Sequencing Sub-problem Research Articles

A Benders decomposition algorithm for resource allocation with multi-resource operations

This paper addresses a real life scheduling problem characterised by multi-resource operations whose completion simultaneously requires more than one (renewable) resource of different types. Such problems arise in various companies not only in manufacturing but also in services. Solving such a problem needs to address two interconnected subproblems: a sequencing subproblem and a resource-allocation subproblem if more than one resource is available in some types. The resource-allocation subproblem consists of allocating to each operation the resources it requires while the sequencing subproblem consists of determining the order in which each resource performs the operations assigned to it. This paper focuses on the resource-allocation subproblem. It generalises the basic scheduling problems which consist of determining the operations' starting or completion times for a given processing sequence for every resource. We consider a cost function taking into account the makespan, the cost of resource utilisation, and the load imbalance among the resources of the same type. We first formulate the problem into a mixed-integer linear program (MILP). To efficiently solve it, even in practical-sized instances, an exact algorithm called BD (Benders decomposition with enhancing cuts) is developed where the master problem only considers integer variables. We prove that the slave problem can be transformed into finding the longest paths in a digraph and therefore can be solved with the Bellman–Ford algorithm. To enhance the efficiency of the method, equivalent solutions are limited in the master problem. The performance of the approach is evaluated by comparing it against CPLEX, a state-of-the-art commonplace MILP solver, used to directly solve the initial MILP. The computational results demonstrate that BD provides competitive solutions in all upper and lower bounds. In particular, it improves, compared with CPLEX, the upper and lower bounds by 5.07% and 4.63%, respectively, in solving practical-sized instances. The experiment also shows that considering load balancing can make more rational use of resources and avoid adverse effects caused by excessive workload of staff and imbalanced use of equipment, which is very important in real-world production.

Multiobjective Sequence-Dependent Job Sequencing and Tool Switching Problem

This article considers the extension of the job sequencing and tool switching problem with sequence-dependent setup times (SDSSP) and with the requirement to comply with the due date of the processed jobs. This extension is motivated by the practical application in manufacturing environment where the products manufactured may be subjected to a specific due date. This study develops a multiobjective SDSSP model (MO-SDSSP) to simultaneously minimize the total setup time of tool switches and the tardiness of the machining process. Then, a two-stage Multiobjective Adaptive Large Neighborhood Search (MOALNS) and Simulated Annealing (SA) is presented as a heuristic algorithm for the MO-SDSSP, in which the MOALNS is proposed to solve the job sequencing subproblem while the SA is used to solve the tool switching subproblem. Subsequently, the performance of MOALNS-SA is compared to several popular multiobjective optimization algorithms. Comparison on four performance criteria has shown the applicability of the MOALNS. Finally, managerial analysis is performed to analyze the relationship between the total tool setup time and the compliance of due dates.

An exact decomposition method for unrelated parallel machine scheduling with order acceptance and setup times

In this paper, an unrelated parallel machine scheduling problem is studied, where order acceptance, sequence and machine-dependent setup times and the maximum available times of machines are additionally considered. The objective is to maximize the profit, which is the difference between the total revenues of accepted jobs and the cost associated with makespan. A mixed integer programming (MIP) model is formulated. To tackle this problem efficiently, an exact decomposition method, which is a two-layer logic-based Benders decomposition (LBBD) based (denoted by TL-LBBD) method, is developed, where an inner LBBD is embedded into an outer LBBD. Specifically, in the outer LBBD method, the master problem is used to determine the acceptance of jobs, whereas the subproblem examines the schedule given the accepted jobs from the master problem. The subproblem could be further decomposed into an assignment master problem and a sequencing subproblem by the inner LBBD method as well. Extensive computational experiments are conducted and the results show that the developed TL-LBBD method produce better quality solutions in significantly less computation time than solving the MIP model directly and the classic LBBD method. Moreover, the maximum scales of the problem instances that could be solved to optimality by the developed TL-LBBD method within 30 min are also evaluated.

Robotic Task Sequencing and Motion Coordination for Multiarm Systems

Until now, the robotic task sequencing problem (RTSP) has largely been considered from the viewpoint of a single robotic arm. However, several benefits can be derived from the extension of the problem to multiarm systems. This article presents a modular approach toward solving multiarm RTSPs, validated through simulated and physical trials involving a dual-arm setup. The proposed approach extends the Cluster-RTSP algorithm to efficiently address task allocation, configuration selection, and task sequencing subproblems. Three methods for solving the subsequent motion coordination subproblem are investigated to explore the strengths and drawbacks of each strategy for resolving motion conflict between multiple robots. The method is evaluated against a state-of-the-art baseline, where it is shown that the proposed planning pipeline excels in finding high-quality solutions within competitive planning times for RTSPs involving redundant robots and tasks comprising several hundred to thousands of points.

An Open-Source Simulation Model for Solving Scheduling Problems

In this study, an open-source simulation model is presented for solving scheduling problems. The model is capable of solving different benchmarks. The methods involved in the simulation are mainly based on generating dispatching rules or using them to solve problems, but there are other heuristics as well. Dispatching rules in an evolutionary process are generated using Gene Expression Programming. For this aim, a coding method, which has not been described in the literature before, is explained. Along with the explanation of the properties of the source code, information about deterministic, dynamic models, buffer states, machine breakdown states, and the methods used to deal with them is presented. Concepts are explained with visual examples. In addition, a subject that has not been investigated in the literature before is analyzed by using the simulation model. This topic is to examine the results of solving machine assignment and operation sequencing sub-problems in flexible job shop scheduling problems with different rules. Moreover, objective functions that the source code can handle are discussed. Unlike many studies in the literature, the codes are presented to the readers as open source. Also, it is open to development and can be easily modified by users to solve other types of problems. Finally, in the study, experimental results are presented on the basis of some benchmarks available in the literature, and the limits of the study and source code are explained.

Simulated-annealing-based hyper-heuristic for flexible job-shop scheduling

The flexible job-shop scheduling problem (FJSP) is common in high-mix industries such as semiconductor manufacturing. An FJSP is initiated when an operation can be executed on a machine assigned from a set of alternative machines. Thus, an FJSP consists of the machine assignment and job sequencing sub-problems, which can be resolved using a pair of problem-dependent machine assignment rules (MARs) and job sequencing rules (JSRs). Selecting an MAR–JSR pair that performs efficiently is a challenge. This study proposes a simulated-annealing-based hyper-heuristic (SA-HH) for assembling an heuristic scheme (HS) consisting of MAR–JSR pairs with a set of problem state features. Two variants of SA-HH, i.e. SA-HH based on HS with problem state features (SA-HH) and without problem state features (SA-HH), are investigated. In terms of the best makespan, SA-HH outperforms or is comparable with over 75% of benchmark algorithms on 8 out of 10 instances in the Brandimarte dataset.

Decomposition algorithm for the multi-trip single vehicle routing problem with AND-type precedence constraints

This paper addresses a new variant of the multi-trip single vehicle routing problem where the nodes are related to each other through AND-type precedence constraints. The problem aims at determining a sequence of trips to visit all the nodes respecting every precedence constraint within and among the routes so to minimize the total traveling cost. Our motivation comes from routing problems where a node may have a set of predecessors (not just single one proposed in the dial-a-ride or pickup and delivery problems) resulting in a set of pairwise relations that specify which customers need to be visited before which other ones. We develop three Mixed Integer Programming models to formulate the problem. The models are experimentally compared to determine the best one. Moreover, a solution approach based on the Logic-Based Benders Decomposition algorithm is developed which allows to decompose the original problem into an assignment master problem and independent sequencing subproblems. A new valid optimality cut is devised to achieve faster convergence. The cut performance is experimentally investigated by comparing with a recently proposed one in the literature. We further relax the algorithm to find the sub-optimal solution and demonstrate its efficiency. Extensive computational experiments are conducted to assess the proposed algorithms in terms of solution quality and CPU time.

Multilingual automation of transcript preprocessing in Alzheimer's disease detection.

IntroductionAnalyzing linguistic functions can improve early detection of Alzheimer's disease (AD). To date, no studies have focused on creating a universal pipeline for clinical transcript preprocessing.MethodsThis article presents a simple and efficient method for processing linguistic and phonetic data, sequencing subproblems of cleaning, normalization, and measure extraction tasks. Because some of these tasks are language‐ and context‐ dependent, they were designed to be easily configurable, thus increasing their scalability when dealing with new corpora.ResultsResults show improved performances over previous studies in this time‐consuming preprocessing task. Moreover, our findings showed that some discursive markers extracted from transcripts revealed a significant correlation (>0.5) with cognitive impairment severity.DiscussionThis article contributes to the literature on AD by presenting an efficient pipeline that allows speeding up the transcripts preprocessing task. We further invite other researchers to contribute to this work to help improve the quality of this pipeline (https://github.com/LiNCS-lab/usAge).

An intelligent hybrid approach for task scheduling in cluster computing environments as an infrastructure for biomedical applications

AbstractNowadays, increase in time complexity of applications and decrease in hardware costs are two major contributing drivers for the utilization of high‐performance architectures such as cluster computing systems. Actually, cluster computing environments, in the contemporary sophisticated data centres, provide the main infrastructure to process various data, where the biomedical one is not an exception. Indeed, optimized task scheduling is key to achieve high performance in such computing environments. The most distractive assumption about the problem of task scheduling, made by the state‐of‐the‐art approaches, is to assume the problem as a whole and try to enhance the overall performance, while the problem is actually consisted of two disparate‐in‐nature subproblems, that is, sequencing subproblem and assigning one, each of which needs some special considerations. In this paper, an efficient hybrid approach named ACO‐CLA is proposed to solve task scheduling problem in the mesh‐topology cluster computing environments. In the proposed approach, an enhanced ant colony optimization (ACO) is developed to solve the sequence subproblem, whereas a cellular learning automata (CLA) machine tackles the assigning subproblem. The utilization of background knowledge about the problem (i.e., tasks' priorities) has made the proposed approach very robust and efficient. A randomly generated data set consisting of 125 different random task graphs with various shape parameters, like the ones frequently encountered in the biomedicine, has been utilized for the evaluation of the proposed approach. The conducted comparison study clearly shows the efficiency and superiority of the proposed approach versus traditional counterparts in terms of the performance. From our first metric, that is, the NSL (normalized schedule length) point of view, the proposed ACO‐CLA is 2.48% and 5.55% better than the ETF (earliest time first), which is the second‐best approach, and the average performance of all other competing methods. On the other hand, from our second metric, that is, the speedup perspective, the proposed ACO‐CLA is 2.66% and 5.15% better than the ETF (the second‐best approach) and the average performance of all the other competitors.

A hybrid genetic Tabu search algorithm for minimising total completion time in a flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop problem in which an operation may be executed by any machine out of a set of candidate machines. This paper addresses the FJSP under partial and total flexibility with the objective of minimising the total completion time. The FJSP is one of the most complex problems. Thus, exact methods are not effective for solving this problem and heuristic approaches are generally used to find near optimal solutions within a reasonable computation time. We develop a hybrid approach combining genetic algorithms and the Tabu search metaheuristic. The resolution approach is based on a joint resolution of the inherent assignment and sequencing subproblems. To evaluate the performance of the proposed algorithms, several benchmark instances of FJSP are used. The experimental results prove the effectiveness and efficiency of the proposed hybridisation. [Received 28 May 2019; Revised 2 July 2019; Revised 2 November 2019; Accepted 11 January 2020]

A population-based iterated greedy algorithm for no-wait job shop scheduling with total flow time criterion

The no-wait job shop where no waiting time is allowed between two successive operations of a job has a strong industrial background, especially in steel-making industry and concrete manufacturing. This study formulates the no-wait job shop problem with a total flow time criterion based on time difference and decomposes the problem into timetabling and sequencing subproblems. Several timetabling methods are designed for the total flow time criterion to generate a sequence timetable. By adopting favourable features of the iterated greedy algorithm, the population-based iterated greedy (PBIG) algorithm for the sequencing subproblem is proposed. The individuals in the population evolve by means of a destruction and construction perturbator and an insertion-based local search. In each iteration, a tournament selection is designed to replace a relatively worse solution. In order to generate starting solutions with a certain quality and diversity, the Nawaz–Enscore–Ham-based heuristics for flow shop scheduling are extended in no-wait job shops. In computational experiments based on well-known benchmark instances, timetabling methods are investigated, and it is shown that the left timetabling is superior to other timetabling methods for the total flow time minimisation. Computational results also show that the proposed algorithm significantly outperforms several state-of-the-art metaheuristics, and it could be applicable to practical production environment.

Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling

We model and solve an order acceptance and scheduling problem in an identical parallel machine setting. The goal is to maximize profit by making four decisions: (i) accept or reject an order, (ii) assign accepted orders to identical parallel machines, (iii) sequence accepted orders, and (iv) schedule order starting times. First, we develop a mixed-integer model that simultaneously optimizes the above four decisions. We enhance the model with pre-processing techniques, valid inequalities, and dominance rules. Second, we show that the model has a special structure that allows us to develop both classical and combinatorial Benders decomposition. We thus develop a classical Benders decomposition approach and two combinatorial Benders variants: (i) logic-based Benders decomposition and (ii) Branch-Relax-and-Check (BRC). The BRC, as the primary contribution of this paper, extends the literature in three ways: (1) it incorporates novel sequencing sub-problem relaxations that expedite convergence, (2) it employs a novel cutting-plane partitioning procedure that allows these sub-problem relaxations to be separately optimized outside the master problem, and (3) it uses temporary Benders cuts that communicate sub-problem relaxation solutions to the master problem. Third, we demonstrate that the BRC outperforms significantly other methods and finds integer feasible solutions for 100% of instances, guarantees optimality in 50% of instances, and achieves an average optimality gap of 3.20% within our time limit.

Minimizing the makespan in a flow shop environment under minimum and maximum time-lag constraints

This paper considers the flow shop scheduling problem with minimum and maximum time-lag requirements. According to the time-lag constraints, the starting time of each operation of a job must be within a specified time-window after the completion of its previous operation. The considered objective function is makespan and the problem is strongly NP-hard. In this article, a mixed integer linear programming (MILP) and two constraint programming (CP) models are proposed for the problem. To deal with the larger instances of this problems, it is decomposed into a sequencing and a timetabling sub-problem. A tabu search (TS) is developed to handle the sequencing sub-problem. Furthermore, an exact method based on the developed MILP as well as a greedy algorithm are proposed to deal with the timetabling sub-problem. A large number of test cases with different time-lag settings are solved to assess the performance of the proposed algorithm. Computational results confirm that the proposed TS is efficient and competitive. Moreover, the greedy timetabling method proves to be significantly faster than the exact method without sacrificing the solution quality.

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.

A Modified Iterated Greedy Algorithm for Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them difficult to code and not easy to reproduce. This paper proposes a modified iterated greedy (IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an effective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.

A hybrid multi-objective EDA for robust resource constraint project scheduling with uncertainty

This paper presents a multi-phased algorithm hybrid genetic algorithm and multi-objective Markov network based Estimation of Distribution Algorithm (robust hGMEDA), to solve the robust scheduling problem for resource constrained scheduling problem (RCSP) with time uncertainty. Firstly, for modelling, two kinds of robust measures on time-based-robust and capacity-based-robust are introduced to evaluate the robustness of scheduling solutions. Secondly, for solving methodology, within the multi stage architecture based on sequential co-evolutionary paradigm, genetic algorithm (GA) is used to find feasible solution for sequencing sub-problem, and multi-objective Markov network based Estimation of Distribution Algorithm (MMEDA) is adopted to model the interrelation for resource allocation and calculate the Pareto set with the scenario based approach. Next, the alternative solutions are checked by the chance constraints by using scenario-based simulation. Moreover, one problem-specific local search with considering both makespan and robustness is designed to improve the solution quality. The implementation results provide practical support that experiment results based on a benchmark “Project Scheduling Problems Library” (PSPLIB) and comparisons demonstrate that our approach is highly effective and tolerant of uncertainty.

Modelling and optimizing a system for testing electronic circuit boards

In this article we consider a difficult combinatorial optimization problem arising from the operation of a system for testing electronic circuit boards (ECB). This problem was proposed to us by a company that makes a system for testing ECBs and is looking for an efficient way of planning the tests on any given ECB. Because of its difficulty, we first split the problem into a covering subproblem and a sequencing subproblem. We also give a global formulation of the test planning problem. Then we present and discuss results pertaining to the covering and sequencing subproblems. These results demonstrate that their solution yields testing plans that are much better than those currently used by the company. Finally we conclude our article by outlining avenues for future research.

Collaborative Operating Room Planning and Scheduling

Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utilization is conducive to containing the cost of surgical service delivery, shortening surgical patient wait times, and increasing patient admissions. We extend the OR planning and scheduling problem from a single independent hospital to a coalition of multiple hospitals in a strategic network, where a pool of patients, surgeons, and ORs are collaboratively planned. To solve the resulting mixed-integer dual resource constrained model, we develop a novel logic-based Benders’ decomposition approach that employs an allocation master problem, sequencing sub-problems for each hospital-day, and novel multistrategy Benders’ feasibility and optimality cuts. We investigate various patient-to-surgeon allocation flexibilities, as well as the impact of surgeon schedule tightness. Using real data obtained from the General Surgery Departments of the University Health Network (UHN) hospitals, consisting of Toronto General Hospital, Toronto Western Hospital, and Princess Margret Cancer Centre in Toronto, Ontario, Canada (who already engage in some collaborative resource sharing), we find that on average, collaborative OR scheduling with traditional patient-to-surgeon allocation flexibility results in 6% cost-savings, while flexible patient-to-surgeon allocation flexibility increases cost-savings to 40%, and surgeon schedule tightness can impact costs by 15%. The collective impact of our collaboration and patient flexibility results in between 45% and 63% savings per surgery. We also use a game theoretic approach to fairly redistribute the payoff acquired from a coalition of hospitals and to empirically show coalitional stability among hospitals.Data and the online supplement are available at https://doi.org/10.1287/ijoc.2017.0745 .

A mathematical model and two-stage heuristic for hot rolling scheduling in compact strip production

• We study a new hot rolling scheduling problem from compact strip production process. • We model the problem as a combination of a sheet strip assignment sub-problem and a sheet strip sequencing sub-problem. • We present a two-stage solution approach consisting of a sheet strip assignment heuristic and a sheet strip sequencing heuristic. • The effectiveness of the two-stage heuristic is demonstrated by extensive experiments on both synthetic and real-world instances. This paper addresses a new hot rolling scheduling problem from the compact strip production process, which is the mainstream production technology that is used worldwide for sheet strips. The problem is modeled as a combination of two coupled sub-problems. One sub-problem is a sheet strip assignment problem that assigns sheet strips to rolling turns with the constraints of safe values of different gauge levels, and the other is a sheet strip sequencing problem that decides the rolling sequence for all of the sheet strips in a rolling turn to form a particular parabolic shape in thickness. To solve this hot rolling scheduling problem, we present a novel approach that consists of a sheet strip assignment heuristic and a sheet strip sequencing heuristic. The sheet strip assignment heuristic minimizes the number of virtual sheet strips by generating rolling turns according to the ordered sheet strips with maximum gauge level and their safe values. The sheet strip sequencing heuristic minimizes the average change of the thickness of adjacent sheet strips by arranging a certain number of duplicate sheet strips to the increasing stage of a rolling turn. Extensive experiments based on both synthetic and real-world instances from a compact strip production process show the effectiveness of the proposed two-stage heuristic in solving the hot rolling scheduling problem.

A Hyperheuristic Approach for Intercell Scheduling With Single Processing Machines and Batch Processing Machines

Intercell transfers in cellular manufacturing systems disrupt the philosophy of creating independent cells, but are essential for enterprises to reduce production costs. The problem of intercell scheduling with single processing machines and batch processing machines is considered in this paper, which involves an assignment subproblem, a sequencing subproblem, and a batch formation subproblem. An ant colony optimization (ACO)-based hyperheuristic (ABH) is developed in this paper, searching assignment rules for parts, sequencing rules for single processing machines, and batch formation rules for batch processing machines, simultaneously, and then using the obtained combinatorial rules to generate scheduling solutions. Computational results show that ABH is an effective and significantly efficient approach to provide near-optimum solutions even when CPLEX shows poor performance, and as compared to genetic algorithm that is widely used in hyperheuristics, ABH has better performance with respect to the problem addressed in this paper.