An automated negotiation approach to solve single machine scheduling problems with interfering job sets
Introduction
Increasing attention has been paid to decentralized scheduling approaches in the last decade. Usually, the individual jobs to be processed are considered as agents that are interested in using scarce resources, i.e. machines, or different objectives are considered with one agent per objective. Negotiation approaches based on contract nets and auctions are used to determine schedules. Decentralized scheduling approaches offer advantages for dynamic and stochastic environments and for situations where the data to make scheduling decisions is distributed, i.e., if some information asymmetry occurs. However, we might lose some solution quality compared to a centralized, full information-based scheduling approach.
In this paper, we are interested in solving scheduling problems where a single machine is used by several agents. Each agent has its own set of jobs. The agents pursue different objectives. The disjoint job sets compete or interfere with each other for the single machine. The sharing of expensive bottleneck machines in semiconductor wafer fabrication facilities by production jobs and engineering jobs is a typical example (cf. Crist and Uzsoy, 2011, Mönch et al., 2013). The engineering department runs the engineering jobs for test purposes and is interested in small flow times, whereas the production control department is responsible for production jobs and is interested in achieving a high throughput and in meeting the due dates of the jobs. The jobs of both departments compete for the scarce bottleneck resources. These two departments often do not share their objectives since they are competitors for the same resources. The importance of such resource allocation decisions including several departments is also highlighted in Khowala et al., 2014, Kim and Uzsoy, 2008. A similar situation can be found in maintenance scheduling where preventive maintenance jobs compete with the regular production jobs for the same machine (cf. Khelifati & Bouzid-Sitayeb, 2011). Other applications can be found in supply chain scheduling (cf. Perez-Gonzalez & Framinan, 2014). When customers compete for a common processing resource, for instance a transportation company, then the problem is said to contain interfering jobs. In this situation, the different customers will hide their private objectives since they are competitors.
In this paper, we propose an automated negotiation approach to tackle single machine scheduling problems with interfering job sets where the objective function of the first agent is the total completion time or the total weighted completion time and the objective function of the second agent is the maximum lateness or the total weighted completion time, respectively. It is shown by Baker and Smith (2003) that the scheduling problem with a bi-criteria objective function that is a linear combination of the total weighted completion time and the maximum lateness with given weights for each objective function is NP-hard, whereas the linear combination version of the scheduling problem with total completion time and maximum lateness can be solved in polynomial time.
While automated negotiation schemes are extensively studied to solve scheduling problems for non-interfering job sets, this is not the case for interfering job sets (cf. Agnetis, 2011). In the present paper, we will show that automated negotiation approaches using a mediator are able to find schedules that are close to certain points of the Pareto frontier that are derived when a centralized approach with full information is assumed. It turns out that the objectives of the single agents influence the performance of the algorithms. In addition, we are able to explain the behavior of the decentralized approaches taking into account properties of the full information version of the corresponding problem. The study of negotiation protocols for scheduling problems with interfering job sets and their rigorous computational assessment is rarely addressed in the literature (cf. Agnetis, 2011).
The paper is organized as follows. In the next section, we describe the problem. We discuss related literature in Section 3. The negotiation mechanism is described in Section 4. A brief description of algorithms for determining the Pareto frontier for instances of the scheduling problems with interfering job sets assuming full information is given in Section 5. Computational results for the decentralized scheduling approach are presented and interpreted in Section 6. Finally, we provide conclusions and future research directions in Section 7.
Section snippets
Problem description
Using standard scheduling notation, we consider jobs that are available for processing on a single machine. No preemption of a job is allowed after it starts processing. We denote the processing time of job by . Furthermore, job might have a due date and also a weight to model the importance of the job. The completion time of job in schedule is . The set of all jobs consists of two classes and , where and . We also introduce the notation
Related research
We discuss related research with respect to negotiation approaches for machine scheduling and production planning and with respect to scheduling of interfering job sets. Negotiation approaches are surveyed by Jennings et al. (2001) and by Baarslag et al. (2013). There are papers on decentralized scheduling in manufacturing that are based on the idea to give a certain budget to each job agent (cf. Macchiaroli and Riemma, 2002, Mönch et al., 2002, Ottaway and Burns, 2000). Based on their budgets,
Overall negotiation framework
The negotiation approach of Klein et al., 2003a, Klein et al., 2003b is a decentralized optimization procedure based on multiple agents. Each contract partner is represented by an agent that encapsulates its individual objective. We use a contract space that contains all possible contract instances (cf. Section 4.3). A mediator is responsible for the generation of contract proposals and for the acceptance of incumbent contracts. The incumbent contract is the one that is obligatory for
Algorithms for determining the Pareto frontier taking into account full information
We are interested in assessing the solution quality obtained by the fully decentralized schemes. We use the NSGA-II approach for solving problems (2), (6). NSGA-II (cf. Deb, Pratap, Agarwal, & Meyarivan, 2002) is a metaheuristic for multi-objective combinatorial optimization problems based on the principle of GAs. It uses a non-dominated sorting procedure that determines the fitness of a solution with respect to the solutions that dominate .
A random key approach (cf. Bean, 1994) is taken to
Design of experiments
We expect that the quality of the results will be influenced by the tightness T and the spread R of the due dates of the jobs. Moreover, the results might be influenced by the number of jobs assigned to each agent. Therefore, we use the problem instance scheme proposed by Mehta and Uzsoy (1998). The design of experiments used is summarized in Table 2.
In our experiments, we consider only homogeneous combinations of the acceptance criteria, for instance, a combination of two greedy acceptance
Conclusions and future research
In this paper, we described an automated negotiation approach for scheduling problems with interfering job sets. The first agent owns a TWC or a TC objective function, while the second agent has a TWC or an objective function. Using an extension of the negotiation approach proposed by Klein et al., 2003a, Klein et al., 2003b, Fink, 2004, respectively, we were able to obtain high quality approximated non-dominated solutions. The contract proposing mechanism of the mediator is based on VNS.
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2021, Transportation Research Part C: Emerging TechnologiesCitation Excerpt :In a related approach, Rene Ramacher et al. Ramacher and Monch (2016) design an automated negotiation mechanism using a variable neighborhood search technique to solve a single machine scheduling problem. Compared with these studies, our problem presents highly interdependent decisions constrained by temporal availability and spatial feasibility of both taxi drivers and charging stations, which results in many local optima and non-linear search space.
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2021, European Journal of Operational ResearchCitation Excerpt :Finally, we draw some conclusions in Section 7. Recently, Ramacher and Mönch (2016) propose an automated negotiation approach to deal with two-agent scheduling problems. A mediator that proposes contracts derived by using a variable neighborhood search (VNS) technique is introduced to compromise the objectives of the two agents.
Collaborative job scheduling in the wine bottling process
2020, Omega (United Kingdom)Citation Excerpt :This problem has many applications. These include, for example, shift-scheduling [15], operations at crossdock centres [40], assembly of electronic products [39], integrated-circuit packaging manufacturing systems [65], load balancing in project assignment [41], automobile gear manufacturing processes [26], air blast freezing in the food industry [12], and a negotiation scheme for scheduling problems in semiconductor manufacturing [48]. For a review on job scheduling and parallel machine problems we refer the reader to Allahverdi [2] and Mokotoff [45] respectively.
A hybrid variable neighborhood search algorithm for the hot rolling batch scheduling problem in compact strip production
2018, Computers and Industrial EngineeringCitation Excerpt :By employing a set of neighborhood structures, the VNS focuses on exploring a solution space through a systematic switch between neighborhood structures, attempting to get a more thorough exploration of the solution space. Since then, the VNS has been successfully applied in various fields, such as traveling salesman problems (Soylu, 2015; Wang, Chen, & Lin, 2016), location problems (Bischoff & Dächert, 2009; Babaie-Kafaki, Ghanbari, & Mahdavi-Amiri, 2016; Colombo, Cordone, & Lulli, 2016), assembly line balancing problems (Polat, Kalayci, Mutlu, & Gupta, 2016; Tang et al., 2016), cell formation (Brusco, 2015; Paydar & Saidi-Mehrabad, 2013), network design problems (Eskandarpour, Zegordi, & Nikbakhsh, 2013; Santos, Duhamel, & Belisário, 2016) and scheduling (Li, Pan, & Wang, 2014; Rahmani & Ramezanian, 2016; Ramacher & Mönch, 2016). As described above, a lowest number of rolling turns is required to accommodate all the ordered sheet strips.
Generic negotiation mechanisms with side payments – Design, analysis and application for decentralized resource-constrained multi-project scheduling problems
2017, European Journal of Operational ResearchCitation Excerpt :This idea has been extended by Fink (2004, 2006) by using mandatory acceptance quotas in order to force self-interested agents to behave cooperatively to a certain degree as is required for eventually achieving high-quality solutions. Ramacher and Mönch (2016) describe related approaches for single machine scheduling problems with interfering job sets. Multi-issue negotiation problems are also considered by Homberger (2010, 2011, 2012), who mainly uses population-based concepts (inspired by genetic/evolutionary algorithms); that is, a set of tentative solutions evolves in the course of the negotiation process (instead of a single solution).