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has been cited by the following article:

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

  AUTHORS: Hajime Yokoyama, Hiroyuki Goto

  KEYWORDS: Max-Plus Algebra, Scheduling, Critical Path, Constraint Satisfaction Problems, Mixed Integer Programing

  JOURNAL NAME: American Journal of Operations Research, Vol.7 No.2, March 15, 2017

  ABSTRACT: 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.