Minimizing maximum absolute lateness and range of lateness under generalizeddue dates on a single machine

We investigate the problems of minimizing the maximum absolute lateness and range oflateness under generalized due dates on a single machine. In contrast to the traditional duedate cases, we show that these problems are unary NP‐hard. Furthermore, we present simpleapproximation algorithms for these problems, and show that they achieve the performanceratios of n for the problem of minimizing the maximum absolute lateness and of [ n/2 ] forthe problem of minimizing the range of lateness, where [ x ] is the smallest integer no lessthan x.

[1]  Han Hoogeveen.  Minimizing Maximum Earliness and Maximum Lateness on a Single Machine , 1990, IPCO.

[2]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[3]  Nicholas G. Hall.  Scheduling Problems With Generalized Due Dates , 1986 .

[4]  Jan Karel Lenstra,et al.  Complexity of Scheduling under Precedence Constraints , 1978, Oper. Res..

[5]  Maurice Queyranne,et al.  Generic Scheduling Polyhedra and a New Mixed-Integer Formulation for Single-Machine Scheduling , 1992, IPCO.

[6]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[7]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

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

[9]  Chelliah Sriskandarajah,et al.  On the Complexity of Generalized Due Date Scheduling Problems , 1991 .

[10]  Robert E. Tarjan,et al.  One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties , 1988, Math. Oper. Res..

[11]  Rong-Hwa Huang,et al.  An Algorithm for Minimizing the Range of Lateness on a Single Machine , 1991 .

[12]  Kathryn E. Stecke,et al.  Loading and control policies for a flexible manufacturing system , 1981 .

[13]  Chelliah Sriskandarajah.  A Note on the Generalized Due Dates Scheduling Problems , 1988 .

[14]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[15]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[16]  Jan Karel Lenstra,et al.  Complexity results for scheduling chains on a single machine : (preprint) , 1980 .

[17]  William L. Maxwell,et al.  Theory of scheduling , 1967 .