Optimisation of temporal networks under uncertainty

Abstract

A wide variety of decision problems in operations research are defined on temporal networks, that is, workflows of time-consuming tasks whose processing order is constrained by precedence relations. For example, temporal networks are used to formalise the management of projects, the execution of computer applications, the design of digital circuits and the scheduling of production processes. Optimisation problems arise in temporal networks when a decision maker wishes to determine a temporal arrangement of the tasks and/or a resource assignment that optimises some network characteristic such as the network’s makespan (i.e., the time required to complete all tasks) or its net present value. Optimisation problems in temporal networks have been investigated intensively for more than fifty years. To date, the majority of contributions focus on deterministic formulations where all problem parameters are known. This is surprising since parameters such as the task durations, the network structure, the availability of resources and the cash flows are typically unknown at the time the decision problem arises. The tacit understanding in the literature is that the decision maker replaces these uncertain parameters with their most likely or expected values to obtain a deterministic optimisation problem. It is well-documented in theory and practise that this approach can lead to severely suboptimal decisions. The objective of this thesis is to investigate solution techniques for optimisation problems in temporal networks that explicitly account for parameter uncertainty. Apart from theoretical and computational challenges, a key difficulty is that the decision maker may not be aware of the precise nature of the uncertainty. We therefore study several formulations, each of which requires different information about the probability distribution of the uncertain problem parameters. We discuss models that maximise the network’s net present value and problems that minimise the network’s makespan. Throughout the thesis, emphasis is placed on tractable techniques that scale to industrial-size problems