Project scheduling under resource constraints: Application of the cumulative global constraint in a decision support framework

This paper concerns project scheduling under resource constraints. Traditionally, the objective is to find a unique solution that minimizes the project makespan, while respecting the precedence constraints and the resource constraints. This work focuses on developing a model and a decision support framework for industrial application of the cumulative global constraint. For a given project scheduling, the proposed approach allows the generation of different optimal solutions relative to the alternate availability of outsourcing and resources. The objective is to provide a decision-maker an assistance to construct, choose, and define the appropriate scheduling program taking into account the possible capacity resources. The industrial problem under consideration is modeled as a constraint satisfaction problem (CSP). It is implemented under the constraint programming language CHIP V5. The provided solutions determine values for the various variables associated to the tasks realized on each resource, as well as the curves with the profile of the total consumption of resources on time.     

A two-machine flowshop scheduling problem with a separated maintenance constraint

This paper considers a two-machine flowshop scheduling problem with a separated maintenance constraint. This means that the machine may not always be available during the scheduling period. It needs a constant time to maintain the machine after completing a fixed number of jobs at most. The objective is to find the optimal job combinations and the optimal job schedule such that the makespan is minimized. The proposed problem has some practical applications, for example, in electroplating process, the electrolytic cell needs to be cleaned and made up a deficiency of medicine. In this paper, we propose a heuristic algorithm to solve this problem. Some polynomially solvable cases and computational experiments are also provided.     

The satisfiability problem in regular CNF-formulas

 In this paper we deal with the propositional satisfiability (SAT) problem for a kind of multiple-valued clausal forms known as regular CNF-formulas and extend some known results from classical logic to this kind of formulas. We present a Davis–Putnam-style satisfiability checking procedure for regular CNF-formulas equipped with suitable data structures and prove its completeness. Then, we describe a series of experiments for regular random 3-SAT instances. We observe that, for the regular 3-SAT problem with this procedure, there exists a threshold of the ratio of clauses to variables such that (i) the most computationally difficult instances tend to be found near the threshold, (ii) there is a sharp transition from satisfiable to unsatisfiable instances at the threshold and (iii) the value of the threshold increases as the number of truth values considered increases. Instances in the hard part provide benchmarks for the evaluation of regular satisfiability solvers.     

求解作业排序问题的一种改进修复约束满足算法

修复约束满足算法(修复法)是在完整初始解的基础上不断对变量进行修复,最终得到可行解.对此,提出一种求解flow shop排序问题的改进修复法(IRCS_WT),通过采用新的变量表达方式,设计了一种以启发式优化规则为指导的变量选择算法(LWT),并采用一种变量互换算法(LTEE)保证算法的全局搜索性能.将新算法应用于31个标准算例,与传统算法及遗传算法的优化结果进行比较,结果表明在相同运算时问下改进算法具有明显的优越性.     

Solving a real-time allocation problem with constraint programming

In this paper, we present an original approach (CPRTA for “Constraint Programming for solving Real-Time Allocation”) based on constraint programming to solve a static allocation problem of hard real-time tasks. This problem consists in assigning periodic tasks to distributed processors in the context of fixed priority preemptive scheduling. CPRTA is built on dynamic constraint programming together with a learning method to find a feasible processor allocation under constraints. Two efficient new approaches are proposed and validated with experimental results. Moreover, CPRTA exhibits very interesting properties. It is complete (if a problem has no solution, the algorithm is able to prove it); it is non-parametric (it does not require specific tuning) thus allowing a large diversity of models to be easily considered. Finally, thanks to its capacity to explain failures, it offers attractive perspectives for guiding the architectural design process.     

Accelerating column generation for aircraft scheduling using constraint propagation

We discuss how constraint programming can improve the performance of a column generation solution process for the NP-hard Tail Assignment problem in aircraft scheduling. Combining a constraint model of a relaxed Tail Assignment problem with column generation, we achieve substantially improved performance. A generalized preprocessing technique based on constraint propagation is presented that can dramatically reduce the size of the flight network. We also present a heuristic preprocessing method based on the costs of connections, and show how constraint propagation can be used to improve fixing heuristics. Proof of concept is provided using real world Tail Assignment instances.     

An Iterative local-search framework for solving constraint satisfaction problem

In this article, we introduce a new solving framework based on using alternatively two local-search algorithms to solve constraint satisfaction and optimization problems. The technique presented is based on the integration of local-search algorithm as a mechanism to diversify the search instead of using a build on diversification mechanisms. Thus, we avoid tuning the multiple parameters to escape from a local optimum. This technique improves the existing methods: it is generic especially when the given problem can be expressed as a constraint satisfaction problem. We present the way the local-search algorithm can be used to diversify the search in order to solve real examination timetabling problems. We describe how the local-search algorithm can be used to assist any other specific local-search algorithm to escape from local optimality. We showed that such framework is efficient on real benchmarks for timetabling problems.     

复杂反应约束的流程优化调度问题及求解

由于化工流程的生产过程涉及复杂的化学反应,因此,在研究化工流程中的调度问题的时候需要考虑其化学反应所带来的影响因素;这就使得调度的数学模型的建立变得非常的困难。本文针对中小型合成氨流程中的调度问题进行研究,分析合成氨反应的温度、压力、环境等影响因素建立调度的数学模型,采用基于微粒群算法的多目标优化方法对该流程进行优化调度,其结果表明所建的模型具有很好的收敛性和稳定性。     

Adapting the behavior of a job-shop scheduling system

Factory scheduling consists in assigning resources (e.g. machines) and start and end times to operations. Our work is concerned with the problems of schedule generation and schedule revision when unanticipated events occur on the factory floor. SONIA is a knowledge-based scheduling system provided with a blackboard architecture for coordinating the activation of various scheduling and analyzing knowledge sources. In this paper, we focus on the various behaviors these knowledge sources can have and we gather a collection of conclusions regarding the use of various backtracking strategies and the control of constraint propagation.     

Production management as a constraint satisfaction problem

Production management problems can be quite straightforwardly presented as constraint satisfaction problems, where values for some variables are searched for under a set of constraints. A combination of an operation and a resource is usually interpreted as the variable, and a time window is usually interpreted as the value to be searched for. This convention is challenged. A case is considered where the most appropriate interpretation treats the combination of a resource and a time window as the variable, and an operation as the value. A third possible interpretation is also briefly covered, where the combination of an operation and a time window is the variable, and the resource is the value.     

A constraint programming-based solution approach for medical resident scheduling problems

Persistent calls come from within the graduate medical education community and from external sources for regulating the resident duty hours in order to meet the obligations about the quality of resident education, the well-being of residents themselves, and the quality of patient care services. The report of the Accreditation Council for Graduate Medical Education (ACGME) proposes common program requirements for resident hours. In this paper, we first develop a mixed-integer programming model for scheduling residents’ duty hours considering the on-call night, day-off, rest period, and total work-hour ACGME regulations as well as the demand coverage requirements of the residency program. Subsequently, we propose a column generation model that consists of a master problem and an auxiliary problem. The master problem finds a configuration of individual schedules that minimizes the sum of deviations from the desired service levels for the day and night periods. The formulation of this problem is possible by representing the feasible schedules using column variables, whereas the auxiliary problem finds the whole set of feasible schedules using constraint programming. The proposed approach has been tested on a series of problems using real data obtained from a hospital. The results indicate that high-quality schedules can be obtained within a few seconds.     

Scheduling trains as a blocking parallel-machine job shop scheduling problem

In this paper, the train scheduling problem is modelled as a blocking parallel-machine job shop scheduling (BPMJSS) problem. In the model, trains, single-track sections and multiple-track sections, respectively, are synonymous with jobs, single machines and parallel machines, and an operation is regarded as the movement/traversal of a train across a section. Due to the lack of buffer space, the real-life case should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold the train until next section on the routing becomes available. Based on literature review and our analysis, it is very hard to find a feasible complete schedule directly for BPMJSS problems. Firstly, a parallel-machine job-shop-scheduling (PMJSS) problem is solved by an improved shifting bottleneck procedure (SBP) algorithm without considering blocking conditions. Inspired by the proposed SBP algorithm, feasibility satisfaction procedure (FSP) algorithm is developed to solve and analyse the BPMJSS problem, by an alternative graph model that is an extension of the classical disjunctive graph models. The proposed algorithms have been implemented and validated using real-world data from Queensland Rail. Sensitivity analysis has been applied by considering train length, upgrading track sections, increasing train speed and changing bottleneck sections. The outcomes show that the proposed methodology would be a very useful tool for the real-life train scheduling problems.     

Simplification in a satisfiability checker for VLSI applications

INSTEP is a satisfiability checker designed for the original purpose of solving a specific target set of problems in the formal verification of VLSI circuits. These are real-world problems concerning a sequential circuit that is part of a commercial chip manufactured by Texas Instruments. The program has succeeded in solving these problems, which require satisfiability checking for combinational representations containing up to around 10 000 variables and a graphical representation of around 17 000 nodes. It has also been successfully applied to a number of standard benchmark problems in combinational circuit verification. Results on these benchmarks are overall competitive with those for the widely used method based onbinary decision diagrams, and for the first time demonstrate the solution in polynomial time of certain benchmarks involving combinational multipliers.A central part of the INSTEP algorthim is simplification. Most simplifications that take place in previous tautology checkers consist of the replacement of a formula by a shorter formula that is logically equivalent. Most simplifications in INSTEP replace a formula by another formula which isnot logically equivalent, but such that satisfiability is nevertheless preserved. These new simplifications depend on the pattern of occurrence of one or more variables and particularly on theirpolarity.The simplifications used by INSTEP rest on several new theorems in an area of propositional calculus (or Boolean algebra) which is crucial to the general theory of effective simplification of propositional formulas. The primary purpose of the present paper is to demonstrate these theorems and explain the simplifications that depend on them.For the present paper we have tried INSTEP on the well-known pigeonhole problem. So far as we know INSTEP is the first implemented program to produce proofs of polynomial length for pigeonhole problems. It also produces these proofs in polynomial time.     

A constraint-based approach for the shift design personnel task scheduling problem with equity

This paper presents an industrial problem which arises in a company specialized in drug evaluation and pharmacology research. The aim is to build employee timetables covering the demand given by a set of fixed tasks. The optimality criterion concerns the equity of the workload sharing. A solution to this problem is the assignment of all tasks whose resulting working shifts respect tasks requirements as well as legal and organizational constraints. Scheduling problems usually consider a fixed set of shifts which have to be assigned to a given number of employees whereas in our problem shifts are not fixed and are deduced from the task assignment. In the following, we refer to this problem as the shift-design personnel task scheduling problem with an equity criterion (SDPTSP-E), in reference to the shift minimization personnel task scheduling problem (SMPTSP). Even if the SDPTSP-E is related to several problems, none of them allow to grasp its full complexity. Consequently, we propose a dedicated method based on constraint programming. Several branching and exploration strategies are proposed and tested.     

Using an enhanced scatter search algorithm for a resource-constrained project scheduling problem

The resource-constrained project scheduling problem is one of the classical problems in the field of operations research. There are many criteria to efficiently determine the desired schedule of a project. In this paper, a well-known criterion namely project’s makespan is considered. Due to the complexity of the problem, it is very difficult to obtain optimum solution for this kind of problems by means of traditional methods. Therefore, an enhanced scatter search, based on a new path relinking and two prominent permutation-based and crossover operators, is devised to solve the problem. In order to validate the performance of the proposed algorithm, in terms of solution quality, the algorithm is applied to various test problems available on the literature and the reliability of it, is compared with well-reported benchmark algorithms. The computational results reveal that the proposed algorithm has appropriate results in comparison with the existing benchmark algorithms.     

Branching rules for satisfiability

Recent experience suggests that branching algorithms are among the most attractive for solving propositional satisfiability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules with an empirical model-building approach. One model is based on the rationale given for the Jeroslow-Wang rule, variations of which have performed well in recent work. The model is refuted by carefully designed computational experiments. A second model explains the success of the Jeroslow-Wang rule, makes other predictions confirmed by experiment, and leads to the design of branching rules that are clearly superior to Jeroslow-Wang.GSIA Working Paper 1994-09. The first author is partially supported by ONR grant N00014-92-J-1028. The authors wish to thank Ajai Kapoor for assistance in computational p667 testing and statistical analysis.     

A tabu search heuristic for the quay crane scheduling problem

This paper proposes a tabu search heuristic for the Quay Crane Scheduling Problem (QCSP), the problem of scheduling a fixed number of quay cranes in order to load and unload containers into and from a ship. The optimality criterion considered is the minimum completion time. Precedence and non-simultaneity constraints between tasks are taken into account. The former originate from the different kind of operations that each crane has to perform; the latter are needed in order to avoid interferences between the cranes. The QCSP is decomposed into a routing problem and a scheduling problem. The routing problem is solved by a tabu search heuristic, while a local search technique is used to generate the solution of the scheduling problem. This is done by minimizing the longest path length in a disjunctive graph. The effectiveness of our algorithm is assessed by comparing it to a branch-and-cut algorithm and to a Greedy Randomized Adaptive Search Procedure (GRASP).     

Testing XML constraint satisfiability

In a previous paper, we have showed that Hybrid Modal Logic can be successfully used to model semistructured data and provides a simple and well suited formalism for capturing “well typed” references and of course a powerful language for expressing constraint. This paper builds on the previous one and provides a tableau proof technique for constraint satisfiability testing in the presence of schemas.     

A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding

We consider a monthly crew scheduling problem with preferential bidding in the airline industry. We propose a new methodology based on a graph coloring model and a tabu search algorithm for determining if the problem contains at least one feasible solution. We then show how to combine the proposed approach with a heuristic sequential scheduling method that uses column generation and branch-and-bound techniques.