Published date: Mar 27 2024

Journal Title: KnE Life Sciences

Issue title: International Conference On Mathematics And Science Education (ICMScE 2022): Life Sciences

Pages: 166–176

DOI: 10.18502/kls.v8i1.15545

Nurwan .Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Sunarwin Ismailawinismail29@gmail.comDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Muhammad Rezky F. PayuDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Lailany YahyaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Djihad WungguliDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Asriadi .Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Indonesia

Max-plus algebra is one of the analysis methods of discrete event systems which has many applications on systems theory and graph theory. Max-plus algebra is a set of real numbers R combined with ￿=-∞ equipped with operations max (⊕) and plus (⊗), can be denoted [(R]_ε,⊕,⊗) with [(R]_ε=R⋃{ε}) . The production process of pia saronde is one of the problems that can be analyzed using max-plus algebra. The production process of this product is sequentially carried out by making skin dough, filling, baking, cooling, and packaging the pia. The max-plus algebra theory was used in this research to determine the optimal time in the production scheduling of pia saronde. Meanwhile, the Invarian Max-plus Linear System (IMLS), max-plus algebraic theory, and the Discrete Event System (DES) were used to solve the production-related problems. IMLS analysis produces eigenvalues that represent the optimum production time. The results obtained the max-plus algebra model of x(k+1)=A^-⊗x(k), where A^-=A⊕B⊗C and y=K⊗x_0⊕H⊗u for input-output IMLS analysis. From the matrix A^-, eigenvalue λ= 226 and eigenvector v=[278 278 278 279 299 302 324 356 488] were obtained. Furthermore, the value of λ describes the pia production schedule at a time span of 226 minutes.

Keywords: input-output analysis, pia saronde, scheduling, max-plus linear system

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