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1973•Transactions of the Society of Instrument and Control EngineersOpen access

A Study of Stochastic Linear Programming Problem

Yoshisada Murotsu, Fuminori Ohba, I. OZAWA

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Abstract

This paper presents a new method for finding the optimum solution for a linear programming problem with uncertainty in the coefficients.Total cost is defined by adding penalty cost to activity cost when the constraints are violated, and a stochastic programming problem is set up to minimize the expected total cost.It is shown that the problem is reduced to a convex programming.The algorithm for finding the optimum solution is also presented, using the gradient method.1.

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This paper presents a new method for finding the optimum solution for a linear programming problem with uncertainty in the coefficients.Total cost is defined by adding penalty cost to activity cost when the constraints are violated, and a stochastic programming problem is set up to minimize the expected total cost.It is shown that the problem is reduced to a convex programming.The algorithm for finding the optimum solution is also presented, using the gradient method.1.

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Available abstract

This paper presents a new method for finding the optimum solution for a linear programming problem with uncertainty in the coefficients.Total cost is defined by adding penalty cost to activity cost when the constraints are violated, and a stochastic programming problem is set up to minimize the expected total cost.It is shown that the problem is reduced to a convex programming.The algorithm for finding the optimum solution is also presented, using the gradient method.1.

Key concepts: Mathematical optimization, Stochastic programming, Linear programming, Set (abstract data type), Linear-fractional programming, Computer science, Convex optimization, Total cost

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