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Reduction and Analysis of a Max-Plus Linear System to a Constraint Satisfaction Problem for Mixed Integer Programming

Reduction and Analysis of a Max-Plus Linear System to a Constraint Satisfaction Problem for Mixed Integer Programming
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摘要 This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example. This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.
出处 《American Journal of Operations Research》 2017年第2期113-120,共8页 美国运筹学期刊(英文)
关键词 Max-Plus ALGEBRA Scheduling CRITICAL PATH CONSTRAINT SATISFACTION Problems Mixed INTEGER Programing Max-Plus Algebra Scheduling Critical Path Constraint Satisfaction Problems Mixed Integer Programing
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