Chance constrained programming with some non-normal continuous random variables
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Chance constrained programming with some non‑normal continuous random variables D. K. Mohanty1 · Avik Pradhan2 · M. P. Biswal1 Accepted: 7 May 2020 © Operational Research Society of India 2020
Abstract Stochastic or probabilistic programming is a branch of mathematical programming that deals with some situations in which an optimal decision is desired under random uncertainty of some parameters. In this paper, we consider some chance constrained linear programming problems where the right hand side parameters of the chance-constraints follow some non-normal continuous distributions such as power function distribution, triangular distribution and trapezoidal distribution. To find the solution of the stated problems, we first convert the problems in to equivalent deterministic models. Then standard linear programming techniques are used to solve the equivalent deterministic models. Some numerical examples are presented to illustrate the methodology. Keywords Stochastic programming · Chance constrained programming · Power function distribution · Triangular distribution · Trapezoidal distribution
1 Introduction In most of the real-life decision-making problem, decision maker needs to take decision under some uncertain environment. The uncertainty can be found in parameter space as well as in the decision space of a decision making problem. These uncertainties are addressed by using probability distribution or fuzzy value or intervals. * M. P. Biswal [email protected] D. K. Mohanty [email protected] Avik Pradhan [email protected] 1
Department of Mathematics, Indian Institute of Technology, Kharagpur, Kharagpur 721 302, India
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Department of Humanities and Sciences, Indrashil Institute of Science and Technology, Gujarat Technological University, Mehsana, Gujarat 382740, India
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Stochastic Programming (SP) is concerned with the decision making problems in which some or all parameters are treated as random variables in order to capture the uncertainty. SP is used in several real world decision making areas such as energy management, financial modeling, supply chain and scheduling, hydro thermal power production planning, transportation, agriculture, defence, environmental and pollution control, production and control management, telecommunications, etc. Several models and methodologies have been developed in the field of stochastic programming. In the literature, there exist two very popular approaches to solve SP problems, namely, 1. Chance constrained programming, and 2. Two-stage programming. Chance constrained programming was developed as a means of describing constraints in mathematical programming models in the form of probability levels of attainment. The chance constrained programming (CCP) can be used to solve problems involving chance-constraints, i.e.constraints having violation up to a pre-specified probability level. The use of chance-constraints was initially introduced by Charnes and Cooper [8]. They established three different models for t
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