Robust resource allocations in temporal networks

Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper we study a robust resource allocation problem where the task durations are uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{NP}}$$\end{document} -hard. We then develop convergent bounds on the optimal objective value, as well as feasible allocations whose objective values are bracketed by these bounds. Numerical results provide empirical support for the proposed method.