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Chris N. Potts

Other affiliations: Keele University
Bio: Chris N. Potts is an academic researcher from University of Southampton. The author has contributed to research in topics: Job shop scheduling & Scheduling (computing). The author has an hindex of 52, co-authored 125 publications receiving 10073 citations. Previous affiliations of Chris N. Potts include Keele University.


Papers
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Journal ArticleDOI
TL;DR: This paper reviews the literature on scheduling with batching, giving details of the basic algorithms, and referencing other significant results about efficient dynamic programming algorithms for solving batching problems.

904 citations

Journal ArticleDOI
TL;DR: A general model which combines batching and lot-sizing decisions with scheduling with a review of research on this type of model is given.
Abstract: In many practical situations, batching of similar jobs to avoid set-ups is performed whilst constructing a schedule. On the other hand, each job may consist of many identical items. Splitting a job often results in improved customer service or in reduced throughput time. Thus, implicit in determining a schedule is a lot-sizing decision which specifies how a job is to be split. This paper proposes a general model which combines batching and lot-sizing decisions with scheduling. A review of research on this type of model is given. Some important open problems for which further research is required are also highlighted.

430 citations

Journal ArticleDOI
TL;DR: It is demonstrated that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective, which has practical implications for improving the efficiency of supply chains.
Abstract: Although the supply chain management literature is extensive, the benefits and challenges of coordinated decision making within supply chainscheduling models have not been studied. We consider a variety of scheduling, batching, and delivery problems that arise in an arborescent supply chain where a supplier makes deliveries to several manufacturers, who also make deliveries to customers. The objective is to minimize the overall scheduling and delivery cost, using several classical scheduling objectives. This is achieved by scheduling the jobs and forming them into batches, each of which is delivered to the next downstream stage as a single shipment. For each problem, we either derive an efficient dynamic programming algorithm that minimizes the total cost of the supplier or that of the manufacturer, or we demonstrate that this problem is intractable. The total system cost minimization problem of a supplier and manufacturer who make cooperative decisions is also considered. We demonstrate that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective. Finally, we identify incentives and mechanisms for this cooperation, thereby demonstrating that our work has practical implications for improving the efficiency of supply chains.

427 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times was studied, and it was shown that minimizing the weighted number of tardy jobs and the total weighted tardiness are NP-hard problems.
Abstract: We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times A batching machine is a machine that can handle up to b jobs simultaneously The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time The processing time of a batch is equal to the largest processing time of any job in the batch We analyse two variants: the unbounded model, where b⩾n; and the bounded model, where b1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches © 1998 John Wiley & Sons, Ltd

389 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to introduce constraint statisfaction to the operational researchers.

343 citations


Cited by
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Book
01 Jan 2001
TL;DR: This chapter discusses Decision-Theoretic Foundations, Game Theory, Rationality, and Intelligence, and the Decision-Analytic Approach to Games, which aims to clarify the role of rationality in decision-making.
Abstract: Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

3,569 citations

01 Jan 1989
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.

1,401 citations

Journal ArticleDOI
TL;DR: An extensive review of the scheduling literature on models with setup times (costs) from then to date covering more than 300 papers is provided, which classifies scheduling problems into those with batching and non-batching considerations, and with sequence-independent and sequence-dependent setup times.

1,264 citations