize makespan on a single machine. We focus first on the case that idle times between consecutive jobs are not allowed. We prove that the problem is NP-hard, implying that no polynomial-time solution exists and, consequently, propose a pseudo-polynomial time dynamic programming algorithm. An extensive numerical study is provided to examine the running time of the algorithm with different learning-dates and job processing time ranges. The special case of a common learning-date for all the jobs is also studied, and a (more efficient) pseudo-polynomial dynamic programming is introduced and tested numerically. In the last part of the paper, the more complicated setting in which idle times are allowed is studied. An appropriate dynamic programming is introduced and tested as well. [ABSTRACT FROM AUTHOR]

In this paper, we address single-machine scheduling with sum of logarithm processing times-based learning effect. Under exponential past-sequence-dependent delivery times, we proved that the makespan and total completion time minimizations can be solved by the smallest processing time (SPT) first rule. Under the agreeable weight condition and agreeable due date condition, we show that the total weighted completion time minimization and maximum tardiness minimization can be solved in polynomial time, respectively. [ABSTRACT FROM AUTHOR]

The manufacturing sector faces unprecedented challenges, including intense competition, a surge in product varieties, heightened customization demands, and shorter product life cycles. These challenges underscore the critical need to optimize manufacturing systems. Among the most enduring and complex challenges within this domain is production scheduling. In practical scenarios, setup time is whenever a machine transitions from processing one product to another. Job scheduling with setup times or associated costs has garnered significant attention in both manufacturing and service environments, prompting extensive research efforts. While previous studies on customer order scheduling primarily focused on orders or jobs to be processed across multiple machines, they often overlooked the crucial factor of setup time. This study addresses a sequence-dependent bi-criterion scheduling problem, incorporating order delivery considerations. The primary objective is to minimize the linear combination of the makespan and the sum of weighted completion times of each order. To tackle this intricate challenge, we propose pertinent dominance rules and a lower bound, which are integral components of a branch-and-bound methodology employed to obtain an exact solution. Additionally, we introduce a heuristic approach tailored to the problem's unique characteristics, along with three refined variants designed to yield high-quality approximate solutions. Subsequently, these three refined approaches serve as seeds to generate three distinct populations or chromosomes, each independently employed in a genetic algorithm to yield a robust approximate solution. Ultimately, we meticulously assess the efficacy of each proposed algorithm through comprehensive simulation trials. [ABSTRACT FROM AUTHOR]

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In practical problems, in addition to the processing time of the job, the impact of the time required for delivering the service to customers on the cost is also considered, i.e., delivery time, where the job processing time is a simple linear function of its starting time. This paper considers the impact of past-sequence-dependent delivery times (which can be referred to as p s d d t ) on the studied objectives in three types of due windows (common, slack and different due windows). This serves to minimize the weighted sum of earliness, tardiness, starting time and size of due window, where the weights (coefficients) are related to the location. Through the theoretical analysis of the optimal solution, it is found that these three problems can be solved in time O (N log N) , respectively, where N is the number of jobs. [ABSTRACT FROM AUTHOR]

This paper develops an economic production quantity model for a single-machine multiproduct imperfect production system with a set of alternative assumptions. The system under study can produce different types of products using a single machine. Fresh production and rework of imperfect items are performed on the same production line. The model is developed with different operational possibilities on imperfect items. The model aims to investigate the effects of continuous supply of all products throughout a planning period, unequal production cycles, and removal of idle inventory downtimes. A constrained nonlinear mathematical model is derived for the system. The model is optimized using the logarithmic barrier method that uses Newton's iterative process to calculate the optimal value in each stage. A numerical example and sensitivity analysis are presented to validate the proposed model and optimization method. Some managerial applications of the model are explained. [ABSTRACT FROM AUTHOR]

We study several competitive two-agent scheduling problems with release dates and preemption on a single machine, where the scheduling criterion of the first agent is regular and of the sum-form and the scheduling criterion of the second criterion is regular and of the max-form or the weighted number of tardy jobs. Two variants of the problems are investigated. One is the restricted version, in which the goal is to find a feasible schedule so that the objective value of the first agent is minimized subject to the restriction that the objective value of the second agent does not exceed a given threshold value. The other one is the Pareto version, in which the goal is to find all the Pareto-optimal points and their corresponding Pareto-optimal schedules. We design polynomial-time and pseudo-polynomial-time algorithms for each of the considered problems. [ABSTRACT FROM AUTHOR]

In this paper, the single-machine scheduling problems with deteriorating effects and a machine maintenance are studied. In this circumstance, the deterioration rates of the jobs during the machining process are the same which reduces the production efficiency. The actual processing time of the job is a linearly increasing function of the starting time. In this process, the machine only performs a maintenance activity, and the maintenance time is a fixed value. After the maintenance work is completed, the machine will be restored to the initial state, and the deterioration of the job will be start again. The goal is to determine the optimal schedule in order to minimise the maximum completion time (i.e. the makespan) and the sum of job completion times. We prove that both problems are polynomial time solvable, and we also provide the corresponding algorithms. [ABSTRACT FROM AUTHOR]

We deal with a single-machine scheduling problem with an optional maintenance activity (denoted by $ ma $), where the actual processing time of a job is a function of its starting time and position. The optional $ ma $ means that the machine will perform a $ ma $, after $ ma $ is completed, the machine will return to the initial state. The objective is to determine an optimal job sequence and the location of the maintenance activity such that makespan is to be minimized. Based on some properties of an optimal sequence, we introduce a polynomial time algorithm to solve the problem, and the time complexity is $ O({n}^4) $, where $ {n} $ is the number of jobs.

This paper considers the single-machine problem with job release times and flexible preventive maintenance activities to minimize total weighted tardiness, a complicated scheduling problem for which many algorithms have been proposed in the literature. However, the considered problems are rarely solved by genetic algorithms (GAs), even though it has successfully solved various complicated combinatorial optimization problems. For the problem, we propose a trajectory-based immigration strategy, where immigrant generation is based on the given information of solution extraction knowledge matrices. We embed the immigration strategy into the GA method to improve the population's diversification process. To examine the performance of the proposed GA method, two versions of GA methods (the GA without immigration and the GA method with random immigration) and a mixed integer programming (MIP) model are also developed. Comprehensive experiments demonstrate the effectiveness of the proposed GA method by comparing the MIP model with two versions of GA methods. Overall, the proposed GA method significantly outperforms the other GA methods regarding solution quality due to the trajectory-based immigration strategy. [ABSTRACT FROM AUTHOR]

In this paper, we examined single and parallel machine scheduling problems with a learning effect and job rejection simultaneously. In real life, job processing times decrease when there is a learning effect. In some cases, producers cannot process all the jobs and pay the penalty cost for these jobs that they do not process. In our study, learning effect and job rejection are considered at the same time. We examined four different objective functions. Our objectives for single-machine scheduling problems are makespan and rejection cost minimization, total completion time and rejection cost minimization and total absolute deviation of completion times (TADC) and rejection cost minimization. Our objective for parallel machines is makespan and rejection cost minimization. The problems are solved by mathematical models, and four different algorithms are proposed for the problems. From these algorithms, the same results are obtained with single-machine makespan and rejection cost minimization, parallel machine makespan and rejection cost minimization and total completion time and rejection cost minimization. The accuracy for these models is obtained as 100%. The proposed algorithm for TADC and rejection cost minimization yielded close-to-optimal results. Mathematical model and algorithm results for 10 jobs, 20 jobs and 30 jobs are compared and the results are presented. The obtained solutions are obtained in polynomial time. [ABSTRACT FROM AUTHOR]

In this paper, we consider scheduling problems with slack (different) due-window assignment and time-dependent processing times. The processing time functions are all a proportional linear increasing function of time. On a single-machine setting, the goal is to minimize a cost function that includes earliness, tardiness, due-window starting time and size, and the number of early and tardy jobs. Some relevant optimality properties and polynomial time solution algorithms are proposed to solve these two problems. [ABSTRACT FROM AUTHOR]

In this article, we investigate the single-machine scheduling problem with truncated learning effect and resource allocation, where the actual processing time of a job is a general function of its additional resources and position in a sequence. The goal is to determine the optimal resource allocation and optimal sequence such that a weighted sum of scheduling cost and resource consumption cost is minimized. We show that the problem can be solved in $ O(n^3) $ time by using an assignment formulation, where $ n $ is the number of jobs.

We consider single-machine scheduling problems with a batch-dependent ageing effect and variable maintenance activities between batches. The machine can process several jobs as a batch. It requires maintenance activities where the maintenance time depends on the flow time of the pre-batch, i.e. the batch processed before a batch. A job's actual processing time is an increasing exponential function of its operation time within a batch. The objectives are to minimise the makespan and the total completion time. We develop polynomial time algorithms for the makespan minimisation problem and the total completion time minimisation problem under the condition that the ageing factor is greater than one. We also provide a mathematical programming approach and two heuristic algorithms to analyse the total completion time minimisation problem when the ageing factor is less than one for even one batch. The computational analysis indicates that the proposed heuristic algorithms are more efficient for the smaller ageing factor, whereas the Modified Shortest Processing Time algorithm is more efficient than the proposed heuristic algorithms for the larger ageing factor. [ABSTRACT FROM AUTHOR]

In this paper, we study the single-machine scheduling problems with DeJong’s learning effect and deteriorating maintenance activity, where DeJong’s learning effect is a special position-based learning effect and the duration of the deteriorating maintenance activity is a linear increasing function of its starting time. Our goal is to determine the job sequence of all jobs and the position of the maintenance activity to minimize some performance measures. When the performance measures are the makespan and the total completion time, we show that both of them can be solved in polynomial time. When the performance measure is the total weighted completion time, we develop a pseudo-polynomial time dynamic programming algorithm under a special case. When the performance measure is the maximum lateness, we show that the earliest due date first (EDD) order is a bad algorithm for the general case, and develop a polynomial time algorithm under a special case. [ABSTRACT FROM AUTHOR]

This article investigates the due-window assignment scheduling problem with setup times on a single machine, where setup times of jobs are past-sequence-dependent. Under common, slack and unrestricted due-window assignment methods, the goal is to determine the optimal job sequence and due-window such that the cost function (i.e., the weighted sum of earliness and tardiness, number of early and tardy jobs, due-window starting time and size) is minimized. We solve the problem optimally by introducing a polynomial time algorithm. An extension to the problem with learning and deterioration effects is also studied.

We consider a single machine scheduling problem with slack due date assignment in which the actual processing time of a job is determined by its position in a sequence, its resource allocation function, and a rate-modifying activity simultaneously. The problem is to determine the optimal job sequence, the optimal common flow allowance, the optimal amount of the resource allocation, and the position of the rate-modifying activity such that the two constrained optimization objective cost functions are minimized. One is minimizing the total penalty cost containing the earliness, tardiness, common flow allowance subject to an upper bound on the total resource cost, the other is minimizing the total resource cost subject to an upper bound on the total penalty cost. For two optimization problems, we show that they can be solved in optimal time, respectively. [ABSTRACT FROM AUTHOR]

We tackle a new single-machine scheduling problem, whose objective is to balance the average weighted completion times of two classes of jobs. Because both the job sets contribute to the same objective function, this problem can be interpreted as a cooperative two-agent scheduling problem, in contraposition to the standard multiagent problems, which are of the competitive type since each class of job is involved only in optimizing its agent's criterion. Balancing the completion times of different sets of tasks finds application in many fields, such as in logistics for balancing the delivery times, in manufacturing for balancing the assembly lines and in services for balancing the waiting times of groups of people.To solve the problem, for which we show the NP-hardness, a Lagrangian heuristic algorithm is proposed. In particular, starting from a nonsmooth variant of the quadratic assignment problem, our approach is based on the Lagrangian relaxation of a linearized model and reduces to solve a finite sequence of successive linear assignment problems.Numerical results are presented on a set of randomly generated test problems, showing the efficiency of the proposed technique.

In the literature on multi-scenario scheduling problems, it is assumed that (i) each scenario defines a different possible realization of the job's parameters; and (ii) the value of each parameter is arbitrary for any job in any scenario. Under these assumptions many multi-scenario scheduling problems have been proven to be NP -hard. We study a special case of this set of problems, in which there is an agreeable condition between scenarios on the processing-time parameters. Accordingly, the processing time of job J j under scenario s i is at most its value under scenario s i + 1 , for i = 1 , ... q - 1 , where q is the number of different possible scenarios. We focus on three classical scheduling problems for which the single-scenario case is solvable in polynomial time, while the multi-scenario case is NP -hard, even when there are only two scenarios. The three scheduling problems consist of minimizing either the total completion time or the number of tardy jobs on a single machine, and minimizing the makespan in a two-machine flow-shop system. We show that the multi-scenario version of all three problems remains NP -hard even when processing times are agreeable and there are only two scenarios. We also show that for a more specific structure of job processing times two out of the three problems become easy to solve, while the complexity status of the third remains open for future research. [ABSTRACT FROM AUTHOR]

We consider the single-machine scheduling problem to tradeoff between the number and the length of accepted jobs. The algorithm introduced by Lin and Wang (2007) (called Lin-Wang's algorithm), for solving the single-machine scheduling problem to minimize the number of tardy jobs, is closely related to our research. The original version of Lin-Wang's algorithm runs in O (n 2) time. By using the technique of the preemptive scheduling combined with a data structure, we show in this paper that a variant of Lin-Wang's algorithm actually runs in O (n log ⁡ n) time. This enables us to further show that the tradeoff problem can be solved in O (n log ⁡ n) time. [ABSTRACT FROM AUTHOR]

We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

This article studies scheduling problems with past-sequence-dependent delivery times (denoted by psddt) on a single-machine, i.e., the delivery time of a job depends on its waiting time of processing. We prove that the total (discounted) weighted completion time minimization can be solved in O (n log n) time, where n is the number of jobs, and the weight is a position-dependent weight. For common (denoted by con) and slack (denoted by slk) due-date assignment and position-dependent weights (denoted by pdw), we prove that an objective cost minimization is solvable in O (n log n) time. The model (i.e., psddt and pdw) can also be extended to position-dependent (time-dependent) processing times. [ABSTRACT FROM AUTHOR]

This paper studies a single-machine scheduling problem with a two competing agents in which the performance criteria of the first and second agents are to minimize the mean lateness and number of tardy jobs, respectively. Due to the non-deterministic polynomial-time hardness of this problem, we propose an effective and efficient algorithm, denominated as the SPT-M algorithm, to generate the non-dominated solutions of the Pareto set. Computational results conducted on a test problem set reveal that the proposed SPT-M algorithm can generate an efficient Pareto frontier in remarkably short computing time. The contribution of this paper could help practitioners to determine the tradeoffs between the jobs of two agents competing for a single resource.

This study evaluates various Mixed Integer Programming (MIP) formulations for solving single-machine and parallel-machine scheduling problems, with the objective of minimizing the total completion time and the makespan of jobs. Through extensive numerical study, the MIP formulation, which is suitable for dealing with each specific single-machine or parallel-machine scheduling problem, is identified. Benchmarks are also provided for the development of other algorithms for future research.

The paper studies the single-machine scheduling problem with sequence-dependent setup times under dynamic environment. In this problem, jobs arrive over time and all the information on a job is unknown in advance. The objective is to find a feasible schedule such that the maximum lateness is minimised. This problem represents a very important production scheduling problem but remains under-represented in the literature. To solve the problem, we propose a dynamic differential evolution algorithm that considers the new environment and the previous environment simultaneously. The performance of the algorithm is enhanced by two heuristics for generating efficient initial solutions, a local search procedure and a speed-up method. To evaluate its performance, the proposed algorithm is tested on 1000 instances from the literature. The computational results demonstrate that the proposed algorithm is highly effective as compared to the methods known from the literature. [ABSTRACT FROM AUTHOR]

This paper addresses single machine and flowshop machines with the learning phenomenon. The learning phenomenon means that the actual jobs processing time of a job is a non-increasing function of the sum of processing times of jobs already processed. Under single machine, some properties firstly are presented to solve the objectives of minimizing the makespan problem, the total (weighted) completion time problem, the maximum lateness problem and the total tardiness problem. We show that minimizing the makespan problem and the total completion time problem can be solved in polynomial time. For the weighted completion time problem, the maximum lateness problem and the total tardiness problem, we give heuristic algorithm based on the corresponding optimal schedule and analyze the worst case error bound. Furthermore, we also show that the three problems are polynomially solvable under certain conditions. Under flowshop machines, we finally show that the makespan problem and the total completion time problem under more specialized proportional job processing times can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine so as to minimize the total deviation of the job completion times from an unrestrictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and NP -complete cases. Pseudo-polynomial dynamic programming algorithms are devised for NP -complete variants in the ordinary sense. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper analyzes a supply chain, which consists of a manufacturer, a retailer and several suppliers in which the retailer orders jobs to the manufacturer and the suppliers provide the requiring parts. The manufacturer schedules and processes the orders and dispatches them to the retailer either individually or collectively in batches. The manufacturer incurs a penalty cost for each tardy job and a transportation cost for every delivered batch and therefore, searches for a schedule that yields minimum number of tardy jobs and batches. Moreover, the manufacturer tries to optimize its supplying cost through locating the suppliers that offer appropriate release times and costs for manufacturing parts. Since the release times of parts directly affect scheduling of orders, in this research, we develop an integrated mathematical model for the manufacturer that incorporates suppliers' selection issue into the scheduling and batching decisions. Furthermore, we present a heuristic algorithm (greedy algorithm) and also a local search to quickly determine the optimal or near-optimal solutions. The computational analysis shows the importance of the integrated model and also the superiority and effectiveness of the heuristic algorithms.

The manufacturing sector faces unprecedented challenges, including intense competition, a surge in product varieties, heightened customization demands, and shorter product life cycles. These challenges underscore the critical need to optimize manufacturing systems. Among the most enduring and complex challenges within this domain is production scheduling. In practical scenarios, setup time is whenever a machine transitions from processing one product to another. Job scheduling with setup times or associated costs has garnered significant attention in both manufacturing and service environments, prompting extensive research efforts. While previous studies on customer order scheduling primarily focused on orders or jobs to be processed across multiple machines, they often overlooked the crucial factor of setup time. This study addresses a sequence-dependent bi-criterion scheduling problem, incorporating order delivery considerations. The primary objective is to minimize the linear combination of the makespan and the sum of weighted completion times of each order. To tackle this intricate challenge, we propose pertinent dominance rules and a lower bound, which are integral components of a branch-and-bound methodology employed to obtain an exact solution. Additionally, we introduce a heuristic approach tailored to the problem's unique characteristics, along with three refined variants designed to yield high-quality approximate solutions. Subsequently, these three refined approaches serve as seeds to generate three distinct populations or chromosomes, each independently employed in a genetic algorithm to yield a robust approximate solution. Ultimately, we meticulously assess the efficacy of each proposed algorithm through comprehensive simulation trials., Competing Interests: The authors declare there are no competing interests., (©2024 Xu et al.)

This paper considers a single-machine scheduling problem with deteriorating jobs and convex resource allocation. We assume that the actual processing time of a job is a function of its convex resource allocation and its starting time. For the multi-objective single-machine scheduling problem, we show that the problem is polynomially solvable in O (n log n) time, where n is the total number of jobs. [ABSTRACT FROM AUTHOR]

This paper introduces the serial batching scheduling problems with position-based learning effect, where the actual job processing time is a function of its position. Two scheduling problems respectively for single-machine and parallel-machine are studied, and in each problem the objectives of minimizing maximum earliness and total number of tardy jobs are both considered respectively. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on the serial-batching machine. We take some practical production features into consideration, i.e., setup time before processing each batch increases with the time, regarded as time-dependent setup time, and we formalize it as a linear function of its starting time. Under the single-machine scheduling setting, structural properties are derived for the problems with the objectives of minimizing maximum earliness and number of tardy jobs respectively, based on which optimization algorithms are developed to solve them. Under the parallel-machine scheduling setting, a hybrid VNS-GSA algorithm combining variable neighborhood search (VNS) and gravitational search algorithm (GSA) is proposed to solve the problems with these two objectives respectively, and the effectiveness and efficiency of the proposed VNS-GSA are demonstrated and compared with the algorithms of GSA, VNS, and simulated annealing (SA). This paper demonstrates that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings. [ABSTRACT FROM AUTHOR]

The paper deals with resource allocation scheduling problems in which the processing time of a job is defined by a function of its starting times and its position in a sequence. We also assume that the resource-dependent ready times of jobs are continuous functions of their consumed resource. Our objective is to minimize the resource consumption (the makespan) subject to the makespan constraint (limited resource availability). We prove that these two single-machine scheduling problems can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The problem of sequencing jobs on a single machine to minimize total cost (earliness and tardiness) is nowadays not just important due to traditional concerns but also due to its importance in the context of Collaborative Networked Organizations and Virtual Enterprises, where precision about promptly responses to customers' requests, along with other important requirements, assume a crucial role. In order to provide a contribution in this direction, in this paper the authors contribute with an applied constructive heuristics that tries to find appropriate solutions for single machine scheduling problems under different processing times and due dates, and without preemption allowed. In this paper, two different approaches for single-machine scheduling problems, based on external and internal performance measures are applied to the problem and a comparative analysis is performed. Computational results are presented for the problem under Just-in-Time and agile conditions on which each job has a due date, and the objective is to minimize the sum of holding costs for jobs completed before their due date and tardiness costs for jobs completed after their due date. Additional computational tests were developed based on different customer and enterprise oriented performance criteria, although preference is given to customer-oriented measures, namely the total number of tardy jobs and the maximum tardiness. [ABSTRACT FROM AUTHOR]

This paper deals with a single machine common due window assignment resource allocation scheduling problem with job-dependent learning effect. The objective is to find the due window starting time, a due window size, resource allocation and a job schedule such that total resource consumption cost is minimized subject to a cost function associated with the window location, window size, earliness, tardiness and makespan is less than or equal to a fixed constant number. We show that the problem can be solved in polynomial time. Some extensions of the problem are also given. [ABSTRACT FROM AUTHOR]

This article considers the single-machine serial-batching scheduling problem with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. The objective of this problem is to make the decision of batching jobs and sequencing batches to minimize the makespan. To solve the problem, three cases of machine non-availability periods are considered, and the structural properties of the optimal solution are derived for each case. Based on these structural properties, an optimization algorithm is developed and an example is proposed to illustrate this algorithm. [ABSTRACT FROM AUTHOR]

In this paper, two-agent scheduling problems are presented. The different agents share a common processing resource, and each agent wants to minimize a cost function depending on its jobs only. The objective functions we consider are the total weighted late work and the maximum cost. The problem is to find a schedule that minimizes the objective function of agent A, while keeping the objective function of agent B cannot exceed a given bound U. Some different scenarios are presented by depending on the objective function of each agent. We address the complexity of those problems, and present the optimal polynomial time algorithms or pseudo-polynomial time algorithm to solve the scheduling problems, respectively. [ABSTRACT FROM AUTHOR]

Two-agent scheduling has gained a lot of research attention recently. Two competing agents who have their own objective functions have to perform their respective set of jobs on one or more shared machines. This study considers a two-agent single-machine earliness and tardiness scheduling problem where jobs have distinct due dates and unforced idleness in between any two consecutive jobs is allowed. The objective is to minimize the total earliness and tardiness of jobs from one agent given that the maximum earliness–tardiness of jobs from the other agent cannot exceed an upper bound. In other words, each job from the second agent has a hard due window, whereas each job from the first agent will incur a penalty if completed either before or after its due date. Two mathematical models of the problem are presented, and several necessary optimality conditions are derived. By exploiting the established dominance properties, heuristic algorithms are developed for the problem. Finally, computational experiments are conducted to assess the models and heuristic procedures. [ABSTRACT FROM AUTHOR]