Bicriteria Scheduling on Single-Machine with inventory Operations

In this paper, we consider the single machine scheduling problem with inventory operations. The objective is to minimize makespan subject to the constraint that the total number of tardy jobs is minimum. We show the problem is strongly NP-hard. A polynomial $1 + \frac{1}{m-1}$-approximation scheme for the problem is presented, where m is defined as the total job's processing times ∑ pj divided by the capacity c of the storage, and an optimal algorithm for a special case of the problem, in which each job is one unit in size.

[1]  Candace Arai Yano,et al.  Minimizing mean tardiness and earliness in single machine scheduling problems with unequal due-dates , 1994 .

[2]  R. Bulfin,et al.  Complexity of single machine, multi-criteria scheduling problems , 1993 .

[3]  A. Nagar,et al.  Multiple and bicriteria scheduling : A literature survey , 1995 .

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

[5]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[6]  John J. Kanet,et al.  Single-machine scheduling with early and tardy completion costs , 1993 .

[7]  Yih-Long Chang,et al.  MINIMIZING MEAN ABSOLUTE DEVIATION OF COMPLETION TIMES ABOUT A COMMON DUE DATE. , 1986 .

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

[9]  Marc E. Posner,et al.  Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date , 1991, Oper. Res..

[10]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[11]  George L. Vairaktarakis,et al.  The single-machine scheduling problem to minimize total tardiness subject to minimum number of tardy jobs , 1995 .

[12]  T. Cheng,et al.  Minimizing flowtime and missed due-dates in single-machine sequencing , 1990 .

[13]  Joseph Y.-T. Leung,et al.  Complexity of two dual criteria scheduling problems , 2007, Oper. Res. Lett..

[14]  H. Emmons.  One machine sequencing to minimize mean flow time with minimum number tardy , 1975 .

[15]  Robert L. Bulfin,et al.  Scheduling unit processing time jobs on a single machine with multiple criteria , 1990, Comput. Oper. Res..

[16]  Chung-Lun Li,et al.  A note on one-processor scheduling with asymmetric earliness and tardiness penalties , 1993, Oper. Res. Lett..