A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Analysis of road network pattern considering population distribution and central business district.

This paper proposes a road network growing model with the consideration of population distribution and central business district (CBD) attraction. In the model, the relative neighborhood graph (RNG) is introduced as the connection mechanism to capture the haracteristics of road network topology. The simulation experiment is set up to illustrate the effects of population distribution and CBD attraction on the characteristics of road network. Moreover, several topological attributes of road network is evaluated by using coverage, circuitness, treeness and total length in the experiment. Finally, the suggested model is verified in the simulation of China and Beijing Highway networks

Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits

[[abstract]]In practice, a supplier often offers its retailers a permissible delay period M to settle their unpaid accounts. Likewise, a retailer in turn offers another trade credit period N to its customers. The benefits of trade credit are not only to attract new buyers who consider it a type of price reduction, but also to provide a competitive strategy other than introduce permanent price reductions. On the other hand, the policy of granting credit terms adds an additional cost to the seller as well as an additional dimension of default risk. In this paper, we first incorporate the fact that trade credit has a positive impact on demand but negative impacts on costs and default risks to establish an economic order quantity model for the seller in a supply chain with up-stream and down-stream trade credits. Then we derive the necessary and sufficient conditions to obtain the optimal replenishment time and credit period for the seller. Finally, we use some numerical examples to illustrate the theoretical results.[[incitationindex]]SCI[[booktype]]電子

Convex Cost Multicommodity Flow Problems : Applications and Algorithms

We review and analyze nonlinear programming approaches to model-ing and solving certain flow problems in telecommunications, trans-portation and supply chain management. We emphasize the commonaspects of telecommunications and road networks, and indicate the im-portance of game theoretic and equilibrium approaches. Algorithmsbased on the Frank-Wolfe method are developed in depth and theirimplementations on sequential and parallel machines are discussed andevaluated for large-scale real-world networks. Several research direc-tions are also stated.SUMMER COURSE ON OPERATIONAL RESEARCH AND APPLICATIONS, May 15-18, 2013LABORATORY OF ALGORITHMS AND TECHNOLOGIES FOR NETWORK ANALYSIS (LATNA)HIGHER SCOOL OF ECONOMICS (HSE)NATIONAL RESEARCH UNIVERSITYNizhny Novgorod, Russian Federationhttp://nnov.hse.ru/en/latna/conferences/school2013Upprättat; 2013; 20150306 (athmig

Open problems in optimization and data analysis

Computational and theoretical open problems in optimization, computational geometry, data science, logistics, statistics, supply chain modeling, and data analysis are examined in this book. Each contribution provides the fundamentals needed to fully comprehend the impact of individual problems. Current theoretical, algorithmic, and practical methods used to circumvent each problem are provided to stimulate a new effort towards innovative and efficient solutions. Aimed towards graduate students and researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, this book provides a broad comprehensive approach to understanding the significance of specific challenging or open problems within each discipline. The contributions contained in this book are based on lectures focused on “Challenges and Open Problems in Optimization and Data Science” presented at the Deucalion Summer Institute for Advanced Studies in Optimization, Mathematics, and Data Science in August 2016.

Discrete compettitive facility location : Modelling and optimization approaches

Competitive facility location problems are concerned with thefollowing situation: a firm wants to locate a predefined num-ber of facilities to serve customers locate in some region wherethere already exist (or will be) other firms offering the sameservice. Both new and existing firms compete for optimizingtheir market share of profit. A discrete version of such problemsarises when it is assumed that there is a ( rather small ) finitenumber of candidate locations and the markets consist of pointdemands. We review modelling and optimization approaches forthis type of problems and we emphasize and develop the bi-levelprogramming methodology.Godkänd; 2014; 20141124 (athmig