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Managing a patient waiting list with time-dependent priority and adverse events

Daiki Min, Yuehwern Yih (2014)

RAIRO - Operations Research - Recherche Opérationnelle

This paper addresses the problem of managing a waiting list for elective surgery to decide the number of patients selected from the waiting list and to schedule them in accordance with the operating room capacity in the next period. The waiting list prioritizes patients not only by their initial urgency level but also by their waiting time. Selecting elective surgery patients requires a balance between the waiting time for urgent patients and that for less urgent patients. The problem is formulated...

Markov decision processes on finite spaces with fuzzy total rewards

Karla Carrero-Vera, Hugo Cruz-Suárez, Raúl Montes-de-Oca (2022)

Kybernetika

The paper concerns Markov decision processes (MDPs) with both the state and the decision spaces being finite and with the total reward as the objective function. For such a kind of MDPs, the authors assume that the reward function is of a fuzzy type. Specifically, this fuzzy reward function is of a suitable trapezoidal shape which is a function of a standard non-fuzzy reward. The fuzzy control problem consists of determining a control policy that maximizes the fuzzy expected total reward, where...

Markov decision processes with time-varying discount factors and random horizon

Rocio Ilhuicatzi-Roldán, Hugo Cruz-Suárez, Selene Chávez-Rodríguez (2017)

Kybernetika

This paper is related to Markov Decision Processes. The optimal control problem is to minimize the expected total discounted cost, with a non-constant discount factor. The discount factor is time-varying and it could depend on the state and the action. Furthermore, it is considered that the horizon of the optimization problem is given by a discrete random variable, that is, a random horizon is assumed. Under general conditions on Markov control model, using the dynamic programming approach, an optimality...

Mathematical and numerical analysis of an alternative well-posed two-layer turbulence model

Bijan Mohammadi, Guillaume Puigt (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects...

Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model

Bijan Mohammadi, Guillaume Puigt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical...

Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes

A. Caboussat (2011)

Mathematical Modelling of Natural Phenomena

Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol...

Mathematical Optimization for the Train Timetabling Problem

Stanojević, Predrag, Marić, Miroslav, Kratica, Jozef, Bojović, Nebojša, Milenković, Miloš (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 90C57; 90C10;Rail transportation is very rich in terms of problems that can be modelled and solved using mathematical optimization techniques. The train scheduling problem as the most important part of a rail operating policy has a very significant impact on a rail company profit considering the fact that from the quality of a train timetable depends a flow of three most important resources on rail network: cars, locomotives and crews. The train timetabling problem aims at...

Mathematical programming via the least-squares method

Evald Übi (2010)

Open Mathematics

The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding...

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