All solution graphs in multidimensional screening

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs

Simultaneous minimisation of water and energy within a water and membrane network superstructure

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering, 2015The scarcity of water and strict environmental regulations have made sustainable engineering a prime concern in the process and manufacturing industries. Water minimisation involves the reduction of freshwater use and effluent discharge in chemical plants. This is achieved through water reuse, water recycle and water regeneration. Optimisation of the water network (WN) superstructure considers all possible interconnections between water sources, water sinks and regenerator units (membrane systems). In most published works, membrane systems have been represented using the “black-box” approach, which uses a simplified linear model to represent the membrane systems. This approach does not give an accurate representation of the energy consumption and associated costs of the membrane systems. The work presented in this dissertation therefore looks at the incorporation of a detailed reverse osmosis network (RON) superstructure within a water network superstructure in order to simultaneously minimise water, energy, operating and capital costs. The WN consists of water sources, water sinks and reverse osmosis (RO) units for the partial treatment of the contaminated water. An overall mixed-integer nonlinear programming (MINLP) framework is developed, that simultaneously evaluates both water recycle/reuse and regeneration reuse/recycle opportunities. The solution obtained from optimisation provides the optimal connections between various units in the network arrangement, size and number of RO units, booster pumps as well as energy recovery turbines. The work looks at four cases in order to highlight the importance of including a detailed regeneration network within the water network instead of the traditional “black-box’’ model. The importance of using a variable removal ratio in the model is also highlighted by applying the work to a literature case study, which leads to a 28% reduction in freshwater consumption and 80% reduction in wastewater generation.GR201

Optimal Power Generation under Uncertainty via Stochastic Programming

A power generation system comprising thermal and pumped-storage hydro plants is considered. Two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dynamic model for the short-term operation and (ii) a power production planning model. In both cases, the presence of stochastic data in the optimization model leads to multi-stage and two-stage stochastic programs, respectively. Both stochastic programming problems involve a large number of mixed-integer (stochastic) decisions, but their constraints are loosely coupled across operating power units. This is used to design Lagrangian relaxation methods for both models, which lead to a decomposition into stochastic single unit subproblems. For the dynamic model a Lagrangian decomposition based algorithm is described in more detail. Special emphasis is put on a discussion of the duality gap, the efficient solution of the multi-stage single unit subproblems and on solving the dual problem by bundle methods for convex nondifferentiable optimization

Distance Oracles for Time-Dependent Networks

We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes $(1+\epsilon)-$approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and $(1+\sigma)-$approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant $\sigma > \epsilon$. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

An O(nlogn) algorithm for the two-machine flow shop problem with controllable machine speeds

Production Planning;Scheduling;produktieleer/ produktieplanning