Performance of scheduling algorithms for no-wait flowshops with parallel machines

We study the performance of scheduling algorithms for a manufacturing system, called the ‘no-wait flowshop’, which consists of a certain number of machine centers. Each center has one or more identical parallel machines. Each job is processed by at most one machine in each center. The problem of finding the minimum finish time schedule is considered here in a flowshop consisting of two machine centers. Heuristic algorithms are presented and are analyzed in the worst case performance context. For the case of two centers, one with a single machine and the other with m, two heuristics are presented with tight performance guarantees of 3 − (1/m) and 2. When both centers have m machines, a heuristic is presented with an upper bound performance guarantee of 83 − 2/(3m). It is also shown that this bound can be reduced to 2(1 + ϵ). For the flowshop with any number of machines in each center, we provide a heuristic algorithm with an upper bound performance guarantee that depends on the relative number of machines in the centers.

[1]  Chelliah Sriskandarajah,et al.  Scheduling algorithms for flexible flowshops: Worst and average case performance , 1988 .

[2]  Michael A. Langston,et al.  Evaluation of a MULTIFIT-Based Scheduling Algorithm , 1986, J. Algorithms.

[3]  Donald K. Friesen,et al.  Tighter Bounds for the Multifit Processor Scheduling Algorithm , 1984, SIAM J. Comput..

[4]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[5]  Michael A. Langston,et al.  Interstage Transportation Planning in the Deterministic Flow-Shop Environment , 1987, Oper. Res..

[6]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[7]  Jan Karel Lenstra,et al.  Recent developments in deterministic sequencing and scheduling: a survey : (preprint) , 1981 .

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

[9]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

[10]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[11]  Edward G. Coffman,et al.  An Application of Bin-Packing to Multiprocessor Scheduling , 1978, SIAM J. Comput..

[12]  Chelliah Sriskandarajah,et al.  Some no-wait shops scheduling problems: Complexity aspect , 1986 .

[13]  Robert J. Wittrock,et al.  An Adaptable Scheduling Algorithm for Flexible Flow Lines , 1988, Oper. Res..

[14]  Jan Karel Lenstra,et al.  Sequencing and scheduling : an annotated bibliography , 1997 .

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

[16]  R. E. Buten,et al.  Scheduling model for computer systems with two classes of processors , 1972 .

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .