Operational model for empty container repositioning

Ph.DDOCTOR OF PHILOSOPH

A stochastic programming approach for chemotherapy appointment scheduling

Chemotherapy appointment scheduling is a challenging problem due to the uncertainty in pre-medication and infusion durations. In this paper, we formulate a two-stage stochastic mixed integer programming model for the chemotherapy appointment scheduling problem under limited availability and number of nurses and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime, chair idle time, and patient waiting time. The computational burden to solve real-life instances of this problem to optimality is significantly high, even in the deterministic case. To overcome this burden, we incorporate valid bounds and symmetry breaking constraints. Progressive hedging algorithm is implemented in order to solve the improved formulation heuristically. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and a linear approximation of the objective function. Using numerical experiments based on real data from a major oncology hospital, we compare our solution approach with several scheduling heuristics from the relevant literature, generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules, and estimate the value of stochastic solution to assess the significance of considering uncertainty

Spatial Decomposition for Differential Equation Constrained Stochastic Programs

Rozsáhlá třída inženýrských optimalizačních úloh vede na modely s omezeními ve tvaru obyčejných nebo parciálních diferenciálních rovnic (ODR nebo PDR). Protože diferenciálních rovnice je možné řešit analyticky jen v nejjednodušších případech, bylo k řešení použito numerických metod založených na diskretizaci oblasti. Zvolili jsme metodu konečných prvků, která umožňuje převod omezení ve tvaru diferenciálních rovnic na omezení ve tvaru soustavy lineárních rovnic. Reálné problémy jsou často velmi rozsáhlé a přesahují dostupnou výpočetní kapacitu. Výpočetní čas lze snížit pomocí progressive hedging algoritmu (PHA), který umožňuje paralelní implementaci. PHA je efektivní scénářová dekompoziční metoda pro řešení scénářových stochastických úloh. Modifikovaný PHA byl využit pro původní přístup prostorové dekompozice. Aproximace diferenciálních rovnic v modelu problému je dosaženo pomocí diskretizace oblasti. Diskretizace je dále využita pro prostorovou dekompozici modelu. Algoritmus prostorové dekompozice se skládá z několika hlavních kroků: vyřešení problému s hrubou diskretizací, rozdělení oblasti problému do překrývajících se částí a iterační řešení pomocí PHA s jemnější diskretizací s využitím hodnot z hrubé diskretizace jako okrajových podmínek. Prostorová dekompozice byla aplikována na základní testovací problém z oboru stavebního inženýrství, který se zabývá návrhem rozměrů průřezu nosníku. Algoritmus byl implementován v softwaru GAMS. Získané výsledky jsou zhodnoceny vzhledem k výpočetní náročnosti a délce překrytí.Wide variety of optimum design problems in engineering leads to optimization models constrained by ordinary or partial differential equations (ODE or PDE). Numerical methods based on discretising domain are required to obtain a non-differential numerical description of the differential parts of constraints because the analytical solutions can be found only for simple problems. We chose the finite element method. The real problems are often large-scale and exceed computational capacity. Hence, we employ the progressive hedging algorithm (PHA) - an efficient scenario decomposition method for solving scenario-based stochastic programs, which can be implemented in parallel to reduce the computing time. A modified PHA was used for an original concept of spatial decomposition based on the mesh created for approximation of differential equation constraints. The algorithm consists of a few main steps: solve our problem with a raw discretization, decompose it into overlapping parts of the domain, and solve it again iteratively by the PHA with a finer discretization - using values from the raw discretization as boundary conditions until a given accuracy is reached. The spatial decomposition is applied to a basic test problem from the civil engineering area: design of beam cross section dimensions. The algorithms are implemented in GAMS software and finally results are evaluated with respect to a computational complexity and a length of overlap.

Sampling based progressive hedging algorithms for stochastic programming problems

Many real-world optimization problems have parameter uncertainty. For instances where the uncertainties can be estimated to a certain degree, stochastic programming (SP) methodologies are used to identify robust plans. Despite advances in SP, it is still a challenge to solve real world stochastic programming problems, in part due to the exponentially increasing number of scenarios. For two-stage and multi-stage problems, the number of scenarios increases exponentially with the number of uncertain parameters, and for multi-stage problems also with the number of decision stages. In the case of large scale mixed integer stochastic problem instances, there are usually two common approaches: approximation methods and decomposition methods. Most common sampling-based approximation (SAA) SP technique is the Monte Carlo sampling-based method. The Progressive Hedging Algorithm (PHA) on the other hand can optimally solve large problems through the decomposition into smaller problem instances. The SAA, while effectively used in many applications, can lead to poor solution quality if the selected sample sizes are not sufficiently large. With larger sample sizes and multi-stage SPs, however, the SAA method is not practical due to the significant computational effort required. In contrast, PHA suffers from the need to solve many sub-problems iteratively which is computationally expensive. In this dissertation, we develop novel SP algorithms integrating sampling based SAA and decomposition based PHA SP methods. The proposed integrated methods are novel in that they marry the complementary aspects of PHA and SAA in terms of exactness and computational efficiency. Further, the developed methods are practical in that they allow the analyst to calibrate the tradeoff between the exactness and speed of attaining a solution. We demonstrate the effectiveness of the developed integrated approaches, Sampling Based Progressive Hedging Algorithm (SBPHA) and Discarding SBPHA (d-SBPHA), over the pure strategies (i.e. SAA or PHA) as well as other commonly used SP methods through extensive experimentation. In addition, we develop alternative hybridization strategies and present results of extensive experiments for these strategies under different uncertainty models. The validation of the methods is demonstrated through Capacitated Reliable facility Location Problem (CRFLP) and Multi-stage stochastic lot-sizing problems

Decomposition and duality based approaches to stochastic integer programming

Stochastic Integer Programming is a variant of Linear Programming which incorporates integer and stochastic properties (i.e. some variables are discrete, and some properties of the problem are randomly determined after the first-stage decision). A Stochastic Integer Program may be rewritten as an equivalent Integer Program with a characteristic structure, but is often too large to effectively solve directly. In this thesis we develop new algorithms which exploit convex duality and scenario-wise decomposition of the equivalent Integer Program to find better dual bounds and faster optimal solutions. A major attraction of this approach is that these algorithms will be amenable to parallel computation

Accounting for water-, energy- and food-security impacts in developing country water infrastructure decision-making under uncertainty

Decision makers lack information and tools to help them understand non-revenue impacts of different water infrastructure investment and operation decisions on different stakeholders in developing countries. These challenges are compounded by multiple sources of uncertainty about the future, including climatic and socio-economic change. Many-objective trade-off analysis could improve understanding of the relationships between diverse stakeholder-defined benefits from a water resources system. It requires a river basin simulation model to evaluate the performance of the system resulting from different decisions. Metrics of performance can be defined in conjunction with stakeholders, relating the level of benefits they receive (monetised or otherwise) to flows or storages in the system. Coupling the model to a many-objective search algorithm allows billions of possible combinations of available decisions to be efficiently filtered to find those which maximise stakeholder benefits. Competition for water requires trade-offs, so a range of options can be generated which share resources differently. Uncertainties can be included in the analysis to help identify sets of decisions which provide acceptable benefits regardless of the future which manifests, i.e. perform robustly. From these options, decision makers can select a balance representing their preferences. This thesis reports the development of such a state-ofthe-art approach through applications in three real-world developing country contexts, with increasing levels of complexity and uncertainty. The first application in Brazil’s Jaguaribe Basin uses environmental and livelihoods indicators to help re-operate three existing dams. The second in Kenya’s Tana Basin adds new irrigation infrastructure investment options to decisions about re-operating a cascade of five existing dams in a more complex case. Finally robust portfolios of new hydropower investments are identified in Nepal’s Koshi Basin, accounting for climate and other uncertainties using a four-phased analytical approach. These applications confirm the approach’s utility and inform future research and practical use

Decision support systems for large dam planning and operation in Africa

Decision support systems/ Dams/ Planning/ Operations/ Social impact/ Environmental effects

La métaheuristique CAT pour le design de réseaux logistiques déterministes et stochastiques

De nos jours, les entreprises d’ici et d’ailleurs sont confrontées à une concurrence mondiale sans cesse plus féroce. Afin de survivre et de développer des avantages concurrentiels, elles doivent s’approvisionner et vendre leurs produits sur les marchés mondiaux. Elles doivent aussi offrir simultanément à leurs clients des produits d’excellente qualité à prix concurrentiels et assortis d’un service impeccable. Ainsi, les activités d’approvisionnement, de production et de marketing ne peuvent plus être planifiées et gérées indépendamment. Dans ce contexte, les grandes entreprises manufacturières se doivent de réorganiser et reconfigurer sans cesse leur réseau logistique pour faire face aux pressions financières et environnementales ainsi qu’aux exigences de leurs clients. Tout doit être révisé et planifié de façon intégrée : sélection des fournisseurs, choix d’investissements, planification du transport et préparation d’une proposition de valeur incluant souvent produits et services au fournisseur. Au niveau stratégique, ce problème est fréquemment désigné par le vocable « design de réseau logistique ». Une approche intéressante pour résoudre ces problématiques décisionnelles complexes consiste à formuler et résoudre un modèle mathématique en nombres entiers représentant la problématique. Plusieurs modèles ont ainsi été récemment proposés pour traiter différentes catégories de décision en matière de design de réseau logistique. Cependant, ces modèles sont très complexes et difficiles à résoudre, et même les solveurs les plus performants échouent parfois à fournir une solution de qualité. Les travaux développés dans cette thèse proposent plusieurs contributions. Tout d’abord, un modèle de design de réseau logistique incorporant plusieurs innovations proposées récemment dans la littérature a été développé; celui-ci intègre les dimensions du choix des fournisseurs, la localisation, la configuration et l’assignation de mission aux installations (usines, entrepôts, etc.) de l’entreprise, la planification stratégique du transport et la sélection de politiques de marketing et d’offre de valeur au consommateur. Des innovations sont proposées au niveau de la modélisation des inventaires ainsi que de la sélection des options de transport. En deuxième lieu, une méthode de résolution distribuée inspirée du paradigme des systèmes multi-agents a été développée afin de résoudre des problèmes d’optimisation de grande taille incorporant plusieurs catégories de décisions. Cette approche, appelée CAT (pour collaborative agent teams), consiste à diviser le problème en un ensemble de sous-problèmes, et assigner chacun de ces sous-problèmes à un agent qui devra le résoudre. Par la suite, les solutions à chacun de ces sous-problèmes sont combinées par d’autres agents afin d’obtenir une solution de qualité au problème initial. Des mécanismes efficaces sont conçus pour la division du problème, pour la résolution des sous-problèmes et pour l’intégration des solutions. L’approche CAT ainsi développée est utilisée pour résoudre le problème de design de réseaux logistiques en univers certain (déterministe). Finalement, des adaptations sont proposées à CAT permettant de résoudre des problèmes de design de réseaux logistiques en univers incertain (stochastique)

Developing collaborative planning support tools for optimised farming in Western Australia

Land-use (farm) planning is a highly complex and dynamic process. A land-use plan can be optimal at one point in time, but its currency can change quickly due to the dynamic nature of the variables driving the land-use decision-making process. These include external drivers such as weather and produce markets, that also interact with the biophysical interactions and management activities of crop production.The active environment of an annual farm planning process can be envisioned as being cone-like. At the beginning of the sowing year, the number of options open to the manager is huge, although uncertainty is high due to the inability to foresee future weather and market conditions. As the production year reveals itself, the uncertainties around weather and markets become more certain, as does the impact of weather and management activities on future production levels. This restricts the number of alternative management options available to the farm manager. Moreover, every decision made, such as crop type sown in a paddock, will constrains the range of management activities possible in that paddock for the rest of the growing season.This research has developed a prototype Land-use Decision Support System (LUDSS) to aid farm managers in their tactical farm management decision making. The prototype applies an innovative approach that mimics the way in which a farm manager and/or consultant would search for optimal solutions at a whole-farm level. This model captured the range of possible management activities available to the manager and the impact that both external (to the farm) and internal drivers have on crop production and the environment. It also captured the risk and uncertainty found in the decision space.The developed prototype is based on a Multiple Objective Decision-making (MODM) - á Posteriori approach incorporating an Exhaustive Search method. The objective set used for the model is: maximising profit and minimising environmental impact. Pareto optimisation theory was chosen as the method to select the optimal solution and a Monte Carlo simulator is integrated into the prototype to incorporate the dynamic nature of the farm decision making process. The prototype has a user-friendly front and back end to allow farmers to input data, drive the application and extract information easily