A Primal-Dual Approach to Analyzing ATO Systems

2020 ◽  
Vol 66 (11) ◽  
pp. 5389-5407
Author(s):  
Levi DeValve ◽  
Saša Pekeč ◽  
Yehua Wei
Keyword(s):  
General Structure ◽  
Asymptotic Optimality ◽  
Problem Instance ◽  
Worst Case ◽  
Lp Rounding ◽  
Approximation Factor ◽  
Primal Dual ◽  
The One ◽  
Approximation Guarantee ◽  
Rounding Algorithm

We study assemble-to-order (ATO) problems from the literature. ATO problems with general structure and integrality constraints are well known to be difficult to solve, and we provide new insight into these issues by establishing worst-case approximation guarantees through primal-dual analyses and linear programming (LP) rounding. First, we relax the one-period ATO problem using a natural newsvendor decomposition and use the dual solution for the relaxation to derive a lower bound on optimal cost, providing a tight approximation guarantee that grows with the maximum product size in the system. Then, we present an LP rounding algorithm that achieves both asymptotic optimality as demand grows large, and a 1.8 approximation factor for any problem instance. In addition to theoretical guarantees, we perform comprehensive numerical simulations and find that our rounding algorithm outperforms existing techniques and is close to optimal. Finally, we demonstrate that our one-period LP rounding results can be used to develop an asymptotically optimal integral policy for dynamic ATO problems with backlogging and identical component lead-times. This paper was accepted by Yinyu Ye, optimization.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals Analysis of the robustness of a steel frame structure with composite floors subject to multiple fire scenarios

2021 ◽  
pp. 136943322199249
Author(s):  
Riza Suwondo ◽  
Lee Cunningham ◽  
Martin Gillie ◽  
Colin Bailey
Keyword(s):  
Progressive Collapse ◽  
Three Dimensional ◽  
Steel Structure ◽  
Frame Structure ◽  
Worst Case ◽  
Collapse Resistance ◽  
Fire Scenarios ◽  
Element Approach ◽  
The One ◽  
Steel Frame Structure

This study presents robustness analyses of a three-dimensional multi-storey composite steel structure under the action of multiple fire scenarios. The main objective of the work is to improve current understanding of the collapse resistance of this type of building under different fire situations. A finite element approach was adopted with the model being firstly validated against previous studies available in the literature. The modelling approach was then used to investigate the collapse resistance of the structure for the various fire scenarios examined. Different sizes of fire compartment are considered in this study, starting from one bay, three bays and lastly the whole ground floor as the fire compartment. The investigation allows a fundamental understanding of load redistribution paths and member interactions when local failure occurs. It is concluded that the robustness of the focussed building in a fire is considerably affected by the size of fire compartments as well as fire location. The subject building can resist progressive collapse when the fire occurs only in the one-bay compartment. On the other hand, total collapse occurs when fire is located in the edge three-bay case. This shows that more than one fire scenario needs to be taken into consideration to ensure that a structure of this type can survive from collapse in the worst-case situation.

scholarly journals Parallel One-Step Control of Parametrised Boolean Networks

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 560 ◽  
Author(s):  
Luboš Brim ◽  
Samuel Pastva ◽  
David Šafránek ◽  
Eva Šmijáková
Keyword(s):  
Control Problem ◽  
Boolean Networks ◽  
Actual State ◽  
Worst Case ◽  
Symbolic Data ◽  
One Step ◽  
The One ◽  
Step Control ◽  
Symbolic Algorithm ◽  
Naive Approach

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

Topology Optimization of Dynamic Systems Under Uncertain Loads: An H∞-Norm-Based Approach

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Paolo Venini
Keyword(s):  
Topology Optimization ◽  
Structural Parameters ◽  
Goal Function ◽  
Dynamic Compliance ◽  
Case Scenario ◽  
Worst Case ◽  
Original Definition ◽  
Optimal Material ◽  
The One ◽  
Definition Of

An innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H∞-norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development.

scholarly journals Intelligent design af fokusgrupper - om metodisk design af fokusgrupper og menneskets forskellige intelligenser

2008 ◽  
Vol 24 (45) ◽  
pp. 13
Author(s):  
Lene Heiselberg
Keyword(s):  
Focus Groups ◽  
Intelligent Design ◽  
Verbal Intelligence ◽  
Case Scenario ◽  
Worst Case ◽  
Apparent Lack ◽  
Self Confidence ◽  
Media Research ◽  
The One ◽  
Interviewing Techniques

Når man arbejder professionelt med at gennemføre kvalitative mini- og fokusgruppeanalyser, kan det ikke undgås, at man som moderator indimellem tænker: Hvorfor deltager hun ikke? Hvad kan jeg gøre for at inkludere hende i diskussionen? Ofte skyldes nogle deltageres manglende engagement, at mini- eller fokusgruppens metodiske design favoriserer de deltagere, som har en fremtrædende verbalsproglig intelligens, og samtidig ekskluderes de, der har andre fremtrædende intelligenser, fra at yde det maksimale. En sådan situation er meget uheldig og kan i værste fald give en undersøgelse bias. Derfor har vi i DR Medieforskning arbejdet med en pragmatisk tilgang til problemet, hvor vi har afprøvet et metodisk design, som inkluderer kvalitative interviewteknikker og procesværktøjer, som appellerer til samtlige intelligenser. Som et resultat af en målrettet indsats for at inkludere flere intelligenser i det metodiske design, oplever vi, at deltagerne har mere lyst til at engagere sig og gør det med større selvsikkerhed. Desuden oplever vi i mindre grad fænomenet “cognitive tuning” , og derfor kan vi arbejde med flere og bedre data i analyse- og fortolkningsfasen. Intelligent design of focus groups - article about methodological design of focus groups and the different intelligences When you work professionally with the conducting and moderating of qualitative mini- and focus groups, you can't avoid sometimes thinking: Why isn’t she participating? What can I do to include her in the discussion? A participant's apparent lack of enthusiasm is often caused by the methodological design of the focus group giving preference to participants who have an explicit verbal intelligence, and as a consequence excludes participants with other explicit intelligences from contributing. A situation like the one described above is very undesirable and in a worst-case scenario it can cause a study to be biased. In order to try to solve this problem DR Media Research applied a methodological design which includes qualitative interviewing techniques and processing tools, which appeal to all of the intelligences instead of just one. As a result of this work, we find that the participants are more eager to participate and that they do it with greater self-confidence. In addition we encounter less cognitive tuning, and are therefore able to work with richer data in the phases of analysis and interpretation.

scholarly journals An Analytic Theologian Stance on the Existence of God

2013 ◽  
Vol 5 (2) ◽  
pp. 129-146 ◽  
Author(s):  
Benedikt Paul Göcke
Keyword(s):  
Point Of View ◽  
The Other ◽  
Philosophical Discussion ◽  
Existence Of God ◽  
Worst Case ◽  
The One

The existence of God is once again the focus of vivid philosophical discussion. From the point of view of analytic theology, however, people often talk past each other when they debate about the putative existence or non- existence of God. In the worst case, for instance, atheists deny the existence of a God, which no theists ever claimed to exist. In order to avoid confusions like this we need to be clear about the function of the term ‘God’ in its different contexts of use. In what follows, I distinguish between the functions of ‘God’ in philosophical contexts on the one hand and in theological contexts on the other in order to provide a schema, which helps to avoid confusion in the debate on the existence or non-existence of God.

APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS

2013 ◽  
Vol 23 (06) ◽  
pp. 461-477 ◽  
Author(s):  
MINATI DE ◽  
GAUTAM K. DAS ◽  
PAZ CARMI ◽  
SUBHAS C. NANDY
Keyword(s):  
Approximation Algorithms ◽  
Simple Algorithm ◽  
Constant Factor ◽  
Performance Ratio ◽  
Approximation Result ◽  
Worst Case ◽  
Approximation Factor ◽  
Minimum Number ◽  
Unit Disks ◽  
Set Of Points

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n8 log n) and O(n15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio [Formula: see text] in nO(k) time.

scholarly journals Morphological and radiological study of lymph nodes in dromedaries in Algeria

2020 ◽  
Vol 11 (2) ◽  
pp. 330-337
Author(s):  
D. E. Rahmoun ◽  
M. A. Lieshchova ◽  
M. A. Fares
Keyword(s):  
Lymph Node ◽  
Lymph Nodes ◽  
General Structure ◽  
Lymphatic Vessels ◽  
Conventional Radiography ◽  
Farm Animals ◽  
Relative Mass ◽  
Linear Measurements ◽  
X Ray ◽  
The One

Despite significant progress in the study of the subtle mechanisms of interaction between cellular and molecular elements in immune responses, the general structure of the organs of the immune system, including the lymph node, has not been sufficiently studied, in particular in large farm animals. The lymph nodes of sexually mature camels have been studied anatomically and morphologically and advanced studies conducted using an X-ray system and a computer densitometer scanner with injection of a contrast medium. The topography and characteristics of the morphometric parameters (absolute and relative mass, linear measurements, volume) of certain somatic and visceral lymph nodes were determined. The mass of the lymph nodes studied varies according to the location and the interest of the organ in the satellite defense of the lymphoid system, For part of the x-ray examination of the lymph nodes, organs of large inguinal and axillary shape were selected after passing through a solution of tetraethyl-4,4-diamino-triphenylmethane oxalate, the lymph vessels were dilated and darkened, then iodine injections were made into the afferent lymphatic vessel of two lymph nodes; they were placed on the radiological cassette, a photograph taken on conventional radiography, for computer densitometer, the examination was made without preparation of the organs. A capsule encompasses the parenchyma of the lymph node, whose internal structure is composed of different zones, cortical, paracortical and medullary, on the one hand the lymphatic vessels were very clear especially with the conventional radiography with preparation of the organs, while the computer densitometer clearly revealed the deep texture of the parenchyma, basing it on the intensity of emission saturation from the use of computer densitometer.

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