Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)

SP models combine the paradigm of dynamic linear programming with modelling of random parameters, providing optimal decisions which hedge against future uncertainties. Advances in hardware as well as software techniques and solution methods have made SP a viable optimisation tool. We identify a growing need for modelling systems which support the creation and investigation of SP problems. Our SPInE system integrates a number of components which include a flexible modelling tool (based on stochastic extensions of the algebraic modelling languages AMPL and MPL), stochastic solvers, as well as special purpose scenario generators and database tools. We introduce an asset/liability management model and illustrate how SPInE can be used to create and process this model as a multistage SP application

Approximation in stochastic integer programming

Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions. However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality. Only recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.

Planning of FiWi Networks to Support Communications Infrastructure of SG and SC

Nowadays, growth in demand for bandwidth, due to new and future applications being implemented, for services provided from smart grids (SG), smart cities (SC) and internet of things (IoT), it has drawn attention of scientific community, on issues related to planning, and optimization of communication infrastructure resources, in addition is necessary comply with requirements such as scalability, coverage, security, flexibility, availability, delay and security. Another important point is how to find and analyze possible solutions that seek to minimize the costs involved by capital expenditure (CAPEX) and operational expenditure (OPEX), but where it is possible to measure the uncertainty coming from stochastic projections, in order to obtain the maximum benefit expected to give access to users Who benefits from the services provided by SG, SC and IoT, on the other hand, we must look for communications architectures that generate optimum topologies to meet demanded requirements and at the same time save energy, possible alternatives highlight the use of hybrid networks of optical fiber links combined with wireless links (Fiber-Wireless, FiWi). This chapter seeks to provide planning alternatives to network segments linking universal data aggregation point (UDAP) with base stations (BS), this segment joins wide area network (WAN) with metropolitan area network (MAN)

Economic Optimization of Fiber Optic Network Design in Anchorage

Presented to the Faculty of the University of Alaska Anchorage in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE, ENGINEERING MANAGEMENTThe wireline telecommunications industry is currently involved in an evolution. Growing bandwidth demands are putting pressure on the capabilities of outdated copper based networks. These demands are being meet by replacing these copper based networks with fiber optic networks. Unfortunately, telecommunications decision makers are tasked with figuring out how best to deploy these networks with little ability to plan, organize, lead, or control these large projects. This project introduces a novel approach to designing fiber optic access networks. By leveraging well known clustering and routing techniques to produce sound network design, decision makers will better understand how to divide service areas, where to place fiber, and how much fiber should be placed. Combining this output with other typical measures of costs and revenue, the decision maker will also be able to focus on the business areas that will provide the best outcome when undertaking this transformational evolution of physical networks.Introduction / Background / Clustering, Routing, and the Model / Results and Analysis / Conclusion / Reference

Modelling and solution methods for stochastic optimisation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.Financial support was obtained from OptiRisk Systems

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects.variability, peakedness, supply chain

Design and architecture of a stochastic programming modelling system

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Decision making under uncertainty is an important yet challenging task; a number of alternative paradigms which address this problem have been proposed. Stochastic Programming (SP) and Robust Optimization (RO) are two such modelling ap-proaches, which we consider; these are natural extensions of Mathematical Pro-gramming modelling. The process that goes from the conceptualization of an SP model to its solution and the use of the optimization results is complex in respect to its deterministic counterpart. Many factors contribute to this complexity: (i) the representation of the random behaviour of the model parameters, (ii) the interfac-ing of the decision model with the model of randomness, (iii) the difficulty in solving (very) large model instances, (iv) the requirements for result analysis and perfor-mance evaluation through simulation techniques. An overview of the software tools which support stochastic programming modelling is given, and a conceptual struc-ture and the architecture of such tools are presented. This conceptualization is pre-sented as various interacting modules, namely (i) scenario generators, (ii) model generators, (iii) solvers and (iv) performance evaluation. Reflecting this research, we have redesigned and extended an established modelling system to support modelling under uncertainty. The collective system which integrates these other-wise disparate set of model formulations within a common framework is innovative and makes the resulting system a powerful modelling tool. The introduction of sce-nario generation in the ex-ante decision model and the integration with simulation and evaluation for the purpose of ex-post analysis by the use of workflows is novel and makes a contribution to knowledge

Robust and stochastic approaches to network capacity design under demand uncertainty

This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique