Approximately optimal algorithms for scheduling a single machine with general convex resource functions

This paper studies batch-scheduling problems with different resource-allocation polices and general convex g-conv resource functions to minimise the total completion time. To reflect the focused batch-scheduling problems more appropriately in real-life production systems, two different resource-allocation policies were introduced and the g-conv resource function, which has been proven to be more implementable than previous resource functions in the literature, was employed. The authors proposed a novel concept of resource sensitivity according to the unique characteristic of the problems, in order to illustrate the differences in the time-compression effects among various jobs. Through the analysis of the properties for optimal solutions, the authors deduced the construction of the equivalent relations among these effects and consequently developed two approximately optimal algorithms, which have reasonably great accuracies. For performance comparison, other state-of-the-art algorithms were introduced, which are extensively applied for solving continuous optimisation problems. The results showed that the proposed algorithms outperform the compared approaches with respect to both solution quality and stability.