Tight LP bounds for resource constrained project scheduling

The best lower bound for the Resource Constrained Project Scheduling Problem is currently based on the resolution of several large Linear Programs (Brucker & Knust, EJOR, 107: 272-288, 1998). In this paper, we show that (1) intensive constraint propagation can be used to tighten the initial formulation of the linear programs and (2) we introduce several sets of valid cutting planes. These improvements allow us to close 16 new instances of the PSPLIB with 60 activities and to improve the best known lower bounds of 64 instances.Correspondence to:Philippe BaptisteThe authors would like to thank Peter Brucker and Sigrid Knust for providing their source code as well as Christian Artigues, Jacques Carlier and Philippe Michelon for enlightening discussions on project scheduling.     

Tabu search for the job-shop scheduling problem with multi-purpose machines

In this paper we study the following generalization of the job-shop scheduling problem. Each operation can be performed by one machine out of a set of machines given for this operation. The processing time does not depend on the machine which has been chosen for processing the operation. This problem arises in the area of flexible manufacturing. As a generalization of the jobshop problem it belongs to the hardest problems in combinatorial optimization. We show that an application of tabu search techniques to this problem yields excellent results for benchmark problems.Supported by Deutsche Forschungsgemeinschaft, Project JoP-TAG     

An effective genetic algorithm for the resource levelling problem with generalised precedence relations

Resource levelling aims to obtain a feasible schedule to minimise the resource usage fluctuations during project execution. It is of crucial importance in project scheduling to ensure the effective use of scarce and expensive renewable resources, and has been successfully applied to production environments, such as make-to-order and engineering-to-order systems. In real-life projects, general temporal relationships are often needed to model complex time-dependencies among activities. We develop a novel genetic algorithm (GA) for the resource levelling problem with generalised precedence relations. Our design and implementation of GA features an efficient schedule generation scheme, built upon a new encoding mechanism that combines the random key representation and the shift vector representation. A two-pass local search-based improvement procedure is devised and integrated into the GA to enhance the algorithmic performance. Our GA is able to obtain near optimal solutions with less than 2% optimality gap for small instances in fractions of a second. It outperforms or is competitive with the state-of-the-art algorithms for large benchmark instances with size up to 1000 activities.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

分布式实时系统任务调度算法的设计和实现

针对分布式实时任务中容易引起的任务分配不合理及系统负载不平衡的情况,根据分布式实时任务多机执行的特点及分布式实时系统在同一结点上有多任务执行,提出了两级分布式系统结构下实时任务的调度策略：任务分配和任务调度。实验表明,在任务分配阶段提出的算法可以更合理地平衡任务,在任务调度阶段采用的调度算法能够更好地完成任务的执行。     

A scatter search for the extended resource renting problem

In this paper, the extended Resource Renting Problem (RRP/extended) is presented. The RRP/extended is a time-constrained project scheduling problem, in which the total project cost is minimised. In the RRP/extended, this total project cost is determined by a number of extra costs, which are defined in this paper. These costs are based on the costs that are used in the traditional Resource Renting Problem and the Total Adjustment Cost Problem. Therefore, the RRP/extended represents a union of these two problems. To solve the RRP/extended, a scatter search is developed. The building blocks of this scatter search are specifically designed for the RRP/extended. We introduce two crossovers and an improvement method. The efficiency of these building blocks will be shown in the paper. Furthermore, a sensitivity analysis is presented in which the five costs have diverse values.     

Ant colony optimisation with parameterised search space for the job shop scheduling problem

The job-shop scheduling problem (JSSP) is known to be NP-hard. Due to its complexity, many metaheuristic algorithm approaches have arisen. Ant colony metaheuristic algorithm, lately proposed, has successful application to various combinatorial optimisation problems. In this study, an ant colony optimisation algorithm with parameterised search space is developed for JSSP with an objective of minimising makespan. The problem is modelled as a disjunctive graph where arcs connect only pairs of operations related rather than all operations are connected in pairs to mitigate the increase of the spatial complexity. The proposed algorithm is compared with a multiple colony ant algorithm using 20 benchmark problems. The results show that the proposed algorithm is very accurate by generating 12 optimal solutions out of 20 benchmark problems, and mean relative errors of the proposed and the multiple colony ant algorithms to the optimal solutions are 0.93% and 1.24%, respectively.     

A model, heuristic procedure and decision support system for solving the movie shoot scheduling problem

Creating a movie shoot schedule is an important part of the movie production process. Even for a small movie project already 50 activities requiring 130 resources such as different actors, director, team, special effects and locations etc. have to be scheduled respecting complex constraints which may be imposed on single resources as well as on every activity. In this paper, we present the movie shoot scheduling problem and formulate a conceptual model. We present a metaheuristic approach for generating operational schedules, outline the modules of the decision support system Schedule This which we have developed and finally we shortly report practical experiences. Our experience from using the DSS in real movie shooting projects shows significant improvements with respect to faster and better scheduling as well as ad hoc re-scheduling.     

Modelling and solving algorithm for two-stage scheduling of construction component manufacturing with machining and welding process

This paper focuses on a two-stage machining and welding scheduling problem based on an investigation at a structural metal manufacturing plant, aiming to minimise the total makespan. Several parts processed at Stage one according to classical job-shop scheduling are grouped into a single construction component at the second welding stage. Fabrication of the construction component cannot begin until all comprising parts have been completed at Stage one. This paper establishes a novel mathematic model to minimise the total makespan by mainly considering the dominance relationship between the construction component and the corresponding parts. In order to solve this two-stage problem, we propose an improved harmony search algorithm. A local search method is applied to the best vector at each iteration, so that a more optimal vector can be subsequently realised. The average value, minimum value, relative percentage deviation and standard deviation are discussed in the experimental section, and the proposed local best harmony search algorithm outperforms the genetic algorithm, immune algorithm and harmony search algorithm without local search. Moreover, six optimal solutions are given as Gantt charts, which vividly illustrate that the mathematical model established in this paper can facilitate the development of a better scheduling scheme.     

A random-key encoded harmony search approach for energy-efficient production scheduling with shared resources

When seeking near-optimal solutions for complex scheduling problems, meta-heuristics demonstrate good performance with affordable computational effort. This has resulted in a gravitation towards these approaches when researching industrial use-cases such as energy-efficient production planning. However, much of the previous research makes assumptions about softer constraints that affect planning strategies and about how human planners interact with the algorithm in a live production environment. This article describes a job-shop problem that focuses on minimizing energy consumption across a production facility of shared resources. The application scenario is based on real facilities made available by the Irish Center for Manufacturing Research. The formulated problem is tackled via harmony search heuristics with random keys encoding. Simulation results are compared to a genetic algorithm, a simulated annealing approach and a first-come-first-served scheduling. The superior performance obtained by the proposed scheduler paves the way towards its practical implementation over industrial production chains.     

Single machine due-window assignment scheduling with resource-dependent processing times to minimise total resource consumption cost

This paper considers a single-machine scheduling problem involving convex resource-dependent processing times and due-window assignment simultaneously. The goal is to minimise the total resource consumption cost under the constraint that the schedule cost involving earliness, tardiness, window location, window size and makespan does not exceed a given limit for two popular due window assignment methods: the common flow allowance (slack) due window assignment method (referred to SLKW) and the common due window assignment method (referred to CONW). We show that the problem can be solved in polynomial time. Some extensions of the problem are also given.     

A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron–steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.     

A project scheduling approach to production planning with feeding precedence relations

In Manufacturing-to-Order or Engineering-to-Order systems producing complex and highly customised items, each item has its own characteristics that are often tailored for a specific customer. Project scheduling approaches are suitable for production planning in such environments. However, when we consider the production of complex items, the distinct production operations are often aggregated into activities representing whole production phases. In such cases, the planning and scheduling problem works on the aggregate activities, considering that, in most cases, such activities also have to be manually executed. Moreover, simple finish-to-start precedence relations no longer correctly represent the real production process, but overlapping among activities should be allowed. In this paper, a project scheduling approach is proposed for production planning in Manufacturing-to-Order systems. The Variable Intensity formulation is used to allow the effort committed to the execution of activities to vary over time. Feeding precedences are developed to model generalised precedence relations when the execution mode of activities is not known a priori. Two mathematical formulations of these precedence relations are proposed. The formulations are applied both to randomly generated instances and to an industrial system producing machining centres and are compared in terms of computational efficiency.     

An adaptive scheduling algorithm for a parallel machine problem with rework processes

The development of a scheduling methodology for a parallel machine problem with rework processes is presented in this paper. The problem is to make a schedule for parallel machines with rework probabilities, due-dates, and sequence dependent setup times. Two heuristics are developed based on a dispatching algorithm and problem-space-based search method. In order to evaluate the efficacy of the proposed algorithms, six performance indicators are considered: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of tardy jobs, and the number of reworks. This paper shows how these algorithms can adaptively capture the characteristics of manufacturing facilities for enhancing the performance under changing production environments. Extensive experimental results show that the proposed algorithms give very efficient performance in terms of computational time and each objective value.     

基于MPSO的有限缓冲区多产品厂间歇调度问题的研究

研究了以最小化最大完工时间为目标的有限缓冲区多产品厂间歇调度问题,提出了一种基于多种群粒子群优化(MPSO)的间歇调度算法.该算法采用多种群,增加了种群初始粒子的多样性,在每一代子种群并行进化的过程中引入移民粒子,使子种群之间相互影响和促进,避免算法过早地陷入局部最优,提高了算法的全局搜索能力;每代进化后选出子种群中的优秀粒子作为精华种群,并对其进行变邻域搜索(VNS),进一步提高了算法的收敛精度.通过对不同规模调度问题的仿真,以及与其它算法的对比,证明了该算法解决有限缓冲区多产品厂间歇调度问题的有效性和优越性.     

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.     

An effective hybrid immune algorithm for solving the distributed permutation flow-shop scheduling problem

In this article, an effective hybrid immune algorithm (HIA) is presented to solve the distributed permutation flow-shop scheduling problem (DPFSP). First, a decoding method is proposed to transfer a job permutation sequence to a feasible schedule considering both factory dispatching and job sequencing. Secondly, a local search with four search operators is presented based on the characteristics of the problem. Thirdly, a special crossover operator is designed for the DPFSP, and mutation and vaccination operators are also applied within the framework of the HIA to perform an immune search. The influence of parameter setting on the HIA is investigated based on the Taguchi method of design of experiment. Extensive numerical testing results based on 420 small-sized instances and 720 large-sized instances are provided. The effectiveness of the HIA is demonstrated by comparison with some existing heuristic algorithms and the variable neighbourhood descent methods. New best known solutions are obtained by the HIA for 17 out of 420 small-sized instances and 585 out of 720 large-sized instances.     

Dynamic scheduling in steelmaking-continuous casting production for continuous caster breakdown

In the steelmaking-continuous casting (SCC) production process, machine breakdown is one of the most common disturbances which may make the current schedule unrealisable. Existing rescheduling models for machine breakdown only employ one constraint that charges cannot be processed on this machine in its failure period. However, this method is effective for steelmaking furnace breakdown and refining furnace breakdown but invalid for continuous caster breakdown. Due to the production characteristics of continuous caster, reallocating a casting order and a continuous caster for each unfinished charge on the broken down continuous caster is necessary before making a new schedule. Different reallocation strategies have different impacts on charge’s processing time and processing stage route in the dynamic scheduling process. Therefore, SCC dynamic scheduling for the continuous caster breakdown is different from the other machines. In this paper, the impacts of these strategies are studied, and a dynamic scheduling model which can be used to generate a new schedule for each strategy is built. To obtain a high-quality solution in acceptable computational time for this model with NP-hard feature, a hybrid algorithm featuring a genetic algorithm combined with a general variable neighbourhood search is developed based on the problem-specific characteristics. Computational experiments on practical production data show that the proposed rescheduling method is effective for SCC dynamic scheduling with continuous caster breakdown.