Competitive Two-Agent Scheduling and Its Applications

Abstract

We consider a scheduling environment with m (m ≥ 1) identical machines in parallel and two agents. Agent A is responsible for n1 jobs and has a given objective function with regard to these jobs; agent B is responsible for n2 jobs and has an objective function that may be either the same or different from the one of agent A. The problem is to find a schedule for the n1 + n2 jobs that minimizes the objective of agent A (with regard to his n1 jobs) while keeping the objective of agent B (with regard to his n2 jobs) below or at a fixed level Q. The special case with a single machine has recently been considered in the literature, and a variety of results have been obtained for two-agent models with objectives such as fmax, ∑ wjCj, and ∑ Uj. In this paper, we generalize these results and solve one of the problems that had remained open. Furthermore, we enlarge the framework for the two-agent scheduling problem by including the total tardiness objective, allowing for preemptions, and considering jobs with different release dates; we consider also identical machines in parallel. We furthermore establish the relationships between two-agent scheduling problems and other areas within the scheduling field, namely rescheduling and scheduling subject to availability constraints.

Single machine scheduling with interfering job sets

“…For the first problem (P1) the interfering jobs from the two disjoint sets have the objective of (a) minimizing total completion time and (b) minimizing the total number of tardy jobs, respectively. The complexity of this problem is NP-hard as established by Leung et al [2010]. A pseudo-polynomial algorithm is presented by Ng et al [2006] for this problem under binary encoding.…”

Two-agent single-machine scheduling with release times and deadlines

“…Agnetis et al (2009) applied a Lagrangian dual to obtain a good bound and solved all the considered problems in strongly polynomial time. Leung et al (2010) generalised the results for some two-agent problems and solved one open problem involving identical parallel machines. For more results on multi-agent scheduling, the reader may refer to Yuan et al (2005), Ng et al (2006), Wan et al (2010), Cheng et al (2011aCheng et al ( , 2011b, Liu et al (2010Liu et al ( , 2011, Mosheiov (2010, 2011), Nong et al (2011), Li and Hsu (2012), and Yin et al (2012), among others.…”

A two-agent scheduling problem in a two-machine flowshop

“…They developed a branch-and-bound and several simulated annealing algorithms to solve the problem. For more studies on this line of research, the reader may refer to Alessandro Agnetis et al (2007) and Leung et al (2010).…”