Open AccessExact Solutions for Minimizing cost Function with Five Criteria and Release Dates on Single Machine
Author(s) -
Hanan Ali Chachan,
Hussein Abdullah Jaafar
Publication year - 2020
Publication title -
mağallaẗ ibn al-haytam li-l-ʻulūm al-ṣirfaẗ wa-al-taṭbīqiyyaẗ/ibn al-haitham journal for pure and applied sciences
Language(s) - English
Resource type - Journals
eISSN - 2521-3407
pISSN - 1609-4042
DOI - 10.30526/33.3.2479
Subject(s) - tardiness , upper and lower bounds , single machine scheduling , branch and bound , mathematical optimization , scheduling (production processes) , mathematics , due date , function (biology) , heuristic , dominance (genetics) , computer science , job shop scheduling , algorithm , schedule , mathematical analysis , biochemistry , chemistry , evolutionary biology , gene , biology , operating system
In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm). And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restricting the search.