Batch Scheduling and Common Due-date Assignment on a Single Machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.

[1]  Mihalis Yannakakis,et al.  Batch sizing and job sequencing on a single machine , 1991 .

[2]  M. Y. Kovalyov.  Improving the complexities of approximation algorithms for optimization problems , 1995, Oper. Res. Lett..

[3]  Gary L. Ragatz,et al.  A framework for the study of due date management in job shops , 1984 .

[4]  Susanne Albers,et al.  The Complexity of One-Machine Batching Problems , 1993, Discret. Appl. Math..

[5]  Denis Naddef,et al.  One-pass batching algorithms for the one-machine problem , 1988, Discret. Appl. Math..

[6]  Clyde L. Monma,et al.  On the Complexity of Scheduling with Batch Setup Times , 1989, Oper. Res..

[7]  Mihalis Yannakakis,et al.  Optimal Scheduling of Products with Two Subassemblies on a Single Machine , 1989, Oper. Res..

[8]  T.C.E. Cheng,et al.  Survey of scheduling research involving due date determination decisions , 1989 .

[9]  G. Hägele,et al.  Phosphinic and Phosphonic Acids I: Protonation and Complex Formation Equilibria of Some Substituted Ethane-1,1,2-tris-(P-methyl-phosphinie Acids) , 1990 .

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

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

[12]  John L. Bruno,et al.  Complexity of Task Sequencing with Deadlines, Set-Up Times and Changeover Costs , 1978, SIAM J. Comput..

[13]  Uday S. Karmarkar,et al.  Batching to minimize flow times on one machine , 1987 .