Machine Scheduling Problem Research Articles

Optimal dual cycling operations in roll-on roll-off terminals

Roll-on roll-off (RoRo) shipping plays an important role in freight transport on the European continent, and is faced with the challenge of reducing its CO2 emissions while increasing its efficiency. Dual cycling, in which loading and discharging processes are carried out simultaneously, achieves this goal by reducing the turnaround time of vessels in port and thus the CO2 output of handling equipment in port and fuel consumption through slow steaming at sea. Optimizing the dual cycling operations on RoRo vessels has not yet been investigated in the literature. This paper presents the novel RoRo dual cycling problem (RRDCP), and formulates it using integer programming (IP) with the objective to minimize the total makespan of discharging and loading operations. We further prove that the RRDCP is NP-complete by a reduction from a general machine scheduling problem, and introduce a novel heuristic to solve the problem called a generalized random key algorithm (GRKA). We evaluate the IP model and GRKA approach on both generated and industrial instances, showing that the GRKA heuristic finds optimal or near-optimal solutions to real-world problems in just seconds. We provide managerial insights on industrial instances, which indicate that our approach leads to a reduction in fuel consumption and CO2 emissions of up to 25% for RoRo operations.

Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work

Traditional scheduling models assume that due dates are predefined and the aim is to find a schedule that minimizes a given scheduling criterion with respect to the given set of due dates. A more recent trend consists of models that focus on coordinating two sets of decisions: due date assignment to customers and determining a job schedule. We follow this trend by analyzing a single machine scheduling problem, where the scheduler is tasked with assigning a common due date to all jobs in order to minimize an objective function that includes job-dependent penalties due to early and late work. We show that the problem is solvable in linear time if the common due date value is unbounded, and in O(nlogn) time if it is bounded from above. We then extend the analysis to the case where a common due window has to be assigned to all jobs. We show that when the location of the due window is unbounded, the problem is solvable in O(nlogn) time (and further in linear time if the length of the due window is unbounded as well). However, it becomes NP-hard when it is bounded. We complement our analysis by (i) providing a pseudo-polynomial time algorithm to solve this hard variant of the problem, and (ii) study two special cases of this hard variant that are solvable in polynomial time.

An exact algorithm for the preemptive single machine scheduling of equal-length jobs

Many real-world production and service environments can be modeled using the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights (priorities) minimizing the total weighted completion time. For this problem we propose a Boolean Linear Programming model, two heuristics based on the model’s relaxation, and an exact Branch and Bound algorithm incorporating the model and heuristics. Our computational study involved more than one million problem instances with up to 350 jobs. Each generated instance has been solved to optimality within 31 min. That improves state-of-the art (at most 20 jobs in 60 min) by more than an order of magnitude. Our benchmark instances and optimal schedules are publicly available at https://data.mendeley.com/datasets/nrkx7467tf/1.

New complexity and approximability results for minimizing the total weighted completion time on a single machine subject to non-renewable resource constraints

We consider single machine scheduling problems with additional non-renewable resource constraints. Examples for non-renewable resources include raw materials, energy, or money. Usually they have an initial stock and replenishments arrive over time at a-priori known time points and quantities. The jobs have some requirements from the resources and a job can only be started if the available quantity from each of the required resources exceeds the requirements of the job. Upon starting a job, it consumes its requirements which decreases the available quantities of the respective non-renewable resources. There is a broad background for this class of problems. Most of the literature concentrate on the makespan, and the maximum lateness objectives. This paper focuses on the total weighted completion time objective for which the list of the approximation algorithms is very short. We extend that list by considering new special cases and obtain new complexity results and approximation algorithms.

A no-delay single machine scheduling problem to minimize total weighted early and late work

A no-delay single machine scheduling problem to minimize total weighted early and late work

A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling.

In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost. We propose a mixed-integer linear programming formulation based on the weighted sum method to obtain the Pareto front. We also developed an NSGA-II method to address large instances of the problem since the formulation cannot solve it in an acceptable computational time for decision-making. The results showed that the proposed NSGA-II is able to find a good approximation for the Pareto front when compared with the weighted sum method in small instances. Besides, in large instances, NSGA-II outperforms, with 95% confidence level, the MOGA and NSGA-I multi-objective techniques concerning the hypervolume and hierarchical cluster counting metrics. Thus, the proposed algorithm finds non-dominated solutions with good convergence, diversity, uniformity, and amplitude.

Influence of probability distribution initialization methods on the performance of advanced arithmetic optimization algorithm with application to unrelated parallel machine scheduling problem

AbstractThe article investigates the influence of several initialization methods on the performance of the newly proposed advanced arithmetic optimization algorithm, also known as the nAOA. The initialization conditions considered include population sizes, diversity of the population, and the number of iterations. We used 23 different probability distributions with different diversity to test the influence of initialization schemes on the convergence and accuracy of the nAOA. The benchmark classical test functions and the functions defined in the CEC 2020 suite having different properties and modalities were used to compare the possible effects of the initialization methods. The numerical results showed that the nAOA is sensitive to population size and the number of iterations, which must be large for optimal performance. Friedman's and correlation tests were used to gain useful insight into the results we obtained. Findings showed that the performance of the nAOA is not particularly sensitive to the different initialization schemes used for most test functions. The implication is that nAOA is relatively stable and robust. However, the variant of beta distribution, b(3,2), recorded the lowest mean rank for most functions. Hence, it is the best performing initialization distribution scheme for the test problems considered. We can also observe from the experimental results that 47.83% and 100% of the classical and CEC2020 test functions used in this article show significant differences for different initialization methods, respectively. We also investigated the applicability of the nAOA to solve the unrelated parallel machine scheduling problem with sequence‐dependent setup times by using the best‐identified set of initialization methods. The performance of the nAOA is evaluated by comparing its solution to seven other well‐known metaheuristic algorithms, and the results reveal that the nAOA can provide promising results in solving all problem instances of the problem under study using the best initialization schemes.

A multiproject scheduling and resource management model in projects construction

PurposeThis research presents a multiproject scheduling and resource management (MPSRM) model that includes an M/M/c/n queue system, a p-hub median model, a parallel machine scheduling and a hub location problem solution method. This research aims to design a project network and then sequence raw materials delivery to hub factories.Design/methodology/approachThis research is implemented as a case study in construction and industrial company. It considers several mines to supply raw materials for production in hub factories. In the sequencing phase, a parallel mine scheduling problem specifies the delivery of raw materials to hub factories. Furthermore, a multisource project scheduling model is studied and designed for building project-oriented companies.FindingsThe results suggest that the proposed MPSRM model in this study significantly reduces project transportation costs. Therefore, creating accurate planning in projects, especially in construction projects where transportation plays an important role, can help reduce time and costs. Researchers, project managers and those dealing with projects can use this model to exploit their projects.Research limitations/implicationsWhen the number of construction projects in a construction company increases in a region, choosing an appropriate strategy to supply resources and raw materials becomes very important in terms of profit and loss and project completion as scheduled. An increase in transportation demands alongside the economic development on the one hand and providing competitive transportation services, on the other hand, have increasingly spotlighted the significance of hub networks in transportation systems. In addition, in this research, there is no suitable access road from the mines to the project sites, and considering the workload, if any of the projects become a hub, a proper road should be built.Originality/valueTo the best of the knowledge, there is no outstanding research in which a p-hub median location problem by considering queuing model and different transportation modes and a parallel machine scheduling problem are studied simultaneously.

A robust optimization approach for the unrelated parallel machine scheduling problem

A robust optimization approach for the unrelated parallel machine scheduling problem

A Hybrid Imperialist Competitive Algorithm for the Distributed Unrelated Parallel Machines Scheduling Problem

In this paper, the distributed unrelated parallel machines scheduling problem (DUPMSP) is studied and a hybrid imperialist competitive algorithm (HICA) is proposed to minimize total tardiness. All empires were categorized into three types: the strongest empire, the weakest empire, and other empires; the diversified assimilation was implemented by using different search operator in the different types of empires, and a novel imperialist competition was implemented among all empires except the strongest one. The knowledge-based local search was embedded. Extensive experiments were conducted to compare the HICA with other algorithms from the literature. The computational results demonstrated that new strategies were effective and the HICA is a promising approach to solving the DUPMSP.

Hybrid meta-heuristics for the unrelated parallel machine scheduling problem with setup times

This study focuses on an unrelated parallel machine scheduling problem with machine and job sequence-dependent setup times (UPMST) aiming to minimise the makespan. Recently, adaptive large neighbourhood search with learning automata (LA-ALNS) has been employed to tackle the UPMST with excellent performance. However, its search efficiency is heavily affected by re-visiting the recent solutions, which is known as the short-term cycle. Moreover, it remains challenging to balance the computational cost and quality of the solutions. To address these challenges, we propose a hybrid meta-heuristic method based on LA-ALNS and tabu search (LA-ALNS-TS). In the proposed algorithm, LA-ALNS is used to guide the exploration and TS is used to alleviate the short-term cycle experienced during the search process. In addition, we design two local search operators to achieve a balanced trade-off between the search efficiency and quality of the solutions. A dynamic perturbation scheme is proposed to improve the solution and help the algorithm escape from local optima. Comprehensive experiments were conducted to assess the performance of the algorithm on two exhaustive benchmarks. Experimental results demonstrate the effectiveness and efficiency of the proposed hybrid meta-heuristic method.

Hybrid tabu search algorithm for unrelated parallel machine scheduling in semiconductor fabs with setup times, job release, and expired times

This research is motivated by a scheduling problem arising in the ion implantation process of wafer fabrication. The ion implementation scheduling problem is modeled as an unrelated parallel machine scheduling (UPMS) problem with sequence-dependent setup times that are subject to job release time and expiration time of allowing a job to be processed on a specific machine, defined as: R|rj,eij,STsd|Cmax. The objective is first to maximize the number of processed jobs, then minimize the maximum completion time (makespan), and finally minimize the maximum completion times of the non-bottleneck machines. A mixed-integer programming (MIP) model is proposed as a solution approach and adopts a hybrid tabu search (TS) algorithm to acquire approximate feasible solutions. The MIP model has two phases and attempts to achieve the first two objectives. The hybrid TS algorithm has three phases and attempts to achieve all three objectives. In a real setting, computational results demonstrate that the maximum number of processed jobs can be acquired within a short time utilizing the hybrid TS algorithm (average 8 s). By comparing the two approaches, the TS outperforms the MIP model regarding solution quality and computational time for the second objective, minimizing the makespan. Furthermore, the third phase of the hybrid TS algorithm shows the effectiveness further to enhance the utilization of the ion implantation equipment.

Some Scheduling Problems With Job Rejection And A Learning Effect

AbstractIn 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.

A branch and bound algorithm for optimal television commercial scheduling.

In the current era of multimedia, television (TV) plays an important role in transmitting advertising messages. In addition, advertising is the primary source of revenue for the TV industry. Thus, a critical issue for TV stations is the scheduling of commercials in suitable advertising breaks on different TV channels to maximize revenue and minimize penalties. This type of TV commercial scheduling problem is similar to the machine scheduling problem, and both have availability constraints. However, the literature on TV commercial scheduling has not considered this perspective. Motivated by this, we consider the problem of scheduling commercials with specific service-level requirements on TV channels while minimizing the maximum lateness. The lateness of a commercial is defined to be its completion time minus its due date, and the maximum lateness is the maximum value of lateness among all commercials. We propose an exact branch and bound algorithm based on the LFJ (least flexible job first)/EDD (earliest due date first) rules and network flow methods, which were developed to solve the machine scheduling problem with availability constraints. Computational analysis shows that the bounding scheme proposed is highly effective, and a very low percentage of nodes is generated by the branch and bound algorithm. The algorithm can obtain an optimal solution for the problem.

Modeling and solving a real world machine scheduling problem with due windows and processing set restrictions

Motivated by a real-world problem situation faced by a large manufacturing company in the last step of their production process, we model and solve an offline, deterministic, non-preemptive, identical, parallel machine scheduling problem with processing set restrictions, availability constraints, release dates, bounded tardiness, blocking constraints and due windows. The objective is to minimize the total tardiness while penalizing the assignment of jobs to larger than necessary machines. We develop a mixed integer linear program and we propose a heuristic solution approach relying on the well known large neighborhood search paradigm which relies on tailored destroy and repair operators, embedded into a simulated annealing framework. The proposed algorithm is tested on artificial instances as well as on real-world data provided by the company and compared to optimal solutions obtained by means of CPLEX. The developed tool is now used for decision support by the company partner.

Single Machine Scheduling Problem with Batch Outsourcing

Outsourcing as a useful strategy in the industry can be integrated into scheduling problems. Moreover, batch outsourcing is a practical assumption owing to the logistics issues for transferring the parts between the manufacturer and the subcontractors. However, this assumption is rarely addressed in the scheduling literature. In this paper, a novel single machine scheduling problem with the option of batch outsourcing is studied. The objective is to minimize the sum of the total completion time of the jobs and the total outsourcing cost. To solve the problem, first, two mixed-integer linear programming (MILP) models, named MP1 and MP2, are developed, which respectively use a straightforward and an innovative approach to model the outsourcing batches. Next, an optimal property for the outsourcing batches is proven. This property is used to establish a valid inequality for model MP2, which is added to it to obtain a third MILP model, MP3. Extensive computational experiments showed that MP2 outperforms MP1 significantly. Moreover, including the derived valid inequality in MP3 enhances its performance considerably in comparing to MP2. Furthermore, it is observed that MP3 is capable of solving many practical-size problem instances optimally or with a low maximum optimality gap.

A Bi-Objective Optimization Approach for a Parallel Machine Scheduling Problem Minimizing Total Quality Loss and Total Tardiness

A Bi-Objective Optimization Approach for a Parallel Machine Scheduling Problem Minimizing Total Quality Loss and Total Tardiness

A mixed integer formulation and an efficient metaheuristic for the unrelated parallel machine scheduling problem: Total tardiness minimization

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for higher size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising. • A new mixed integer programming formulation for the Unrelated Parallel Machine Scheduling Problem. • The formulation uses positional variables, is linear and does not use the Big-M technique. • The formulation solves instances up to 150 jobs and 20 machines to optimality. • An efficient iterated local search metaheuristic is presented. • A potential issue in the commonly used instance-generation procedure is discussed and a new set of instances is proposed.

Bi-objective optimization of identical parallel machine scheduling with flexible maintenance and job release times

This paper investigates an identical parallel machine scheduling problem with flexible maintenance and job release times and attempts to optimize two objectives: the minimization of the makespan and total tardiness simultaneously. A mixed-integer programming (MIP) model for solving small-scale instances is presented first, and then a modified NSGA-Ⅱ (M-NSGA-Ⅱ) algorithm is constructed for solving medium- and large-scale instances by incorporating several strategies. These strategies include: (ⅰ) the proposal of a decoding method based on dynamic programming, (ⅱ) the design of dynamic probability crossover and mutation operators, and (ⅲ) the presentation of neighborhood search method. The parameters of the proposed algorithm are optimized by the Taguchi method. Three scales of problems, including 52 instances, are generated to compare the performance of different optimization methods. The computational results demonstrate that the M-NSGA-Ⅱ algorithm obviously outperforms the original NSGA-II algorithm when solving medium- and large-scale instances, although the time taken to solve the instances is slightly longer.

A new interpolation-based polynomial algorithm for estimating lateness in single machine scheduling problem

This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is used in the presented modified interpolation polynomial algorithm which is used to estimate the approximation error.