Worst-Case Analysis of Cash Inventory in Single Machine Scheduling

Abstract

This paper studies the inventory of cash as a renewable resource in single machine scheduling problem. The status of cash is incorporated in to the objective function. Average and minimum available cash and maximum and average cash deficiency are contemplated subject to a worst-case scenario that for each job the cost [price] is paid [received] entirely at the start [end] of processing the job. For each objective, either proof of NP-hardness or optimal scheduling rule are provided. Some scenario-based numerical experiments are also carried out which reveal and emphasize the effect of financial assumptions of this research in single machine scheduling.