An automated negotiation approach to solve single machine scheduling problems with interfering job sets

doi:10.1016/j.cie.2016.01.013

Computers & Industrial Engineering

Volume 99, September 2016, Pages 318-329

https://doi.org/10.1016/j.cie.2016.01.013 Get rights and content

Highlights

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A negotiation scheme for scheduling problems with interfering job sets is proposed.
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Such problems can be found in semiconductor manufacturing.
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The scheme applies a mediator that proposes contracts using VNS.
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The solutions are close to the Pareto frontier derived using full information.
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We analyze the cooperative behavior of the agents. It depends on the objectives.

Abstract

In this paper, we propose a decentralized approach to solve multiple-criteria single machine scheduling problems. We consider a single machine that is utilized by two agents where each of them has its own jobs and a private objective. The objective function of the first agent is the total completion time or the total weighted completion time of its jobs, respectively, whereas the objective function of the second agent is the maximum lateness or the total weighted completion time of its jobs. The problem is motivated by scheduling problems found in semiconductor manufacturing. An automated negotiation mechanism is presented to solve the scheduling problems. The basic ingredient of the mechanism is a mediator that proposes contracts using a variable neighborhood search (VNS) technique. We study the behavior of both greedy and cooperative agents. In addition, a hybrid strategy is developed where the mediator accepts deteriorations of the objective values with a certain probability. The performance of the negotiation schemes is assessed using randomly generated problem instances. It turns out that the solutions determined by the negotiation mechanism are close to the Pareto frontier from a centralized approach with full information. We use a problem-specific Non-Dominated Sorting Genetic Algorithm (NSGA)-II scheme to determine the solutions on the Pareto frontier. It is shown that the degree of cooperation of the two agents depends on the objective function used.

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 $n$ 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 $j$ by $p_{j}$ . Furthermore, job $j$ might have a due date $d_{j}$ and also a weight $w_{j}$ to model the importance of the job. The completion time of job $j$ in schedule $s$ is $C_{j} (s)$ . The set of all jobs consists of two classes $C 1$ and $C 2$ , where $C 1 \cap C 2 = \emptyset$ and $card (C 1 \cup C 2) = n$ . We also introduce the notation $n_{i} : = card ($

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 $C$ 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 $c_{inc .} \in C$ 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 $S$ with respect to the solutions that dominate $S$ .

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 $C 2$ 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 $L_{max}$ 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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View full text

An automated negotiation approach to solve single machine scheduling problems with interfering job sets

Highlights

Abstract

Introduction

Section snippets

Problem description

Related research

Overall negotiation framework

Algorithms for determining the Pareto frontier taking into account full information

Design of experiments

Conclusions and future research

Artificial Intelligence

European Journal of Operational Research

Computers & Operations Research

European Journal of Operational Research

Computers & Operations Research

European Journal of Operational Research

Expert Systems with Applications

Multiagent scheduling: Models and algorithms

Nondominated schedules for a job-shop with two competing users

Computational & Mathematical Organization Theory

Scheduling problems with two competing agents

Operations Research

Multi-agent single machine scheduling

Annals of Operations Research

A lagrangian approach to single-machine scheduling problems with two competing agents

Journal of Scheduling

A multiple-criterion model for machine scheduling

Journal of Scheduling

Scheduling interfering job sets on parallel machines

European Journal of Operational Research

Genetic algorithm and random keys for sequencing and optimization

ORSA Journal of Computing

Efficient fair division: Help the worst off or avoid envy?

Rationality and Society

Prioritising production and engineering lots in wafer fabrication facilities: A simulation study

International Journal of Production Research

A market-based multi-agent system model for decentralized multi-project scheduling

Annals of Operations Research

A fast and elitist genetic algorithm: NSGA-II

IEEE Transactions on Evolutionary Computation

Supply chain coordination by means of automated negotiations between autonomous agents

Multiagent based Supply Chain Management, Studies in Computational Intelligence

An ant-based coordination mechanism for resourse-constrained project scheduling with multiple agents and cash flow objectives

Flexible Services and Manufacturing Journal