Scheduling for multiple machines with S-precedence constraints

Abstract

This thesis considers a new type of precedence constraint defined as s-precedence constraints. For s-precedence constraints, job i cannot start processing until all jobs that precede i start. This is different from the standard definition of a precedence relation where i cannot start until all prior jobs complete. While not discussed in the scheduling literature, s-precedence constraints have wide applicability in real world settings. Examples of hese types of constraints include most queueing systems where earlier arriving jobs start rocessing first. Applications occur in many production and service industries, including telecommunications, health care, and food processing and distribution. This thesis considers three deterministic scheduling problems where jobs with precedence relations are processed by multiple parallel machines. The first problem is scheduling s-precedence constrained jobs on identical parallel machines with the objective of minimizing the total completion time. The problem is shown to be NPhard, and some basic properties of the problem are analyzed. An LP-based heuristic procedure is derived for the problem. Numerical experiments are conducted to show that the derived heuristic provides good solutions within a short time. The second problem is scheduling s-precedence constrained jobs on machines in parallel with different speeds (referred to as uniform parallel machines). The objective is to minimize the weighted total completion time. An LP-based heuristic procedure is derived for the problem. Numerical experiments are conducted to show that the derived heuristic provides good solutions within a short time. The third problem is scheduling s-precedence constrained jobs on identical parallel machines. The objective is to find the minimum makespan (the completion time of the last job). The problem is shown to be strongly NP-hard. A heuristic procedure is developed and tight worst case bounds on the relative error are derived. ...