Optimal WACC in tariff regulation under uncertainty

In the regulation of network tariffs, the compensation for the opportunity costs of capital through the Weighted Average Costs of Capital (WACC) plays a crucial role. Determining the appropriate level for the WACC is, though, problematic because of the uncertainty about the future conditions in capital markets. When the WACC is set above the future opportunity costs of capital, consumers will pay too much, while when the WACC is below that level, network operators may be unable to finance investments affecting quality of network services. In this paper, we explicitly take this uncertainty into account when we determine the optimal WACC for the tariff regulation of an electricity network. By trading off consumer surplus and expected disruption costs in the electricity grid, we conclude that from a social-welfare perspective in most cases the optimal WACC in tariff regulation is above the historical mean costs of capital. Only in case of high uncertainty about the true costs of capital while network operators are able to quickly increase investment levels, the optimal WACC is below the historical mean because then it is less likely that the WACC is constantly insufficient to cover actual costs of capital. However, when network operators cannot quickly increase investment levels the optimal WACC is always above the historical mean cost of capital

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically nonconvex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q.In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the `1-norm of q

Total variation error bounds for convex approximations of two-stage mixed-integer recourse models

Many practical decisions have to be made while future data are uncertain. The stochastic programming approach to such decision problems is to model the uncertain data as random parameters and to assume that all probabilistic information concerning these random parameters is known or can be accurately estimated. A particular class of such models, studied in this thesis, comprises mixed-integer recourse models. These models have a wide range of applications in e.g. engineering, logistics, energy, and finance. They combine the modeling power but also the difficulties of random parameters and integer decision variables, so that in general they are extremely difficult to solve. This thesis contributes to the theory of mixed-integer recourse models by constructing approximations having desirable properties (such as convexity) for optimization purposes. To guarantee the performance of these approximations, error bounds on the approximation error are derived. Several subclasses and problem instances of mixed-integer recourse models are considered, ranging from simple integer recourse models to mixed-integer recourse models in general

A compact arc-based ILP formulation for the pickup and delivery problem with divisible pickups and deliveries

We consider the capacitated single vehicle one-to-one pickup and delivery problem with divisible pickups and deliveries (PDPDPD). In this problem, we do not make the standard assumption of one-to-one pickup and delivery problems that each location has only one transportation request. Instead we assume there are multiple requests per location that may be performed individually. This may result in multiple visits to a location. We provide a new compact arc-based ILP formulation for the PDPDPD by deriving time-consistency constraints that identify the order in which selected outgoing arcs from a node are actually traversed. The formulation can also easily be applied to the one-to-one PDP by restricting the number of times that a node can be visited. Numerical results on standard one-to-one PDP test instances from the literature show that our compact formulation is almost competitive with tailor-made solution methods for the one-to-one PDP. Moreover, we observe that significant cost savings up to 15% on average may be obtained by allowing divisible pickups and deliveries in one-to-one PDPs. It turns out that divisible pickups and deliveries are not only beneficial when the vehicle capacity is small, but also when this capacity is unrestrictive