Approximation schemes for single machine scheduling with non-renewable resource constraints

In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional non-renewable resource constraints. Given the initial stock levels of some non-renewable resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of resource consuming jobs has to be scheduled on the machine such that there are enough resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments.