Scheduling with start time related deadlines

This paper presents a scheduling problem for a monoprocessor without preemption with timing constraints given by a task-on-node graph. The precedence relations are given by an oriented graph where edges are related either to the minimum time or to the maximum time elapsed between start times of the tasks. The processing time of a given task is associated to a given node in the oriented graph. The problem, finding an optimal schedule satisfying the timing constraints while minimizing makespan C_max, is solved by two approaches. The first is implemented as a B&B algorithm using a critical path estimation and estimation of remaining processing time. Since the objective is to find a feasible schedule with minimal C_max, the bounding procedure uses the best known solution as a new dynamic timing constraint. It considers also the scheduling anomaly while deciding the feasibility of the given solution. The second solution is based on ILP. Experimental results show comparison of the B&B and ILP solution