Tehokas ratkaisumenetelmä stokastisiin optimointiongelmiin endogeenisillä ja eksogeenisillä epävarmuuksilla

Despite multi-stage decision problems being common in production planning, there is a class of such problems for which a general solution framework does not exist, namely problems with endogenous uncertainty. Methods from decision analysis and stochastic programming can be used, but both require significantly constraining assumptions. In order to overcome the current challenges, Decision Programming combines approaches from these two fields, making it possible to acquire optimal strategies for different decision problems. Decision Programming is strictly limited to problems in which uncertainty events and decisions are taken from a finite discrete set, reducing its applicability to problems with continuous decision spaces. Discretizing a continuous decision space increases the problem size and can lead to computational intractability. This thesis presents a problem decomposition approach extending the Decision Programming framework. The decomposition approach allows for considering continuous decision and uncertainty spaces in problems with a suitable structure. The proposed framework was applied to three different problems, including a large-scale production planning problem from literature. The main example in this thesis is a novel approach on climate change mitigation cost-benefit analysis, where R&D is carried out simultaneously with the emissions abatement decisions. The R&D projects provide information on the climate damage severity and decrease the price of abatement. Problems with similar structure have not been discussed in the literature, and the extended Decision Programming framework is able to solve the problem to optimality.Vaikka monivaiheiset päätöksenteko-ongelmat ovat yleisiä tuotannon suunnittelussa, erääseen ryhmään näitä ongelmia ei ole yleistä ratkaisumenetelmää. Tämä johtuu niinsanotusta endogeenisestä epävarmuudesta. Näihin ongelmiin voidaan soveltaa stokastisen optimoinnin ja päätösanalyysin menetelmiä, mutta kummatkin vaativat merkittäviä rajoittavia oletuksia. Uusi menetelmä, Decision Programming, yhdistää stokastisen optimoinnin ja päätösanalyysin menetelmiä mahdollistaen optimistrategioden löytämisen erilaisissa päätösongelmissa. Decision Programming rajoittuu ongelmiin joissa satunnaistapahtumat ja päätökset valitaan äärellisistä diskreeteistä joukoista. Tämä rajoittaa sen soveltuvuutta ongelmiin joissa päätösjoukot ovat jatkuvia, sillä tällaisen päätösjoukon diskretointi kasvattaa ongelman kokoa ja saattaa johtaa laskennallisiin haasteisiin. Tässä työssä esitellään Decision Programming -viitekehystä laajentava hajotusmenetelmä jonka avulla voidaan ratkaista ongelmia, jotka sisältävät jatkuvia päätös- ja epävarmuusjoukkoja. Menetelmän soveltaminen vaatii kuitenkin ongelmalta sopivan rakenteen. Työssä esitettyä menetelmää sovellettiin kolmeen esimerkkiongelmaan, joista yksi on suuren mittakaavan tuotannonsuunnitteluongelma kirjallisuudesta. Työn pääesimerkki on uudenlainen lähestymistapa ilmastonmuutoksen hillinnän kustannus-hyötyanalyysiin, jossa tutkimustyötä tehdään samanaikaisesti päästövähennysten kanssa. Tutkimusprojekteilla saadaan lisätietoa ilmastovaikutusten vakavuudesta ja lasketaan päästövähennysten hintaa. Vastaavanlaisia ongelmia ei ole ennen käsitelty kirjallisuudessa ja laajennettu Decision Programming -viitekehys mahdollistaa optimiratkaisun löytämisen tässä esimerkissä

A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming

Despite methodological advances for modeling decision problems under uncertainty, faithfully representing endogenous uncertainty still proves challenging, both in terms of modeling capabilities and computational requirements. A novel framework called Decision Programming provides an approach for solving such decision problems using off-the-shelf mathematical optimization solvers. This is made possible by using influence diagrams to represent a given decision problem, which is then formulated as a mixed-integer linear programming problem. In this paper, we focus on the type of endogenous uncertainty that received less attention in the introduction of Decision Programming: conditionally observed information. Multi-stage stochastic programming (MSSP) models use conditional non-anticipativity constraints (C-NACs) to represent such uncertainties, and we show how such constraints can be incorporated into Decision Programming models. This allows us to consider the two main types of endogenous uncertainty simultaneously, namely decision-dependent information structure and decision-dependent probability distribution. Additionally, we present a decomposition approach that provides significant computational savings and also enables considering continuous decision variables in certain parts of the problem, whereas the original formulation was restricted to discrete variables only. The extended framework is illustrated with two example problems. The first considers an illustrative multiperiod game and the second is a large-scale cost-benefit problem regarding climate change mitigation. Neither of these example problems could be solved with existing frameworks.Comment: 26 pages, 10 figure

Using Light Spanning Graphs for Passenger Assignment in Public Transport

In a public transport network a passenger’s preferred route from a point x to another point y is usually the shortest path from x to y. However, it is simply impossible to provide all the shortest paths of a network via public transport. Hence, it is a natural question how a lighter sub-network should be designed in order to satisfy both the operator as well as the passengers.We provide a detailed analysis of the interplay of the following three quality measures of lighter public transport networks: - building cost: the sum of the costs of all edges remaining in the lighter network, - routing costs: the sum of all shortest paths costs weighted by the demands, - fairness: compared to the original network, for each two points the shortest path in the new network should cost at most a given multiple of the shortest path in the original network. We study the problem by generalizing the concepts of optimum communication spanning trees (Hu, 1974) and optimum requirement graphs (Wu, Chao, and Tang, 2002) to generalized optimum requirement graphs (GORGs), which are graphs achieving the social optimum amongst all subgraphs satisfying a given upper bound on the building cost. We prove that the corresponding decision problem is NP-complete, even on orb-webs, a variant of grids which serves as an important model of cities with a center. For the case that the given network is a parametric city (cf. Fielbaum et. al., 2017) with a heavy vertex we provide a polynomial-time algorithm solving the GORG-problem. Concerning the fairness-aspect, we prove that light spanners are a strong concept for public transport optimization. We underpin our theoretical considerations with integer programming-based experiments that allow us to compare the fairness-approach with the routing cost-approach as well as passenger assignment approaches from the literature.Peer reviewe

A Prescriptive Trilevel Equilibrium Model for Optimal Emissions Pricing and Sustainable Energy Systems Development

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. We present two alternative solution methods for such problems and a comparison of the resulting model sizes. The first method is based on a reformulation of the bottom-level solution set, and the second one uses strong duality. The first approach results in optimality conditions that are both necessary and sufficient, while the second one results in a model with fewer constraints but only sufficient optimality conditions. Using the proposed methods, we are able to obtain globally optimal solutions for a realistic five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.Comment: 21 pages, 5 figure

DecisionProgramming.jl --A framework for modelling decision problems using mathematical programming

We present DecisionProgramming.jl, a new Julia package for modelling decision problems as mixed-integer programming (MIP) equivalents. The package allows the user to pose decision problems as influence diagrams which are then automatically converted to an equivalent MIP formulation. This MIP formulation is implemented using JuMP.jl, a Julia package providing an algebraic syntax for formulating mathematical programming problems. In this paper, we show novel MIP formulations used in the package, which considerably improve the computational performance of the MIP solver. We also present a novel heuristic that can be employed to warm start the solution, as well as providing heuristic solutions to more computationally challenging problems. Lastly, we describe a novel case study showcasing decision programming as an alternative framework for modelling multi-stage stochastic dynamic programming problems.Comment: 23 pages, 6 figure

Low-Dose Doxycycline Treatment Normalizes Levels of Some Salivary Metabolites Associated with Oral Microbiota in Patients with Primary Sjögren’s Syndrome

Saliva is a complex oral fluid, and plays a major role in oral health. Primary Sjögren’s syndrome (pSS), as an autoimmune disease that typically causes hyposalivation. In the present study, salivary metabolites were studied from stimulated saliva samples (n = 15) of female patients with pSS in a group treated with low-dose doxycycline (LDD), saliva samples (n = 10) of non-treated female patients with pSS, and saliva samples (n = 14) of healthy age-matched females as controls. Saliva samples were analyzed with liquid chromatography mass spectrometry (LC-MS) based on the non-targeted metabolomics method. The saliva metabolite profile differed between pSS patients and the healthy control (HC). In the pSS patients, the LDD treatment normalized saliva levels of several metabolites, including tyrosine glutamine dipeptide, phenylalanine isoleucine dipeptide, valine leucine dipeptide, phenylalanine, pantothenic acid (vitamin B5), urocanic acid, and salivary lipid cholesteryl palmitic acid (CE 16:0), to levels seen in the saliva samples of the HC. In conclusion, the data showed that pSS is associated with an altered saliva metabolite profile compared to the HC and that the LLD treatment normalized levels of several metabolites associated with dysbiosis of oral microbiota in pSS patients. The role of the saliva metabolome in pSS pathology needs to be further studied to clarify if saliva metabolite levels can be used to predict or monitor the progress and treatment of pSS

Low-Dose Doxycycline Treatment Normalizes Levels of Some Salivary Metabolites Associated with Oral Microbiota in Patients with Primary Sjögren’s Syndrome

Saliva is a complex oral fluid, and plays a major role in oral health. Primary Sjögren’s syndrome (pSS), as an autoimmune disease that typically causes hyposalivation. In the present study, salivary metabolites were studied from stimulated saliva samples (n = 15) of female patients with pSS in a group treated with low-dose doxycycline (LDD), saliva samples (n = 10) of non-treated female patients with pSS, and saliva samples (n = 14) of healthy age-matched females as controls. Saliva samples were analyzed with liquid chromatography mass spectrometry (LC-MS) based on the non-targeted metabolomics method. The saliva metabolite profile differed between pSS patients and the healthy control (HC). In the pSS patients, the LDD treatment normalized saliva levels of several metabolites, including tyrosine glutamine dipeptide, phenylalanine isoleucine dipeptide, valine leucine dipeptide, phenylalanine, pantothenic acid (vitamin B5), urocanic acid, and salivary lipid cholesteryl palmitic acid (CE 16:0), to levels seen in the saliva samples of the HC. In conclusion, the data showed that pSS is associated with an altered saliva metabolite profile compared to the HC and that the LLD treatment normalized levels of several metabolites associated with dysbiosis of oral microbiota in pSS patients. The role of the saliva metabolome in pSS pathology needs to be further studied to clarify if saliva metabolite levels can be used to predict or monitor the progress and treatment of pSS. </p

National trends in total cholesterol obscure heterogeneous changes in HDL and non-HDL cholesterol and total-to-HDL cholesterol ratio : a pooled analysis of 458 population-based studies in Asian and Western countries

Background: Although high-density lipoprotein (HDL) and non-HDL cholesterol have opposite associations with coronary heart disease, multi-country reports of lipid trends only use total cholesterol (TC). Our aim was to compare trends in total, HDL and nonHDL cholesterol and the total-to-HDL cholesterol ratio in Asian and Western countries. Methods: We pooled 458 population-based studies with 82.1 million participants in 23 Asian and Western countries. We estimated changes in mean total, HDL and non-HDL cholesterol and mean total-to-HDL cholesterol ratio by country, sex and age group. Results: Since similar to 1980, mean TC increased in Asian countries. In Japan and South Korea, the TC rise was due to rising HDL cholesterol, which increased by up to 0.17 mmol/L per decade in Japanese women; in China, it was due to rising non-HDL cholesterol. TC declined in Western countries, except in Polish men. The decline was largest in Finland and Norway, at similar to 0.4 mmol/L per decade. The decline in TC in most Western countries was the net effect of an increase in HDL cholesterol and a decline in non-HDL cholesterol, with the HDL cholesterol increase largest in New Zealand and Switzerland. Mean total-to-HDL cholesterol ratio declined in Japan, South Korea and most Western countries, by as much as similar to 0.7 per decade in Swiss men (equivalent to similar to 26% decline in coronary heart disease risk per decade). The ratio increased in China. Conclusions: HDL cholesterol has risen and the total-to-HDL cholesterol ratio has declined in many Western countries, Japan and South Korea, with only a weak correlation with changes in TC or non-HDL cholesterol.Peer reviewe

Repositioning of the global epicentre of non-optimal cholesterol

High blood cholesterol is typically considered a feature of wealthy western countries(1,2). However, dietary and behavioural determinants of blood cholesterol are changing rapidly throughout the world(3) and countries are using lipid-lowering medications at varying rates. These changes can have distinct effects on the levels of high-density lipoprotein (HDL) cholesterol and non-HDL cholesterol, which have different effects on human health(4,5). However, the trends of HDL and non-HDL cholesterol levels over time have not been previously reported in a global analysis. Here we pooled 1,127 population-based studies that measured blood lipids in 102.6 million individuals aged 18 years and older to estimate trends from 1980 to 2018 in mean total, non-HDL and HDL cholesterol levels for 200 countries. Globally, there was little change in total or non-HDL cholesterol from 1980 to 2018. This was a net effect of increases in low- and middle-income countries, especially in east and southeast Asia, and decreases in high-income western countries, especially those in northwestern Europe, and in central and eastern Europe. As a result, countries with the highest level of non-HDL cholesterol-which is a marker of cardiovascular riskchanged from those in western Europe such as Belgium, Finland, Greenland, Iceland, Norway, Sweden, Switzerland and Malta in 1980 to those in Asia and the Pacific, such as Tokelau, Malaysia, The Philippines and Thailand. In 2017, high non-HDL cholesterol was responsible for an estimated 3.9 million (95% credible interval 3.7 million-4.2 million) worldwide deaths, half of which occurred in east, southeast and south Asia. The global repositioning of lipid-related risk, with non-optimal cholesterol shifting from a distinct feature of high-income countries in northwestern Europe, north America and Australasia to one that affects countries in east and southeast Asia and Oceania should motivate the use of population-based policies and personal interventions to improve nutrition and enhance access to treatment throughout the world.Peer reviewe

Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants

Summary Background Comparable global data on health and nutrition of school-aged children and adolescents are scarce. We aimed to estimate age trajectories and time trends in mean height and mean body-mass index (BMI), which measures weight gain beyond what is expected from height gain, for school-aged children and adolescents. Methods For this pooled analysis, we used a database of cardiometabolic risk factors collated by the Non-Communicable Disease Risk Factor Collaboration. We applied a Bayesian hierarchical model to estimate trends from 1985 to 2019 in mean height and mean BMI in 1-year age groups for ages 5–19 years. The model allowed for non-linear changes over time in mean height and mean BMI and for non-linear changes with age of children and adolescents, including periods of rapid growth during adolescence. Findings We pooled data from 2181 population-based studies, with measurements of height and weight in 65 million participants in 200 countries and territories. In 2019, we estimated a difference of 20 cm or higher in mean height of 19-year-old adolescents between countries with the tallest populations (the Netherlands, Montenegro, Estonia, and Bosnia and Herzegovina for boys; and the Netherlands, Montenegro, Denmark, and Iceland for girls) and those with the shortest populations (Timor-Leste, Laos, Solomon Islands, and Papua New Guinea for boys; and Guatemala, Bangladesh, Nepal, and Timor-Leste for girls). In the same year, the difference between the highest mean BMI (in Pacific island countries, Kuwait, Bahrain, The Bahamas, Chile, the USA, and New Zealand for both boys and girls and in South Africa for girls) and lowest mean BMI (in India, Bangladesh, Timor-Leste, Ethiopia, and Chad for boys and girls; and in Japan and Romania for girls) was approximately 9–10 kg/m2. In some countries, children aged 5 years started with healthier height or BMI than the global median and, in some cases, as healthy as the best performing countries, but they became progressively less healthy compared with their comparators as they grew older by not growing as tall (eg, boys in Austria and Barbados, and girls in Belgium and Puerto Rico) or gaining too much weight for their height (eg, girls and boys in Kuwait, Bahrain, Fiji, Jamaica, and Mexico; and girls in South Africa and New Zealand). In other countries, growing children overtook the height of their comparators (eg, Latvia, Czech Republic, Morocco, and Iran) or curbed their weight gain (eg, Italy, France, and Croatia) in late childhood and adolescence. When changes in both height and BMI were considered, girls in South Korea, Vietnam, Saudi Arabia, Turkey, and some central Asian countries (eg, Armenia and Azerbaijan), and boys in central and western Europe (eg, Portugal, Denmark, Poland, and Montenegro) had the healthiest changes in anthropometric status over the past 3·5 decades because, compared with children and adolescents in other countries, they had a much larger gain in height than they did in BMI. The unhealthiest changes—gaining too little height, too much weight for their height compared with children in other countries, or both—occurred in many countries in sub-Saharan Africa, New Zealand, and the USA for boys and girls; in Malaysia and some Pacific island nations for boys; and in Mexico for girls. Interpretation The height and BMI trajectories over age and time of school-aged children and adolescents are highly variable across countries, which indicates heterogeneous nutritional quality and lifelong health advantages and risks