Flexible job-shop scheduling problem with resource recovery constraints

In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.     

Flexible job-shop scheduling problem under resource constraints

A flexible job-shop-scheduling problem is an extension of classical job-shop problems that permit an operation of each job to be processed by more than one machine. The research methodology is to assign operations to machines (assignment) and determine the processing order of jobs on machines (sequencing) such that the system objectives can be optimized. This problem can explore very well the common nature of many real manufacturing environments under resource constraints. A genetic algorithm-based approach is developed to solve the problem. Using the proposed approach, a resource-constrained operations–machines assignment problem and flexible job-shop scheduling problem can be solved iteratively. In this connection, the flexibility embedded in the flexible shop floor, which is important to today's manufacturers, can be quantified under different levels of resource availability.     

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.     

Multiple colony ant algorithm for job-shop scheduling problem

Ant colony optimization (ACO) is a metaheuristic that takes inspiration from the foraging behaviour of a real ant colony to solve the optimization problem. This paper presents a multiple colony ant algorithm to solve the Job-shop Scheduling Problem with the objective that minimizes the makespan. In a multiple colony ant algorithm, ants cooperate to find good solutions by exchanging information among colonies which are stored in a master pheromone matrix that serves the role of global memory. The exploration of the search space in each colony is guided by different heuristic information. Several specific features are introduced in the algorithm in order to improve the efficiency of the search. Among others is the local search method by which the ant can fine-tune their neighbourhood solutions. The proposed algorithm is tested over set of benchmark problems and the computational results demonstrate that the multiple colony ant algorithm performs well on the benchmark problems.     

Assessing scheduling policies in a permutation flowshop with common due dates

This paper focuses onto a situation arising in most real-life manufacturing environments when scheduling has to be performed periodically. In such a scenario, different scheduling policies can be adopted, being perhaps the most common to assume that, once a set of jobs has been scheduled, their schedule cannot be modified (‘frozen’ schedule). This implies that, when the next set of jobs is to be scheduled, the resources may not be fully available. Another option is assuming that the schedule of the previously scheduled jobs can be modified as long as it does not violate their due date, which has been already possibly committed to the customer. This policy leads to a so-called multi-agent scheduling problem. The goal of this paper is to discern when each policy is more suitable for the case of a permutation flowshop with common due dates. To do so, we carry out an extensive computational study in a test bed specifically designed to control the main factors affecting the policies, so we analyse the solution space of the underlying scheduling problems. The results indicate that, when the due date of the committed jobs is tight, the multi-agent approach does not pay off in view of the difficulty of finding feasible solutions. Moreover, in such cases, the policy of ‘freezing’ the schedule of the jobs leads to a very simple scheduling problem with many good/acceptable solutions. In contrast, when the due date has a medium/high slack, the multi-agent approach is substantially better. Nevertheless, in this latter case, in order to perceive the full advantage of this policy, powerful solution procedures have to be designed, as the structure of the solution space of the latter problem makes extremely hard to find optimal/good solutions.     

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.     

A note on resource allocation scheduling with position-dependent workloads

In this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.     

Reheat furnace scheduling with energy consideration

This paper focuses on the reheat furnace scheduling problem (RFSP) which is to assign the slabs to the reheat furnace, make the slab sequence for each furnace and determine the feed-in time and the residence time for each slab in order to reduce the unnecessary energy consumption reflected by minimising the objective under consideration. Differing from the traditional scheduling problem, the actual residence time of each slab in RFSP needs to be decided and it is correlated with its neighbour slabs in the reheating sequence of the same furnace. Firstly, the RFSP is formulated as a mixed integer programming model with consideration of the practical production requirements. The strong NP-hardness of the problem motivates us to develop a scatter search (SS) algorithm to solve the problem approximately. The SS algorithm is improved by constraint propagation (CP) for filtering the infeasible solutions in both the generation of the initial solutions and the improvement procedure. To verify the algorithm performance, the proposed algorithm is compared with ILOG CP Optimiser for small-scaled problems and the standard SS, genetic algorithm (GA) for large-scaled practical problems, respectively. The computational results illustrate that the proposed algorithm is relatively effective and efficient.     

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.     

A new scheduling technique for the resource–constrained project scheduling problem with discounted cash flows

In this paper, we discuss the resource–constrained project scheduling problem with discounted cash flows. We introduce a new schedule construction technique which moves sets of activities to improve the project net present value and consists of two steps. In particular, the inclusion of individual activities into sets, which are then moved together, is crucial in both steps. The first step groups the activities based on the predecessors and successors in the project network, and adds these activities to a set based on their finish time and cash flow. The second step on the contrary does so based on the neighbouring activities in the schedule, which may but need not include precedence related activities. The proposed scheduling method is implemented in a genetic algorithm metaheuristic and we employ a penalty function to improve the algorithm’s feasibility with respect to a tight deadline. All steps of the proposed solution methodology are tested in detail and an extensive computational experiment shows that our results are competitive with existing work.     

Mixed graph colouring for unit-time scheduling

We consider the job shop scheduling problem with unit-time operations and the makespan criterion. This problem is reduced to finding an optimal colouring of a special class of mixed graph, where its partial graph without edges represents the union of maximal directed paths and its partial graph without arcs represents the union of maximal cliques. As the problem is known to be NP-hard, both exact and heuristic methods are proposed to solve it. This study is carried out in three steps. First, a new lower and upper bounds for the mixed chromatic number are proposed. Afterwards, a colour-indexed mathematical model using the proposed bounds is developed. Then, a tabu search using a dynamic neighbourhood structure is adapted for solving large instances. Computational experiments conducted on several modified benchmarks show the efficiency and effectiveness of the proposed resolution methods.     

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。     

Finite capacity scheduling with mixed duration tooling trees

Finite capacity scheduling is a research area which has much practical application and the quality of the schedules has a major impact on the delivery performance, profitiability and finance requirements of companies. This paper proposes a method of finite capacity scheduling where activities have a range of mandatory and alternative tools which can be used, and some of the less preferred tools run at a slower rate. The calculations are presented by example, and in the context of a computer program to implement the algorithms.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

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.