Earliness-tardiness scheduling problems with a common delivery window

This paper deals with the scheduling of n jobs on a single machine to minimize the sum of weighted earliness and weighted number of tardy jobs given a delivery window. Penalties are not incurred if jobs are completed within the delivery window. The length of this delivery window (which corresponds to the time period within which the customer is willing to take deliveries) is a given constant. We consider two cases of the problem; one where the position of the delivery parameter (restricted window case). We present some optimal properties, prove that the problem (even for the unrestricted window case) is NP-complete, and present dynamic programming algorithms for both cases.

[1]  Han Hoogeveen.  Minimizing Maximum Promptness and Maximum Lateness on a Single Machine , 1996, Math. Oper. Res..

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

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

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

[5]  Chung-Yee Lee,et al.  Error Bound of a Heuristic for the Common Due Date Scheduling Problem , 1993, INFORMS J. Comput..

[6]  Chung-Yee Lee,et al.  Minimizing weighted number of tardy jobs and weighted earliness-tardiness penalties about a common due date , 1991, Comput. Oper. Res..

[7]  Sheldon Epstein,et al.  Optimal common due-date with limited completion time , 1991, Comput. Oper. Res..

[8]  H. G. Kahlbacher,et al.  Single-machine scheduling to minimize earliness and number of tardy jobs , 1993 .

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

[10]  Suresh P. Sethi,et al.  Earliness-Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date , 1991, Oper. Res..

[11]  S. S. Panwalkar,et al.  Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem , 1982, Oper. Res..

[12]  Yih-Long Chang,et al.  Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date , 1987 .

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

[14]  Evan L. Porteus.  Investing in Reduced Setups in the EOQ Model , 1985 .