Abstract
This study focuses on solving the scheduling problem associated with a single bounded parallel-batch machine, where jobs have equal lengths but different sizes. The size of each job can be arbitrarily split into two parts, which are processed in consecutive lots. Two different definitions of job completion time are considered: Generic Completion Time, the common definition in classical parallel-batch scheduling, and Percentage Completion Time, calculated as the sum of the products of completion times and the percentages of job size in two lots. The primary contribution of this research is the development of an O(n3) time algorithm to optimize simultaneously total completion time and maximum cost, considering both completion time definitions separately. The algorithms can provide all Pareto optimal points and corresponding schedules for two criteria.
Published Version
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