The lockmaster's problem.

Inland waterways form a natural network that is an existing, congestion free infrastructure with capacity for more traffic.Transportation of goods by ship is widely promoted as it is a reliable, efficient and environmental friendly way of transport. A bottleneck for transportation over water are the locks that manage the water level. The lockmaster's problem concerns the optimal strategy for operating such a lock. In the lockmaster's problem we are given a lock, a set of ships coming from downstream that want to go upstream, and another set of ships coming from upstream that want to go downstream. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper a dynamic programming algorithm (DP) is proposed that solves the lockmaster's problem in polynomial time. We extend this DP to different generalizations that consider weights, water usage, capacity, and (a fixed number of) multiple chambers. Finally, we prove that the problem becomes strongly NP-hard when the number of chambers is part of the input.Lock scheduling; Batch scheduling; Dynamic programming; Complexity;

A Methodology for the Range Ordering of Alternatives using a Bayesian Decision Model with Applications to the Space Program

The primary objective of this paper is to provide a reasonably general and essentially unified approach to those problems involving value judgments and subjective decision making, without regard to excessive rigor. The principle areas and methods of attack developed are: (1) The selection of a value measure which emphasizes the fact that the criterion of optimum performance is quite arbitrary, its merits reflecting only the constraints on the problem and the objectives sought, (2) The utilization of statistical decision theory as a basis for the solution and subsequent ev aluation of a class of problems in which a priori value judgments must be assigned by an individual or committee under uncertainty, and (3) The application of the methodology to those areas in which the relative uncertainty level of a decision need be assessed in terms of a cost or penalty incurred in reaching the conclusion. A parti cularly important application is the selection of alternatives (ioe., projects by corporate executives) and the subsequent sensitivity analysis of the decision

Efficient Duration-Based Workload Balancing for Interdependent Vehicle Routes

Vehicle routing and scheduling problems with interdependent routes arise when some services must be performed by at least two vehicles and temporal synchronization is thus required between the starting times of these services. These problems are often coupled with time window constraints in order to model various real-world applications such as pickup and delivery with transfers, cross-docking and home care scheduling. Interdependent routes in these applications can lead to large idle times for some drivers, unnecessarily lengthening their working hours. To remedy this unfairness, it is necessary to balance the duration of the drivers\u27 routes. However, quickly evaluating duration-based equity functions for interdependent vehicle routes with time windows poses a significant computational challenge, particularly when the departure time of routes is flexible. This paper introduces models and algorithms to compute two well-known equity functions in flexible departure time settings: min-max and range minimization. We explore the challenges and algorithmic complexities of evaluating these functions both from a theoretical and an experimental viewpoint. The results of this paper enable the development of new heuristic methods to balance the workload of interdependent vehicle routes with time windows

Optimal Decision Trees for the Algorithm Selection Problem: Integer Programming Based Approaches

Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this paper, we propose Integer Programming based approaches to build decision trees for the Algorithm Selection Problem. These techniques allow automate three crucial decisions: (i) discerning the most important problem features to determine problem classes; (ii) grouping the problems into classes and (iii) select the best algorithm configuration for each class. To evaluate this new approach, extensive computational experiments were executed using the linear programming algorithms implemented in the COIN-OR Branch & Cut solver across a comprehensive set of instances, including all MIPLIB benchmark instances. The results exceeded our expectations. While selecting the single best parameter setting across all instances decreased the total running time by 22%, our approach decreased the total running time by 40% on average across 10-fold cross validation experiments. These results indicate that our method generalizes quite well and does not overfit.Comment: International Transactions in Operational Research. 201

Optimisation de laboratoires médicaux

This thesis focuses on the optimization of clinical laboratory design and operating decisions. A clinicallaboratory is an organization gathering human and machinery resources to analyze blood samples. Inthis thesis, a decision support tool including mathematical models, a heuristic algorithm and acustomized simulation model is developed to aid decision makers for the main strategic, tactical andoperational problems in clinical laboratory design and operations management. This decision supporttool follows a top-down stepwise framework starting from strategic problems and ending withoperational ones, including a recursive loop for modification and improvement. In this thesis, machineselection and facility layout are studied as the main strategic problems, analyzer configuration problemas the tactical problem, and assignment, aliquoting, and scheduling as the principal operationalproblems. In order to deal with machine selection problem for clinical laboratory, a mathematical modelis proposed which aids to select the most appropriate machines to equip the system. To tackle physicalarrangement of instruments within the laboratory area, a heuristic approach is developed. The proposedheuristic comprises the key constraints of laboratory layout design. To address the analyzerconfiguration problem which mainly deals with the assignment of chemical materials to the analyzersin clinical laboratory, a bi-objective mathematical model is developed. In addition, to determine anefficient assignment of sample tubes to the analyzers, a mathematical model with three objectives isproposed. A customized, flexible, and fine-grained simulation model is developed in FlexSim to studythe clinical laboratory designed through the outputs of developed mathematical models and layoutalgorithm. Simulation model plays a key role in the proposed framework as it is used for many purposes.The simulation model helps the designer to construct and analyze a complete clinical laboratory takinginto account all major features of the system. This simulation attribute provides the ability to scrutinizethe system behaviour and to find out whether the designed system is efficient. System performanceanalysis through simulation and resulting key performance indicators give helpful feedbacks for systemimprovement. Furthermore, simulation model can be fruitful to decide on scheduling, aliquoting andstaffing problems through the evaluation of various scenarios proposed by decision maker for each ofthese problems. To verify the validity of the proposed framework, data extracted from a real case isused. The output results seal on the applicability and the efficiency of the proposed framework as wellas competency of proposed techniques to deal with each optimization problem. To the best of ourknowledge, this thesis is one of the leading studies on the optimization of clinical laboratories.Cette thèse porte sur l'optimisation de la conception et des décisions opérationnelles des laboratoires d'analyses médicales. Dans cette thèse, un outil d'aide à la décision comprenant des modèles mathématiques, un algorithme heuristique et un modèle de simulation personnalisé est développé pour aider les décideurs à résoudre les principaux problèmes stratégiques, tactiques et opérationnels en conception et gestion des opérations des laboratoires d'analyses médicales. Dans cette thèse, la sélection des machines et la disposition des instruments sont étudiées en tant que principaux problèmes stratégiques, le problème de configuration des analyseurs en tant que problème tactique et l’affectation, l’aliquotage et l'ordonnancement en tant que principaux problèmes opérationnels. Un modèle de simulation personnalisé et flexible est développé dans FlexSim pour étudier le laboratoire d'analyse médicale conçu à l'aide des résultats de modèles mathématiques et d'un algorithme de layout développés. Le modèle de simulation aide le concepteur à construire et à analyser un laboratoire complet en tenant compte de toutes les principales caractéristiques du système. Cet attribut de simulation permet d'analyser le comportement du système et de déterminer si le système conçu est efficace. Pour vérifier la validité du cadre proposé, les données extraites d’un cas réel sont utilisées. Les résultats de sortie scellent l'applicabilité et l'efficacité du cadre proposé ainsi que la compétence des techniques proposées pour traiter chaque problème d'optimisation. À notre connaissance, cette thèse est l’une des principales études sur l’optimisation des laboratoires d'analyses médicales