Approximation algorithms for flexible job shop problems

The Flexible Job Shop problem is a generalization of the classical job shop scheduling problem in which for every operation there is a group of machines that can process it. The problem is to assign operations to machines and to order the operations on the machines so that the operations can be processed in the smallest amount of time. This models a wide variety of problems encountered in real manufacturing systems. We present a linear time approximation scheme for the non-preemptive version of the problem when the number m of machines and the maximum number μ of operations per job are fixed. We also study the preemptive version of the problem when m and μ are fixed, and present a linear time approximation scheme for the problem without migration and a (2+e)-approximation algorithm for the problem with migration.

[1]  S. Sevast’yanov.  Bounding algorithm for the routing problem with arbitrary paths and alternative servers , 1986 .

[2]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[3]  Sartaj Sahni,et al.  Approximate Algorithms for the 0/1 Knapsack Problem , 1975, JACM.

[4]  M. Klein.  A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems , 1966 .

[5]  Aravind Srinivasan,et al.  Better approximation guarantees for job-shop scheduling , 1997, SODA '97.

[6]  Han Hoogeveen,et al.  Short Shop Schedules , 1997, Oper. Res..

[7]  Luca Maria Gambardella,et al.  An optimization methodology for intermodal terminal management , 2001, J. Intell. Manuf..

[8]  Peter Brucker,et al.  Complexity of scheduling problems with multi-purpose machines , 1997, Ann. Oper. Res..

[9]  David B. Shmoys,et al.  Improved approximation algorithms for shop scheduling problems , 1991, SODA '91.

[10]  Eugene L. Lawler,et al.  On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming , 1978, JACM.

[11]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..

[12]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[13]  Luca Maria Gambardella,et al.  Effective Neighborhood Functions for the Flexible Job Shop Problem , 1998 .

[14]  Eugene L. Lawler,et al.  Chapter 9 Sequencing and scheduling: Algorithms and complexity , 1993, Logistics of Production and Inventory.

[15]  Leonid Khachiyan,et al.  Coordination Complexity of Parallel Price-Directive Decomposition , 1996, Math. Oper. Res..

[16]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.