constraint solvers have proved to be a powerful tool for both expressing and solving complex problems in many contexts, in particular in Automated Planning and Scheduling. In this work, we propose new constraints to e...
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constraint solvers have proved to be a powerful tool for both expressing and solving complex problems in many contexts, in particular in Automated Planning and Scheduling. In this work, we propose new constraints to enhancing an implementation of a constraint solver for sets of integers (ic_sets) embedded in the ECLIPSe system. This way, we confer a new vision of modelling that in particular allows a task to be planned on alternate days. In addition, these new constraints make finite domain and finite sets domains to cooperate, reducing the search space and improving the efficiency of the existing set solvers for some specific cases. We report on a prototype implementation and apply these constraints to modelling scheduling problems as benchmarks for a performance analysis. Experiments reveal a relevant improvement with respect to the standard ic_sets solver which only features cardinality as cooperation mechanism between domains. Both enhanced expressiveness and performance are key points for practical applications of such solvers. (C) 2017 Elsevier Ltd. All rights reserved.
In this paper, a methodology is developed to solve a multiobjective fractional programming problem in which the coefficients of the objective functions and constraints are intervals. This model is transformed into an ...
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In this paper, a methodology is developed to solve a multiobjective fractional programming problem in which the coefficients of the objective functions and constraints are intervals. This model is transformed into an interval-free equivalent optimization problem. A new partial ordering is introduced and the relation between the original problem and the transformed problem is established using this partial ordering. The proposed methodology is illustrated through a numerical example.
A dual resource constrained (DRC) scheduling problem arises at the photolithography area in semiconductor manufacturing wherein reticles are required as an auxiliary resource. Reticles are transferred from one place t...
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A dual resource constrained (DRC) scheduling problem arises at the photolithography area in semiconductor manufacturing wherein reticles are required as an auxiliary resource. Reticles are transferred from one place to another. While this shared resource gives the manufacturer a flexibility, it certainly gives rise to a complex DRC scheduling problem surrounded by jobs, machines, and reticles, restricted by sequence-dependent setup-time and location-dependent reticle transfer-time. This study proposes a constraint programming (CP) approach and investigates methods for improving our initial CP using a hybrid method and variable ordering heuristic. Experiments indicate the variable ordering heuristic brings a significant improvement over a pure CP. Note to Practitioners-There has been yet no successful exact approach that addresses litho scheduling problem, covering jobs, machines, and reticles. This study demonstrates CP is able to find an optimal solution for most of realistic industry-size test problems. In a future smart semiconductor factory, seamlessly orchestrating machines, reticles, and jobs would not be the end state. The next level is to integrate material handling system to this already overcrowded production scheduling problem. The specialized keywords of CP, as demonstrated in this study, will enable practitioners to develop a concise code of integrating vehicles, jobs, machines, and reticles.
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. Th...
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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 in bound 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.
constraint satisfaction problems can be expressed very elegantly in state-based formal methods such as B. But can such specifications be directly used for solving real-life problems? In other words, can a formal model...
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constraint satisfaction problems can be expressed very elegantly in state-based formal methods such as B. But can such specifications be directly used for solving real-life problems? In other words, can a formal model be more than a design artefact but also be used at runtime for inference and problem solving? We will try and answer this important question in the present paper with regard to the university timetabling problem. We report on an ongoing project to build a curriculum timetable validation tool where we use a formal model as the basis to validate timetables from a student's perspective and to support incremental modification of timetables. In this article we describe the problem domain, the formalization in B and our approach to execute the formal model in a production system using ProB.
Propagation is at the very core of t can provide signi: it can provide significant performance boosts as long as the search space reduction is not outweighed by the cost for running the propagators. A lot of research ...
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Propagation is at the very core of t can provide signi: it can provide significant performance boosts as long as the search space reduction is not outweighed by the cost for running the propagators. A lot of research effort in the CP community is directed toward improving this trade-off. While experimental evaluation is here of the greatest importance, there exists no systematic and flexible methodology to measure the exact benefits provided by a given (new) filtering procedure. This work proposes such a framework by relying on replaying search trees to obtain more realistic assessments. Reducing propagation overhead is done chiefly by 1) devising more efficient algorithms or by 2) using on-line control policies to limit the propagator activations, i.e., mechanisms to reduce the number of propagator calls. In both cases, obtaining improvements is a long and demanding process with uncertain outcome. We propose a method to assess the potential gain of both approaches before actually starting the endeavor, providing the community with a tool to best direct the research efforts. In order to visualize benefits of actual global constraints and the potential of their improvement, we suggest the use of performance profiles. Our approach is showcased for well-known global constraints: alldifferent, cumulative, binpacking and unary (with transition times).
Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transi...
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Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labelled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate three semantics for IMCs: once-and for-all, interval-Markov-decision-process, and at-every-step. In particular, we prove that all three semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of plMCs - consistency, qualitative reachability and quantitative reachability - that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results. (C) 2018 Elsevier B.V. All rights reserved.
Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed. First, the makespa...
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Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed. First, the makespan value is minimised with the smallest sublots defined for the problem instance. This makes it possible to shorten the makespan significantly, because each sublot is transferred separately to the next operation of a job. In the second stage, the sizes of the sublots are maximised without increasing the obtained makespan value. In this way, the quantity of sublots and transport activities is limited together with the related manufacturing cost. Two objectives are defined for the second stage. The first one is the maximisation of the sum of the sublot sizes of all operations, the second one is the maximisation of the number of the operations which do not need to be split at all. Mixed-integer linear programming, constraint programming and graph-based models are implemented for the problem. Two optimisation approaches are developed and compared in computational experiments for each stage and objective, one approach is based on a third-party solver, and the second one on an independent own implementation, namely a tabu search and a greedy constructive heuristic.
In almost all Japanese railway companies, rolling stock management still relies on manual procedure. As density of trains and interconnectivity between lines are increased, a support system for the management gets to ...
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In almost all Japanese railway companies, rolling stock management still relies on manual procedure. As density of trains and interconnectivity between lines are increased, a support system for the management gets to be important. This paper focuses on a scheduling task for vehicle units' operation and a support system for rescheduling vehicle units' operation in train service disruption. A schedule of vehicle units' operation is modified by a dispatcher to keep consistency between train timetable and vehicle unit assignment. When there is no solution, the dispatcher has to ask a train service manager to change train timetable. To support this task, we developed an algorithm of rescheduling vehicle unit operation, which included relaxation of constraints. Our algorithm represents constraints as a network model, and, if necessary, relaxes constraints by modifying the network model during search of a solution. This paper indicates the network model, the algorithm of searching for a solution as relaxing constraints, and numerical experiments using a real middle-size data. The results of the experiments showed that our algorithm could calculate various solutions with relaxed constraints. Analyzing the solutions at the viewpoints of train service and rolling stock operation, we showed the effectiveness of a system that proposes various solutions using our algorithm.
Process-aware information systems (PAISs) are increasingly used to provide flexible support for business processes. The support given through a PAIS is greatly enhanced when it is able to provide accurate time predict...
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Process-aware information systems (PAISs) are increasingly used to provide flexible support for business processes. The support given through a PAIS is greatly enhanced when it is able to provide accurate time predictions which is typically a very challenging task. Predictions should be (1) multi-dimensional and (2) not based on a single process instance. Furthermore, the prediction system should be able to (3) adapt to changing circumstances and (4) deal with multi-perspective declarative languages (e.g., models which consider time, resource, data and control flow perspectives). In this work, a novel approach for generating time predictions considering the aforementioned characteristics is proposed. For this, first, a multi-perspective constraint-based language is used to model the scenario. Thereafter, an optimized enactment plan (representing a potential execution alternative) is generated from such a model considering the current execution state of the process instances. Finally, predictions are performed by evaluating a desired function over this enactment plan. To evaluate the applicability of our approach in practical settings we apply it to a real process scenario. Despite the high complexity of the considered problems, results indicate that our approach produces a satisfactory number of good predictions in a reasonable time.
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