Robust and Adaptable Job Shop Scheduling ... - Semantic Scholar

1 downloads 0 Views 834KB Size Report
Tennessee Technological University,. Cookeville, TN38505, USA. Key Words: Dynamic Job Shop Scheduling, Multi-Agent Systems, Scheduling Robustness.
Robust and Adaptable Job Shop Scheduling Using Multiple Agents N. Liu, Mohamed A. Abdelrahman, and

Srini Ramaswamy

Department of Electrical and Computer Eng., Tennessee Technological University, Cookeville, TN38505,USA

Department of Computer Science, Tennessee Technological University, Cookeville, TN38505,USA

Key Words: Dynamic Job Shop Scheduling, Multi-Agent Systems, Scheduling Robustness Abstract-The work presented in this paper is a continuation for efforts to devise a complete multiple agents' framework for real-time dynamic job shop scheduling, which considers robustness and adaptability. Previous work has been reported in [l].The framework inherits the advantages of decentralized models, such as flexibility, robustness, and high fault tolerance. The framework is actually a job dispatching procedure-a completely reactive scheduling approach-combining real time decision making with predictive decision-making based on optimization. It can sohe various disruptions as flexibly as dispatching rules. This paper provides an experimental justincation of the arguments presented above using computational experiments on dynsmic job arrivals. First, it compares computational results on unpredictable job arrivals among the presented framework and commonly used dispatching rules to show the effectiveness and efficiency of the Framework. Then it compares computational results among four cases of dynamic job arrivals to demonstrate the effects of makjng tun use of available information of disruptions.

combination of auction with Lagrangian relaxation. Auctionllagrangian relaxation approaches have been used in a quasidistributed static job shop environment [4] and a holonic system [5]. A variant has been used in a distnbuted static job shop environment 161 and a single machine with dynamic job arrivals [7]. The goal of this research is to explore a methodology that uses distributed problem solvers--multipte agents--to effectively and efficiently schedule job shops in a dynamic environment with minimum global information and without mastedslave relationships between agents, and considers robustness and adaptability. By robustness it is meant that the performance of the schedule still remains satisfactory in the presence of disruptions. By adaptability it is meant that the scheduling system is capable of generating schedules that accommodate a wide range of different,even unforeseen and unidentified disruptions. The research extends the variant of auctionkagmngian relaxation approaches mentioned above [6] with a rolling time horizon procedure to form a complete multi-agent h e w o r k for real-time dynamic job shop scheduling. The work presented in this paper is a continuation for efforts to devise a complete multiple agents' himework for real-time dynamic job shop scheduling, which considers I. INTRODUCTION robustness and adaptability. Previous work has been reported Job shop scheduling can be divided into two classes, in 113. The fiamework inherits the advantages of namely, static and dynamic job shop scheduling. Static decentralized models, such as flexibility, robustness, and high scheduling usually produces schedules in advance in order to fault tolerance. The framework is actually a job dispatching direct operations and resource allocation. Unforhmately, in a procedure-a completely reactive scheduling approach-dynamic environment, as soon as the schedule is released, it combining real time decision making with predictive is immediately subject to random disruptions that may render decision-making based on optimization. It can solve various the initial schedule obsolete and result in the degeneration of disruptions as flexibly as dispatching d e s . This paper provides an experimental justification of the the system performance [2]. Traditional approaches to job shop scheduhg in the arguments presented above using computational experiments presence of uncertainties are based on centralized models that on dynamic job arrivals. First, it compares computational view jobs and machines as passive symbols not as active results on unpredictable job arrivals among the presented entities like in certain decentralized models. This indicates framework and commonly used dispatching rules to show the that centralized approaches are inflexible and slow to satisfy effectiveness and efficiency of the framework Then it scheduling problems under disruptions [3]. One certain type compares computational results among four cases of dynamic of agent-based distributed scheduling can handle the dynamic job arrivals to demonstrate the effects of making full use of nature in the shop quite effectively, because agents directly available information of disruptions. represent physical objects, such as machines, jobs, and The paper is organized as follows. Section II and Section III provide background infomtioq which are mathematical operations, etc., and operate in a distributed architecture. Current research of this certain type of agent-based formulation and iis resolution of the Lagrangian relaxation distributed scheduling mentioned above has evolved into the problem, and the complete multiple agents' framework 0-7803-8808-9/05/$20.00 02005 E E E 45

1

respectively. Section PI provides computational results for dynamicjob arrivals. Section V is conclusions.

U. PROBLEM FORMULATION AND RESOLUTION (4)

Based on the discrete-time, integerprogramming, and deterministic job shop formulation in [6], we extend it with a rolling time horizon to get the following formulation for realtime dynamic job shop. scheduling with weighted tardiness objective. First, the following variables are defined, where operationj of job i is referred to as operation (i, i). r length ofrolling &e horizon time of current decision point ament total number ofjob agents current total number of machine agents start number of unprocessed operations of job i release date of job i processing time of operation ( i , ~ ) due date of job i weight of job i completion time of operation (i, OJ tardiness of job i, T, = max {0, C, ; di} total number of operations ofjob z 0- 1 interger variable equals one if operation (i, j9 is completed at tiuie t 0-1 integer variable equal5 one if operation ((1) is processed on machine m Lagrange multiplier upper bound of iteration r of Lagrangian relaxation problem lower bound of iteration r of Lagrangian LF relaxation problem . step size of iteration r s subgradient of iteration P SCm, subgradient multiplier of iteration r, 0 < d ar

rdo

x,,E @,1), vi,Af cym (0,1), V i ,j , m . E

where constraints (2) are operation precedence constraints; constraints (3) are machine capacity constraints; and constraints (4) are job release date constraints. We introduce here a varying variable M,,which represents a varying number of machine agents. When the machine capacity constraints (3) are relaxed by using Lagrange multipliers ,Iml,the fol1oWing Lagrangian relaxation problem is obtained r

I

-

+LM

ES/zmt r=r,

m=l

subject to (1), (2), and (4). The relaxed problem can be decomposed hto the following independent joblevel subproblems for the given set of

subject to (5)

52

msitive inf-itv INF Then, we introduce two varying variables N, and t,-tL. The former represents a varying number of job agents and the latter represents a rolling time horizon. The integer programming formulation for the dynamic job shop problem is defmed as follows:

f=fc

r, t L Niir

2 pi1 + P;:

(7)

f=f