Abstract
In this paper we analyzed a group of simple heuristic methods, which are used for solving the scheduling problem in manufacturing and services. The analysis was performed on the scheduling problem in a flexible-flow shop production, which is known by the English term - Flexible-Flow Shop (FFS). The task is to determine the schedule of processing multiple products on multiple machines, where all the products have the same sequence of processing and for each process there are multiple machines available. For this FFS problem we present the corresponding mathematical model of mixed integer programming. Among potential methods for solving the set task, we consider simple heuristics because the original scheduling problem is NP-hard and finding the exact optimal solution would require unacceptably long computing time. Heuristic methods are based on priority rules that are performed based on the relations of importance between products and their processing time on individual machines. Heuristic methods are widely used for solving practical problems, which was the motivation for the analysis performed in this paper. The aim of the analysis is to identify those priority rules, from a set of considered, which provide a good solution to a hypothetical scheduling problem example, where the evaluation of solution is performed using different criteria functions. The analysis that is presented in the paper was obtained by using the computer program LEKIN. The main results of the analysis indicated that priority rules give different solutions to the problem of FFS and that each of these solutions is a significantly good result in terms of some of the considered criteria functions.
Highlights
Nakon rasporeñivanja na mašini koja u datom trenutku predstavlja usko grlo, heuristika pokušava da ponovo revidira već rasporeñene proizvode kako bi se dobio bolji raspored
The aim of the analysis is to identify those priority rules, from a set of considered, which provide a good solution to a hypothetical scheduling problem example, where the evaluation of solution is performed using different criteria functions
Summary
Problem rasporeñivanja u protočnoj proizvodnji je problem rasporeda n proizvoda na m mašina u kome svi proizvodi imaju identičnu putanju obrade koju slede, a koja se sastoji od unapred odreñenog niza operacija na mašinama. FFS se sastoji od m ≥ 2 proizvodnih faza ili mašinskih centara sa l faza koje imaju kl≥ 1 identičnih mašina sa istom vrstom obrade Pl1,Pl2,...,Plk. Za svaki proizvod Jj, vektor [p1j, p2j,...,pmj]T vremena obrade su unapred poznata, gde je plj ≥0 za svako (l,j). Problem rasporeñivanja se sastoji u dodeljivanju operacija obrade proizvoda mašinama na svakoj fazi obrade i definisanje redosleda kojim se proizvodi obrañuju na mašinama a sve u cilju minimizacije kriterijumske funkcije. Ograničenje (1.2) garantuje da za svaku fazu obrade l za svaki proizvod Jj postoji jedna mašina tako da se ili Jj obrañuje prvi ili posle nekog drugog proizvoda na toj mašini. Nejednakost (1.3) govori da na svakoj fazi obrade postoji mašina na kojoj proizvod koji se obrañuje ima proizvod koji ga sledi u nizu ili se taj proizvod obrañuje poslednji. Ograničenje (1.4) kaže da na svakoj fazi za svaki proizvod postoji samo jedna mašina koja zadovoljava prethodna dva uslova. Složenost algoritama prva dva pristupa je eksponencijalna funkcija dimenzije problema i zato su
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