Robust optimization criteria: state-of-the-art and new issues

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria and introduce two new classifications criteria for measuring the robustness of both scenarios and solutions. They can be used independently or coupled with classical robust optimization criteria and could work as a complementary tool for intensification in local searches

A game-theoretic optimisation approach to fair customer allocation in oligopolies

Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach

Telecommunications network design and max-min optimization problem, Journal of Telecommunications and Information Technology, 2005, nr 3

Telecommunications networks are facing increasing demand for Internet services. Therefore, the problem of telecommunications network design with the objective to maximize service data flows and provide fair treatment of all services is very up-to-date. In this application, the so-called maxmin fair (MMF) solution concept is widely used to formulate the resource allocation scheme. It assumes that the worst service performance is maximized and the solution is additionally regularized with the lexicographic maximization of the second worst performance, the third one, etc. In this paper we discuss solution algorithms for MMF problems related to telecommunications network design. Due to lexicographic maximization of ordered quantities, theMMF solution concept cannot be tackled by the standard optimization model (mathematical programme). However, one can formulate a sequential lexicographic optimization procedure. The basic procedure is applicable only for convex models, thus it allows to deal with basic design problems but fails if practical discrete restrictions commonly arriving in telecommunications network design are to be taken into account. Then, however, alternative sequential approaches allowing to solve non-convex MMF problems can be used

An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the p-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm

A game-theoretic optimisation approach to fair customer allocation in oligopolies

AbstractUnder the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.</jats:p

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Incorporating Water Demand Management into a Cooperative Water Allocation Framework

The final publication is available at Springer via http://dx.doi.org/10.1007/s11269-016-1322-xThe impact of a water demand management plan on a water system and its users is investigated within a comprehensive cooperative water allocation framework. In particular, a demand management plan is incorporated into a two-step multi-period fair water allocation model. A modified cooperative game is designed for the sharing of additional net benefits under the scenario having water demand management. The results indicate that cooperation among water users can yield more net benefits, and a water demand management plan is able to lead to a further increase of the aggregated net benefits by means of water transfers from less productive users to more productive ones. By utilizing the modified cooperative game, fair sharing of additional net benefits ensures that every water user can expect to receive more net benefits and thereby water users are motivated by incentives to implement a water demand management plan which in turn improves water use efficiency. The results demonstrate that the demand management plan can be of great assistance in some arid and semi-arid regions.Natural Sciences and Engineering Research Council (NSERC) of CanadaChina Scholarship Council [201206710003

Supply chain management for the process industry

This thesis investigates some important problems in the supply chain management (SCM) for the process industry to fill the gap in the literature work, covering production planning and scheduling, production, distribution planning under uncertainty, multiobjective supply chain optimisation and water resources management in the water supply chain planning. To solve these problems, models and solution approaches are developed using mathematical programming, especially mixed-integer linear programming (MILP), techniques. First, the medium-term planning of continuous multiproduct plants with sequence-dependent changeovers is addressed. An MILP model is developed using Travelling Salesman Problem (TSP) classic formulation. A rolling horizon approach is also proposed for large instances. Compared with several literature models, the proposed models and approaches show significant computational advantage. Then, the short-term scheduling of batch multiproduct plants is considered. TSP-based formulation is adapted to model the sequence-dependent changeovers between product groups. An edible-oil deodoriser case study is investigated. Later, the proposed TSP-based formulation is incorporated into the supply chain planning with sequence-dependent changeovers and demand elasticity of price. Model predictive control (MPC) is applied to the production, distribution and inventory planning of supply chains under demand uncertainty. A multiobjective optimisation problem for the production, distribution and capacity planning of a global supply chain of agrochemicals is also addressed, considering cost, responsiveness and customer service level as objectives simultaneously. Both ε- constraint method and lexicographic minimax method are used to find the Pareto-optimal solutions Finally, the integrated water resources management in the water supply chain management is addressed, considering desalinated water, wastewater and reclaimed water, simultaneously. The optimal production, distribution and storage systems are determined by the proposed MILP model. Real cases of two Greek islands are studied