Input-Output Analysis on Pia Saronde Production Process Scheduling with Invariant Max-Plus Linear System
Abstract
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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