Two-stage distributionally robust mixed-integer optimization model for three-level location–allocation problems under uncertain environment

2021 ◽  
pp. 125872
Author(s):  
Zhimin Liu ◽  
Zhong Wu ◽  
Ying Ji ◽  
Shaojian Qu ◽  
Hassan Raza
Keyword(s):  
Optimization Model ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Two Stage ◽  
Mixed Integer Optimization ◽  
Uncertain Environment ◽  
Location Allocation ◽  
Allocation Problems ◽  
Distributionally Robust ◽  
Mixed Integer Optimization Model

Mixed integer optimization model for utilizing a geothermal reservoir

Geothermics ◽  
2015 ◽  
Vol 55 ◽  
pp. 171-181 ◽  
Author(s):  
Silja R. Sigurdardottir ◽  
Agust Valfells ◽  
Halldor Palsson ◽  
Hlynur Stefansson
Keyword(s):  
Optimization Model ◽  
Geothermal Reservoir ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Mixed Integer Optimization Model

Introduction

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Batch Process ◽  
Mixed Integer ◽  
Optimization Models ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Location Allocation ◽  
Primary Focus

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. A plethora of applications in all areas of science and engineering employ mathematical models. A mathematical model of a system is a set of mathematical relationships (e.g., equalities, inequalities, logical conditions) which represent an abstraction of the real world system under consideration. Mathematical models can be developed using (i) fundamental approaches, (ii) empirical methods, and (iii) methods based on analogy. In (i), accepted theories of sciences are used to derive the equations (e.g., Newton’s Law). In (ii), input-output data are employed in tandem with statistical analysis principles so as to generate empirical or “black box” models. In (iii), analogy is employed in determining the essential features of the system of interest by studying a similar, well understood system. The variables can take different values and their specifications define different states of the system. They can be continuous, integer, or a mixed set of continuous and integer. The parameters are fixed to one or multiple specific values, and each fixation defines a different model. The constants are fixed quantities by the model statement. The mathematical model relations can be classified as equalities, inequalities, and logical conditions. The model equalities are usually composed of mass balances, energy balances, equilibrium relations, physical property calculations, and engineering design relations which describe the physical phenomena of the system. The model inequalities often consist of allowable operating regimes, specifications on qualities, feasibility of heat and mass transfer, performance requirements, and bounds on availabilities and demands. The logical conditions provide the connection between the continuous and integer variables.

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