A note on resource allocation scheduling with position-dependent workloads

In this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.