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عنوان فارسی مقاله:
برنامه ریزی به موقع با دو عامل رقابت در ماشین های موازی نامربوط
عنوان انگلیسی مقاله:
Just-in-time scheduling with two competing agents on unrelated parallel machines
سال انتشار : 2016
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بخشی از مقاله انگلیسی:
2. Problem formulation
We formally describe the problem under study as follows: There are two competing agents (called agent A and agent B, respectively) that have to schedule two families of independent and non-preemptive jobs on m unrelated parallel machines M1; M2; …; Mm. Agent A has to perform the job set J A ¼ fJ A 1; J A 2; …; J A nA g, while agent B has to perform the job set J B ¼ fJ B 1; J B 2; …; J B nB g. We call the jobs of agents A and B the A-jobs and B-jobs, respectively. All the jobs are available for processing from time zero onwards. Let XAfA; Bg and let n ¼ nA þnB denote the total number of jobs. Denote dj X as the due date of job Jj X , wj X as the gain (income) from completing job Jj X just-in-time (i.e., exactly at time dj X ), and pij X as the processing time of job Jj X on machine Mi for i ¼ 1; …; m and j ¼ 1; …; nX. The jobs that are completed exactly on their due dates in some schedule are called just-in-time jobs. We assume, without loss of generality, that all the dj X , wj X , and pij X values are positive integers, and let WA ¼ P J A k AJ AwA k and WB ¼ P J B k AJ BwB k . For any given solution, let Ei be the set of just-in-time jobs allocated to machine Mi for i ¼ 1; …; m, with E ¼ E1 [ E2 [ ⋯ [ Em, and let T ¼ ðJ A [ J BÞ⧹E be the set of the other jobs. A partition of set J A [ J B into two disjointed subsets E and T is considered to be a feasible partition (or a feasible schedule) if it is possible to schedule the jobs belonging to set E on the m unrelated parallel machines such that they are all completed just in time. Following Lann and Mosheiov [15], in a feasible schedule, it is assumed that the jobs in T need not be executed, which means that they are rejected. We also denote by EA and EB the sets of just-in-time Ajobs and B-jobs, respectively. Each agent wants to optimize a certain objective function depending on the completion times of its jobs only. Specifically, agent A wants to maximize QAðSÞ ¼ P J A k AEAwA k (the weighted number of just-in-time A-jobs, i.e., the total gain from completing the jobs in set EA just-in -time), while agent B wants to maximize QB ðSÞ ¼ maxJ B k AEBwB k (the maximum gain from completing the jobs in set EB just-in-time) or to maximize QB ðSÞ ¼ P J B k AEBwB k (the weighted number of just-in-time B-jobs, i.e., the total gain from completing the jobs in set EB just-in-time). Since increasing the objective value of agent A will decrease the objective value of agent B, and vice versa, we need to consider the trade-off between the two objective functions carefully to achieve the best scheduling outcome. For such kind of bicriterion problem, we focus on finding the set of all the Paretooptimal schedules (points) ðQA;QB Þ, where a schedule S with QA ¼ QAðSÞ and QB ¼ QB ðSÞ is called Pareto-optimal (or efficient) if there does not exist another schedule S0 such that QAðS0 ÞZQAðSÞ and QB ðS0 ÞZQB ðSÞ with at least one of these inequalities being strict. Using the three-field notation proposed by Graham et al. [12] and extended to multicriteria scheduling problems by T'kindt and Billaut [25], we denote the problems under consideration by RmjjðP J A k AEAwA k ; maxJ B k AEBwB k Þ and RmjjðP J A k AEAwA k ; P J B k AEBwB k Þ, respectively, when the number of machines m is fixed. Note that the criterion in the classical three-field notation is to be minimized, but in this paper the criterion is to be maximized.
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کلمات کلیدی:
Just-in-time scheduling with two competing agents on unrelated ... https://www.researchgate.net/.../308978683_Just-in-time_scheduling_with_two_competi... Oct 11, 2016 - unrelated parallel machines is equivalent to that of maximizing. the weighted ... There are two competing agents (called agent Aand agent B,. [PDF]Just-in-time scheduling with two competing agents on unrelated ... https://www.researchgate.net/...competing_agents_on_unrelated_parallel_machines/.../... Just-in-time scheduling with two competing agents on unrelated parallel machines$. Yunqiang Yin a, Shuenn-Ren Cheng b, T.C.E. Cheng c, Du-Juan Wang d, ... Just-in-time scheduling with two competing agents on unrelated ... ira.lib.polyu.edu.hk/handle/10397/66701 by YQ Yin - 2016 - Cited by 12 - Related articles Two agents. Unrelated parallel machines. Just-in-time scheduling. FPTAS. Issue Date: 2016. Publisher: Pergamon Press. Source: Omega, Sept. 2016, v. 63, p. An exact extended formulation for the unrelated parallel machine total ... dl.acm.org/citation.cfm?id=3124467.3124492 by K Bülbül - 2017 - Cited by 1 - Related articles An exact extended formulation for the unrelated parallel machine total weighted ... We consider the scheduling problem in which two agents (agents A and B), each ... respectively), compete to process their own jobs in a two-machine flowshop. Proceedings of the Institute of Industrial Engineers Asian ... https://books.google.com/books?isbn=9814451983 Yi-Kuei Lin, Yu-Chung Tsao, Shi Woei Lin - 2013 - Technology & Engineering ... Pacifici A (2004) Scheduling problems with two competing agents. ... Werner F (2001) Heuristic algorithms for unrelated parallel machine scheduling with a ...
