On single‐machine sequencing with order constraints

A collection of jobs is to be processed by a single machine. Each job has a cost function associated with it which may be either linear or exponential, costs accruing when a job is completed. The machine may be allocated to the jobs according to a precedence relation. The problem is to find a strategy for allocating the machine which minimizes the total cost and which is consistent with the precedence relation. The paper extends and simplifies some previous work done by Sidney.