Scheduling with partial rejection

Abstract We study a single machine scheduling problem with partial rejection. Each job is with an integer processing time. Partial rejection occurs when a job is only partly processed with penalty for the rejected part. We focus on integer size rejection. The objective is to minimize the total weighted completion time of processed jobs plus the total rejection cost. We develop a polynomial time optimal algorithm to solve the problem. We also present an easy-to-implement pseudopolynomial time optimal algorithm.

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