دانلود رایگان مقاله لاتین حداقل سازی bin packing از سایت الزویر
عنوان فارسی مقاله:
حداقل سازی حداکثر تاخیر در bin packing تک بعدی
عنوان انگلیسی مقاله:
Maximum lateness minimization in one-dimensional bin packing
سال انتشار : 2017
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بخشی از مقاله انگلیسی:
3. Use of bounds
A careful use of bounds in formulations ðkxÞ and ðgxÞ definitely improves their performance. Dual (i.e., lower) and primal (i.e., upper) bounds to the objective function play a well-known role in pruning the search tree during branch-and-bound and reducing optimality gaps. But separate bounds to the terms that form the objective function are also very useful. On the one hand, upper bounds to Cmax can help reduce T and hence the number of time-indexed variables in both ðkxÞ and ðgxÞ. On the other hand, lower bounds to Lmax can be fruitfully employed to fix variables xjt of ðkxÞ through constraints (5); improve the dual LP bound of ðgxÞ through the reduction of the “big M” f 2 j ðtÞ in the third set of inequalities. Fig. 1 shows a schematic drawing of the objective function space Cmax vs. Lmax. Appealing values belong to the dark grey triangle: the combination of bounds to the two terms and to the objective function as a whole allow to infer new (and possibly stronger) specific bounds to each term. 3.1. Lower bounds If CLB; LLB are individual lower bounds to Cmax; Lmax, then zLB ¼ α1⌈CLB⌉þα2⌈LLB⌉ is indeed a lower bound to (1) – notice that round up of LLB is authorized by Assumption 1.1 (ii) (integer due dates). We can prove the following: Proposition 3.1. Let CLB be any lower bound to Cmax, and Fn be the value of a schedule that minimizes F ¼ maxff jðCjÞg. If the fj are F regular, then α1⌈CLB⌉þα2Fn is a lower bound to f ¼ α1Cmax þα2F. Proof. Under regularity, Fn is in fact a lower bound to the value of F attained by a minimizer of f, see [2].
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کلمات کلیدی:
Scheduling to minimize lateness | Everything Under The Sun https://kartikkukreja.wordpress.com/2013/11/24/scheduling-to-minimize-lateness/ Nov 24, 2013 - If job i is late, its lateness is defined to be li = fi – di. Otherwise, li = 0. So the objective is to find a schedule that minimizes the maximum lateness ... [PDF]Minimizing Maximum Lateness on a single machine 1|r |L www.dii.unisi.it/~detti/Maximum%20lateness.pdf 1|r j. |L max. • Single machine. • n number of jobs. • Due dates of each job,. • Processing me of each job,. • Release date of each job,. • Lateness of a job ... [PDF]An Optimal Incremental Algorithm for Minimizing Lateness with Rejection https://pdfs.semanticscholar.org/391e/08c234a5002ff1c5a5f998711056f3bb19bd.pdf by S Khuller - Cited by 7 - Related articles begin by defining the problem of scheduling jobs to minimize maximum lateness. Given a set of jobs A, each having a processing time and a due date, we want ... Efficient approximation schemes for the maximum lateness ... link.springer.com/article/10.1007/s10878-015-9924-4 by I Kacem - 2016 - Cited by 3 - Related articles Jul 16, 2015 - Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability ... Minimizing Maximum Promptness and Maximum Lateness on a ... - jstor https://www.jstor.org/stable/3690208 by JA Hoogeveen - 1996 - Cited by 54 - Related articles problem of finding a schedule that minimizes a function F of maximum ... maximum lateness subject to release dates that lie in the interval [di - pj - A, dj - A], for. Searches related to Maximum lateness minimization minimize total lateness minimizing lateness greedy algorithm scheduling to minimize lateness greedy algorithm greedy algorithm inversion minimizing maximum lateness proof how to calculate maximum lateness optimal caching greedy algorithm earliest due date scheduling
