Solving scheduling and location problems in the plane simultaneously

In this paper we concentrate on the simultaneous single machine scheduling–location (ScheLoc  ) model in the plane. The model combines both the location of the machine and the scheduling of the jobs executed by the machine. Two objectives are analyzed: the makespan and the total completion time. Basic properties of the models are shown and lower bounds on the value of the objective functions are developed. Single machine ScheLoc problems with Euclidean, rectilinear and general ℓqℓq norms are solved very efficiently by the “big triangle small triangle” branch-and-bound approach. Randomly generated problems with 10,000 jobs are solved in about 5–10 min within a relative accuracy of ε=10-5ε=10-5 from the global optimum.