Determining the Earliest Starting Times in Project Networks with Interval Activity Times Using Interval Max-Plus Algebra

M. Andy Rudhito, Sri Wahyuni, Ari Suparwanto, F. Susilo

Prociding of The First International Seminar on Science and Technology (ISSTEC 2009). UII Yogyakarta. 24-25 Januari 2009.

Abstract: The activity times in a project network are seldom precisely known, and then could be represented into the interval. This paper aims to determine the earliest starting time for each node in the project networks with interval activity times using interval max-plus algebra. The finding shows that the project networks with interval activity can be represented as a matrix over interval max-plus algebra. The project networks dynamics can be represented as a iterative system of interval max-plus linear equations. The interval of earliest start time for each node in the project networks is a solutions vector of the system.

Keywords: max-plus algebra, earliest starting times, project network, interval.

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ITERATIVE SYSTEM OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS

ITERATIVE SYSTEM OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS

Prociding of International Conference on Mathematics and Natural Science 2008. FMIPA ITB Bandung 28-30 Oktober 2008.

M. Andy Rudhito, Sri Wahyuni, Ari Suparwanto, F. Susilo

Abstract. The activity times in a network are seldom precisely known, and then could be represented into the fuzzy numbers. With max-plus algebra approach, the network dynamic could be analyzed through its iterative system of fuzzy number max-plus linear equations. This paper aims to determine the existence and uniqueness of the solution of the iterative system of fuzzy number max-plus linear equations. The finding shows that if the square matrix of the systems is semidefinite, then the solution exists. The solution of the system could be determined the solution of the alpha-cuts of the system firstly. Based on the Decomposition Theorem, we can determine the membership function of the elements of solution

vectors. Moreover, the solution is unique if the square matrix of the systems is definite.

Keywords: Max-Plus Algebra, System of Linear Equations, Fuzzy Number

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