Minimization of Makespan Quantiles

Abstract

In this chapter, we consider temporal networks whose task durations are functions of a resource allocation that can be chosen by the decision maker. The goal is to find a feasible resource allocation that minimizes the network’s makespan. We focus on non-renewable resources, that is, the resources are not replenished, and specified resource budgets must be met. The resource allocation model presented in this chapter is primarily suited for project scheduling problems, and for ease of exposition we will use project scheduling terminology throughout this chapter. In project scheduling, it is common to restrict attention to non-renewable resources and disregard the per-period consumption quotas that exist for renewable and doubly constrained resources, see Sect. 2.1. Apart from computational reasons, this may be justified by the fact that resource allocation decisions are often drawn at an early stage of a project’s lifecycle at which the actual resource availabilities (which are unpredictable due to staff holidays, illness and other projects) are not yet known. Thus, the goal of such resource allocation models is to decide on a rough-cut plan which will be refined later.