Solving Continuous-Time Linear Programming Problems Based on the Piecewise Continuous Functions

ABSTRACT

The numerical method is proposed in this article to solve a general class of continuous-time linear programming problems in which the functions appeared in the coefficients of this problem are assumed to be piecewise continuous. In order to make sure that all the subintervals of time interval will not contain the discontinuities, a different methodology for not equally partitioning the time interval is proposed. The main issue of this article is to obtain an analytic formula of error upper bound. In this article, we shall propose two kinds of computational procedure to evaluate the error upper bounds. One needs to solve the dual problem of the discretized linear programming problem, and another one does not need to solve the dual problem. Finally, we present a numerical example to demonstrate the usefulness of the numerical method.

KEYWORDS:

• Continuous-time linear programming problems
• discretized problems
• piecewise continuous functions
• strong duality theorem
• weak duality theorem

MATHEMATICS SUBJECT CLASSIFICATION:

• 90C05
• 90C46
• 90C90

Acknowledgement

The author would like to thank the reviewers for carefully reading this manuscript.