A single-machine scheduling problem with maintenance activities to minimize makespan

Exploring mathematical approximation for the time spans of transfer operations in parcel transshipment terminals

A single-machine scheduling problem with new maintenance activities is examined in this paper. In the scheduling literature, it is often assumed that the interval between maintenance activities is fixed or within a specified time frame. However, this assumption may not hold true in many real-world situations, such as the maintenance activities in wafer manufacturing of semiconductor. Before the wafer manufacturing process starts, it is imperative that the wafers go through a number of cleaning operations to avoid contamination. Using a cleaning agent as the main material of wafer cleaning, the contamination will be dissolved and removed from wafer surface. In case of contamination being accumulated substantial and going beyond a permitted value, the cleaning agent is highly likely to damage the wafer surfaces. Thus, the interval between maintenance activities in the wafer manufacturing process is deemed irregular. The objective function of the proposed problem is to minimise total completion time. Addressing the problem, a binary integer programming model is formulated in this paper. Furthermore, with the research problem being NP-hard, a heuristic based on two special properties is proposed to address the problem. To evaluate and validate the proposed heuristic, a new lower bound is further developed. Extensive experiments have been conducted showing that the proposed heuristic efficiently yields a near-optimal solution with an average percentage error of 15.4 from lower bound.

An integrated approach for selecting design parameters in smart product-service system conceptual design

One of the most common objectives in single-machine scheduling problems is the minimisation of total tardiness. Due to the non-deterministic polynomial-time hard nature of this problem, different heuristic and metaheuristic algorithms have been employed to solve it. In this article, an integer programming model with non-monotonic time-dependent job processing times is developed in which deterioration and learning considerations are incorporated simultaneously. A hybrid genetic algorithm-tabu search (GA-TS) approach is employed to solve the problem. Also, to improve the performance of the GA, Taguchi method is used for parameter tuning. Lastly, in an attempt to validate the proposed model, different test problems are generated randomly and solved by both the hybrid GA-TS and an optimisation software, and thereafter a comparison is performed between the results obtained by them. According to the results, the developed approach has potential to yield near-optimum solutions in large-sized problems. To the best of our knowledge, this is the first study that considers non-monotonic time-dependent processing times, deterioration and learning effect simultaneously in a single-machine scheduling problem with the objective of total tardiness minimisation.

This paper compares two shift patterns of nurse scheduling, APN and ABC, which are widely used in Chinese intensive care units (ICUs). Two binary integer programming (IP) models for the nurse scheduling problems with APN and ABC patterns are presented, respectively. A general heuristic solution procedure, which considers the equity of nurse schedules and reduction in shift changes, is proposed to solve these problems. A case study of nurse scheduling based on given nurse demands is performed. Two schedules with APN and ABC patterns are constructed. It shows that ABC pattern generally needs fewer nurses and meanwhile is more apt to achieve equity in nurse scheduling, while APN pattern is more likely to reduce shift changes.

This study addresses the issue of scheduling medical treatments for resident patients in a hospital. Schedules are made daily according to the restrictions on medical equipment and physicians who are being assigned at the same time. The problem is formulated as a multi-objective binary integer programming (BIP) model. Three types of metaheuristics are proposed and implemented to deal with the discrete search space, numerous variables, constraints and multiple objectives: a variable neighborhood search (VNS)-based method, scatter search (SS)-based methods and a non-dominated sorting genetic algorithm (NSGA-II). This paper also provides the results of computational experiments and compares their ability to find efficient solutions to the multi-objective scheduling problem.

The research on the theory and method of single machine scheduling is a difficult subject, but it is very important for the companies to improve the production efficiency and effectiveness. The study on single machine scheduling problem has the history of 50 years, but there is still a gap between the classical scheduling theories and practical scheduling problems. According to this characteristic, the problems in practical scheduling area and the various factors need to be concerned are mentioned, and the main methods to solving the single machine scheduling problem and their applications are presented in details. Finally, the directions and suggestions of future work in single machine scheduling problem are summarized.

This paper considers the single machine scheduling problem with cost constraints based on customer driven using noncooperative game theory. The single machine scheduling problem with cost constraints based on customer driven is introduced, and customers bidding strategy is analyzed using noncooperative game method. Then noncooperative game model of single machine scheduling with cost constraints is defined using noncooperative game theory, in which the customer is mapped to the player, customer quotation corresponds to player strategy, and a payoff function of players is defined on condition of two main customer objectives. The satisfactory result of scheduling problem can be achieved by seeking Nash equilibrium solution, and the steps of seeking Nash equilibrium solution for the proposed scheduling game model are given. A single scheduling case is analyzed and solved, and the result verifies the validity of the proposed game model and the solving method.

This paper considers the single batch-processing machine scheduling problem with aging effect and multi-maintenance activity concept. Real processing time of jobs increases due to machine’s aging effect. Maintenance time is constant and the machine returns to its initial condition after each maintenance activity and the aging effect starts anew. Our scheduling problem is under assumptions: non identical job sizes and dynamic job arrivals. We have to determine jointly (1) the maintenance frequencies, (2) the position of the maintenance activities on the machine, (3) the grouping of the jobs into the batches, and (4) the sequence of the batches on the machine, to minimize makespan. At first, we formulate the problem as a mathematical model. Since this problem has been proved to be NP-hard; therefore, a heuristic and two meta-heuristic algorithms are offered for the real-sized problems. The performance of the proposed algorithms is analyzed on the various test problems based on the considered measures.

An uncertain single machine scheduling problem with periodic maintenance

Railway transportation is one of the most popular options for Urban Massive Transportation Systems (UMTS) because of many attractive features. A robust electric power supply is essential to enable normal operation. However, the power peaks appearing at the start time of the vehicles put heavy pressure on the power grid. Reduction of the power peak is a key issue in improving urban railway transit's power efficiency. Researchers have tried to address this problem by making a delicate timetable, but this method often failed to serve the purpose because of the punctuality problem. In this work, taking advantage of real-time estimation of the single train's power consumption, an online Power peak Reduction by real-time Scheduling (PReS) solution for trains' departure is proposed. Particularly, a Binary Integer Programming (BIP) model is introduced that is able to avoid power consumption peak caused by multiple trains departure simultaneously. The simulation result verified that the proposed real-time scheduling approach can effectively reduce the occurrences of power peak without bringing in additional train travel delay.

Owing to the Network Function Virtualization (NFV) and Software-Defined Networks (SDN), Service Function Chain (SFC) has become a popular service in SDN and NFV-enabled network. However, as the Virtual Network Function (VNF) of each type is generally multi-instance and flows with SFC requests must traverse a series of specified VNFs in predefined orders, it is a challenge for dynamic SFC formation to optimally select VNF instances and construct paths. Moreover, the load balancing and end-to-end delay need to be paid attention to, when routing flows with SFC requests. Additionally, fine-grained scheduling for traffic at flow level needs differentiated routing which should take flow features into consideration. Unfortunately, traditional algorithms cannot fulfill all these requirements. In this paper, we study the Differentiated Routing Problem considering SFC (DRP-SFC) in SDN and NFV-enabled network. We formulate the DRP-SFC as a Binary Integer Programming (BIP) model aiming to minimize the resource consumption costs of flows with SFC requests. Then a novel routing algorithm, Resource Aware Routing Algorithm (RA-RA), is proposed to solve the DRP-SFC. Performance evaluation shows that RA-RA can efficiently solve the DRP-SFC and surpass the performance of other existing algorithms in acceptance rate, throughput, hop count and load balancing.

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP.

A modified harmony search for the T-single machine scheduling problem with variable and flexible maintenance