Approximation algorithms for multi-agent scheduling to minimize total weighted completion time

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

“…These papers assume various combinations of scheduling measures and machine settings. The relevant reference list contains Baker and Smith (2003) (focused on a single machine and the criteria of makespan, maximum lateness and total weighted completion time), Agnetis et al (2004) (considered the same and additional measures, eg the number of tardy jobs and maximum regular functions, and studied multi-machine settings as well), Cheng et al (2006) (proved that the problem with minimum number of tardy jobs for each agent is strongly NP-hard, and introduced a polynomial time solution for the case of unit time jobs), Ng et al (2006) (studied minimum weighted completion time for one agent subject to an upper bound on the number of tardy jobs for the second agent), Cheng et al (2007) (studied total tardiness), Agnetis et al (2007) (focused on a multi-agent setting), Cheng et al (2008) (multi-agent problems with precedence constraints), Liu and Tang (2008) and Liu et al (2009) (two agent scheduling with deteriorating jobs), Agnetis et al (2009) (branch-andbound algorithms for minimum total weighted completion time of the first agent, subject to an upper bound on several measures of the second agent), Lee et al (2009) (introduced multi-agent scheduling with total weighted completion time, and provided fully polynomial approximation schemes), Mor and Mosheiov (2010) (two-agent scheduling with various earliness measures), Leung et al (2010) (twoagent scheduling with preemption and release dates), Wan et al (2010) (two-agent problems with controllable processing times), Liu et al (2010) (two-agent single-machine scheduling with position-dependent processing times), Cheng et al (2011) (minimum weighted completion time of the first agent subject to no tardy jobs of the second agent, with learning effect based on sum-of-processing times), Li and Yuan (2012) (two-agent scheduling with batching, where the total processing time of a batch is equal to the maximum processing time of the jobs in the batch), Mor and Mosheiov (2011) (two-agent batch scheduling assuming identical jobs and minimum total flowtime), Li and Hsu (2012) (minimizing total weighted completion time of both agents, subject to an upper bound on the makespan of both agents, with a learning effect), Gawiejnowicz et al (2011) (minimum total tardiness of the first agent subject to no tardy jobs of the second agent, with time-dependent proce...…”

A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems

“…This complexity also holds for more than two sets of jobs (Lee et al, 2009). These authors provide an FPTAS to solve the goal programming version of this problem for the single machine and the unrelated parallel machines.…”

“…As discussed in Section 4, some authors only provide an algorithm to determine the size of the non- , an algorithm based on the Nash Bargaining Solution is proposed by Agnetis et al (2009b) Lee et al (2009) develop an FPTAS for computing a δ-efficient set (according to the definition given by Warburton, 1987), with δ the error bound. Additionally, Saule and Trystram (2009) consider the case for parallel machines, P m||#(…”

Development of a Collaborative Scheduling System of Offshore Platform Project Based on Multiagent Technology

“…Given that process planning and scheduling are performed sequentially, Li et al [33] designed an agent-based approach to facilitate these two functions and connect them more tightly. In [34], Lee et al regarded the scheduling problem on a single machine and therefore simplified the multiproject scheduling problem into a multiobjective shortest path (MOSP) problem to minimize the weighted completion time. Cheng [35] considered two-agent scheduling problem and discussed some polynomial cases to design the algorithm to optimize task tardiness.…”