Minimising total earliness and tardiness with periodically supplied non-renewable resource profiles

We consider a special class of resource-constrained single machine scheduling problems. In the classical context, resource types are classified into renewable and non-renewable; however, large variety real-world problems may not fit one these classes, e.g. labour regulations in project scheduling, budget allocation to different phases construction project, dose management medical imaging centre. this study, we address non-renewable resources supplied, necessarily immediately, periods planning horizon. The objective is assign jobs supply schedule them such that sum total tardiness earliness minimised. Several properties complexity results optimal schedules discussed, then they used develop tractable algorithm. First, decompose problem several decide through polynomial-time algorithm for each problem. scalability tests indicate promising performance guarantee compared provably integrated framework.