Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

Scheduling model for systems with complex alternative behaviour

In this paper we propose a flexible model for scheduling problems, which allows the modeling of systems with complex alternative behaviour. This model could for example facilitate the step from process planning model to optimization model. We show how automatic constraint generation can be performed for both Constraint Programming and Mixed Integer Linear Programming (MILP) models. Also, for the MILP case, a new formulation for mutual exclusion of resources is proposed. This new formulation works well for proving optimality in systems with multiple capacity resources. Some benchmarks for such job shop scheduling problems as well as systems with a large number of alternatives are also presented

Identifying sources of global contention in constraint satisfaction search

Much work has been done on learning from failure in search to boost solving of combinatorial problems, such as clause-learning and clause-weighting in boolean satisfiability (SAT), nogood and explanation-based learning, and constraint weighting in constraint satisfaction problems (CSPs). Many of the top solvers in SAT use clause learning to good effect. A similar approach (nogood learning) has not had as large an impact in CSPs. Constraint weighting is a less fine-grained approach where the information learnt gives an approximation as to which variables may be the sources of greatest contention. In this work we present two methods for learning from search using restarts, in order to identify these critical variables prior to solving. Both methods are based on the conflict-directed heuristic (weighted-degree heuristic) introduced by Boussemart et al. and are aimed at producing a better-informed version of the heuristic by gathering information through restarting and probing of the search space prior to solving, while minimizing the overhead of these restarts. We further examine the impact of different sampling strategies and different measurements of contention, and assess different restarting strategies for the heuristic. Finally, two applications for constraint weighting are considered in detail: dynamic constraint satisfaction problems and unary resource scheduling problems

Scheduling with Alternative Process Plans

Katedra řídicí technik

Planification socio-responsable du travail dans les chaînes de montage d'aéronefs : comment satisfaire à la fois objectifs ergonomiques et économiques

Dans cette thèse, le problème de planification des tâches dans les chaînes de montage des aéronefs est étudié. Ces lignes de production sont principalement manuelles et tactées. L'échec de la livraison dans les délais pouvant entraîner des pénalités importantes pour le fabricant, il est essentiel de respecter le calendrier de chaque poste de travail en tenant compte à la fois de critères économiques et ergonomiques. Ce problème de planification peut être considéré comme un problème généralisé de planification de projets avec contraintes de ressources (RCPSP). Dans un premier temps, nous passons en revue les méthodes ergonomiques existantes qui peuvent être utilisées pour évaluer la charge de travail physique dans les lignes de production et examinons leur applicabilité au contexte des chaînes de montage d'aéronefs avec des temps de cycle longs. Sur la base de cette évaluation, nous développons des modèles mathématiques à introduire dans les problèmes considérés du RCPSP afin de prendre en compte l'impact ergonomique sur les opérateurs. Tenant compte de ces contraintes ergonomiques, le problème industriel initial est modélisé comme un RCPSP avec des contraintes et des objectifs spéciaux intégrant à la fois des aspects économiques et ergonomiques. Plusieurs formulations avec des opérateurs polyvalents, des ressources avec des capacités dépendantes du temps, des contraintes sur les facteurs ergonomiques et des tâches multimodales ordonnées par des relations de précédence complexes sont considérées. Des modèles de programmation par contraintes et de programmation linéaire en nombres entiers ont été développés pour ces formulations. Afin d'améliorer les procédures de solution, de nouvelles techniques de propagation de contraintes sont proposées et mises en œuvre. Un nouvel algorithme pour le calcul de la borne inférieure est également développé. L'efficacité des modèles et méthodes présentés est validée par des expériences numériques.In this thesis, the scheduling problem of tasks in aircraft assembly lines is studied. These production lines are mainly manual and paced. Since the failure of delivery on time may result in significant penalties for the manufacturer, it is crucial to meet the schedule at each workstation taking into account both economic and ergonomic criteria. This scheduling problem can be considered as a generalized Resource-Constraints Project Scheduling Problem (RCPSP). Firstly, we review the existing ergonomic methods that can be used to evaluate the physical workload in production lines and examine their applicability to the context of aircraft assembly lines with long takt times. On the basis of this evaluation, we develop mathematical models to be introduced in considered RCPSP problems in order to take into account the ergonomic impact on the operators. Taking into consideration these ergonomic constraints, the original industrial problem is modeled as a RCPSP with special constraints and objectives integrating both economic and ergonomic aspects. Several formulations with multi-skilled operators, resources with time-dependent capacities, constraints on ergonomic factors and multi-mode tasks ordered by precedence relations with time lags are considered. Constraint Programming and Integer Linear Programming models are developed for these formulations. In order to enhance the solution procedures, novel constraint propagation techniques are proposed and implemented. A new algorithm for lower bound calculation is developed as well. The efficiency of presented models and methods are validated through numerical experiments

Robust Execution Strategy for Scheduling Under Uncertainity

VARAKANTHAM, Pradeep; CHENG, Shih-Fen ; LIM, Yun Fong</p