%0 Journal Article
%T Reduction and Analysis of a Max-Plus Linear System to a Constraint Satisfaction Problem for Mixed Integer Programming
%A Hajime Yokoyama
%A Hiroyuki Goto
%J American Journal of Operations Research
%P 113-120
%@ 2160-8849
%D 2017
%I Scientific Research Publishing
%R 10.4236/ajor.2017.72008
%X 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.
%K Max-Plus Algebra
%K Scheduling
%K Critical Path
%K Constraint Satisfaction Problems
%K Mixed Integer Programing
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=74725