Composite heuristics and water wave optimality algorithms for tri-criteria multiple job classes and customer order scheduling on a single machine

Among the well-known scheduling problems, the customer order scheduling problem (COSP) has always been of great importance in manufacturing. To reflect the reality of COSPs as much as possible, this study considers that jobs from different orders are classified in various classes. This paper addresses a tri-criteria single-machine scheduling model with multiple job classes and customer orders on which the measurement minimizes a linear combination of the sum of the ranges of all orders, the tardiness of all orders, and the total completion times of all jobs. Due to the NP-hard complexity of the problem, a lower bound and a property are developed and utilized in a branch-and-bound for solving an exact solution. Afterward, four heuristics with three local improved searching methods each and a water wave optimality algorithm with four variants of wavelengths are proposed. The tested outputs report the performances of the proposed methods.