Scheduling about a common due date with job-dependant asymmetric earliness and tardiness penalties

The problem of scheduling n jobs with a common due date on a single machine so as to minimize the total cost arising from earliness and tardiness is considered. A general model is examined, in which earliness penalty and tardiness penalty are, respectively, arbitrary non-decreasing functions. Moreover, the model includes two important features that commonly appear in practical problems, namely: 1. Earliness and tardiness are penalized with different weights which are job-dependent. 2. The earliness (or tardiness) penalty consists of two parts, one is a variable cost dependent on the length of earliness (or tardiness), while the other is a fixed cost incurred when the job is early (or tardy). This model provides a general and flexible performance measure for earliness/tardiness scheduling, which has not been attributed before. A number of results are established on the characterizations of optimal and sub-optimal solutions, and two algorithms are proposed based on these results. Computational results are also reported to demonstrate the effectiveness of the proposed algorithms.