A bicriteria approach to minimize number of tardy jobs and resource consumption in scheduling a single machine

We extend the classical scheduling problem of minimizing the number of tardy jobs in a single-machine to the case where the job processing times are controllable by allocating a continuous and non-renewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between the number of tardy jobs and total resource consumption using a bicriteria approach. Most of the research on scheduling with controllable resource-dependent processing times is done either to a linear resource consumption function or to a specific type of convex resource consumption function. We, in contrast, analyze the problem for a more general type of convex decreasing resource consumption function, which guarantees a very robust analysis that can be applied to a wide range of problems. We present four different variations of the problem and prove them to be NP-hard. We then present a polynomial time algorithm to solve an important special case of the problem and also suggest and compare the performances of three different heuristic algorithms. (C) 2009 Elsevier B.V. All rights reserved.