On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs

Some results of Sidney (Sidney, J. B. 1975. Decomposition algorithms for single machine sequencing with precedence relations and deferral costs. Opns. Res. 23 283–298.) concerning order-constrained deterministic scheduling with linear costs are extended to the more complex discounted costs case. Further, certain order-constrained stochastic scheduling problems are shown to have optimal strategies which are nonpreemptive. When this is so, results for the deterministic case may be utilized to obtain these optimal strategies. The models discussed are of interest in computer and job-shop scheduling and research planning.