Traffic assignment optimization models

Optimalizace toku v síti je klasickou aplikací matematického programování. Tyto modely mají, mimo jiné, široké uplatnění také v logistice, kde se tak snažíme docílit optimálního rozdělení dopravy, např. vzhledem k maximalizaci zisku, či minimalizaci nákladů. Toto pojetí ovšem často problém idealizuje, poněvadž předpokládá existenci jediného rozhodovatele. Takový přístup je možný ve striktně organizovaných sítích jako např. v logistických sítích přepravních společností, železničních sítích či armádním zásobování. Úloha ''Traffic Assignment Problem'' (TAP) se zaměřuje na dopady teorie her na optimalizaci toku, tj. zkoumá vliv více rozhodovatelů na celkové využití sítě. V práci se zaobíráme úlohou TAP s působením náhodných vlivů, k čemuž využíváme metod stochastické a vícestupňové optimalizace. Dále zkoumáme možnosti zlepšení stávajícího využití sítě za rozhodnutí autoritativního rozhodovatele, kterému je umožněn zásah do samotné struktury sítě, k čemuž využíváme víceúrovňové programování.The class of network flow problems is one of the traditional applications of mathematical optimization. Such problems are widely applicable for example in logistics to achieve an optimal distribution of flow with respect to maximization of profit, or minimization of costs. This approach often leads to simplified models of real problems as it supposes the existence of only one decision maker. Such approach is possible in centralised networks, where an authority exists (such as railway network, military supply, or logistic network used by any company). The Traffic Assignment Problem (TAP) deals with impact of game theory to the network flow problem. Hence, we assume multiple decision makers, where each one of them wants to find his optimal behaviour. In this thesis, we focus on stochastic influences in TAP, for which we use methods of stochastic and multi-stage programming. Further, we concentrate on improvement options for the utilization of the system. Hereby, we consider possible actions of the master decision maker, and discuss them by the presence of multi-level mathematical programming.

Modeling and Analysis of Multicommodity Network Flows via Goal Programming

In this research we focused on the mobility system modeled by the AMC mobility planner\u27s calculator (AMPCALC). We developed AMPCALC as a user-friendly tool and allow the user to easily carry out strategic airlift, air refueling and aeromedical evacuation calculations that are covered in Air Force Pamphlet 10-1403. In this study, Excel software and its macro language, Visual Basic for Application, are our two main tools. In the methodology of the thesis we examined fundamental aspects of the mobility system in AMPCALC. We discussed formulation logic of the mobility cycle. We presented ramp use optimization and tanker optimization processes. We also conducted verification and validation of AMPCALC. Sensitivity analysis of the model includes a response surface study. To be able to investigate the main effects and interaction effects of the input factors on closure time, we performed a 26 factorial design. No linear relations are observed, but some relations between inputs and closure time are observed

New optimization models for empty container management

This thesis investigates the reasons why nowadays empty container repositioning represents a crucial issue for the shipping industry. Moreover, taking into account information collected through surveys and meetings with industrial experts, we provide a broad overview of current logistic practices for the management of empty containers in the context of international trade. We develop new optimization models in order to support shipping companies in dealing with empty container repositioning. We determine optimal repositioning plans within the time limits imposed by planning operations. Some optimization models have been tested on real data problems provided by a shipping company. These results show that it is possible to achieve significant savings in costs and times requested to determine repositioning plan

An annotated overview of dynamic network flows

The need for more realistic network models led to the development of the dynamic network flow theory. In dynamic flow models it takes time for the flow to pass an arc, the flow can be delayed at nodes, and the network parameters, e.g., the arc capacities, can change in time. Surprisingly perhaps, despite being closer to reality, dynamic flow models have been overshadowed by the classical, static model. This is largely due to the fact that while very efficient solution methods exist for static flow problems, dynamic flow problems have proved to be more difficult to solve. Our purpose with this overview is to compensate for this eclipse and introduce dynamic flows to the interested reader. To this end, we present the main flow problems that can appear in a dynamic network, and review the literature for existing results about them. Our approach is solution oriented, as opposed to dealing with modelling issues. We intend to provide a survey that can be a first step for readers wondering whether a given dynamic network flow problem has been solved or not. Besides restating the problems, we also describe the main proposed solution methods. An additional feature of this paper is an annotated list of the most important references about the subject

A Mathematical Model to Improve the Performance of Logistics Network

The role of logistics nowadays is expanding from just providing transportation and warehousing to offering total integrated logistics. To remain competitive in the global market environment, business enterprises need to improve their logistics operations performance. The improvement will be achieved when we can provide a comprehensive analysis and optimize its network performances. In this paper, a mixed integer linier model for optimizing logistics network performance is developed. It provides a single-product multi-period multi-facilities model, as well as the multi-product concept. The problem is modeled in form of a network flow problem with the main objective to minimize total logistics cost. The problem can be solved using commercial linear programming package like CPLEX or LINDO. Even in small case, the solver in Excel may also be used to solve such model

Learning to compare nodes in branch and bound with graph neural networks

En informatique, la résolution de problèmes NP-difficiles en un temps raisonnable est d’une grande importance : optimisation de la chaîne d’approvisionnement, planification, routage, alignement de séquences biologiques multiples, inference dans les modèles graphiques pro- babilistes, et même certains problèmes de cryptographie sont tous des examples de la classe NP-complet. En pratique, nous modélisons beaucoup d’entre eux comme un problème d’op- timisation en nombre entier, que nous résolvons à l’aide de la méthodologie séparation et évaluation. Un algorithme de ce style divise un espace de recherche pour l’explorer récursi- vement (séparation), et obtient des bornes d’optimalité en résolvant des relaxations linéaires sur les sous-espaces (évaluation). Pour spécifier un algorithme, il faut définir plusieurs pa- ramètres, tel que la manière d’explorer les espaces de recherche, de diviser une recherche l’espace une fois exploré, ou de renforcer les relaxations linéaires. Ces politiques peuvent influencer considérablement la performance de résolution. Ce travail se concentre sur une nouvelle manière de dériver politique de recherche, c’est à dire le choix du prochain sous-espace à séparer étant donné une partition en cours, en nous servant de l’apprentissage automatique profond. Premièrement, nous collectons des données résumant, sur une collection de problèmes donnés, quels sous-espaces contiennent l’optimum et quels ne le contiennent pas. En représentant ces sous-espaces sous forme de graphes bipartis qui capturent leurs caractéristiques, nous entraînons un réseau de neurones graphiques à déterminer la probabilité qu’un sous-espace contienne la solution optimale par apprentissage supervisé. Le choix d’un tel modèle est particulièrement utile car il peut s’adapter à des problèmes de différente taille sans modifications. Nous montrons que notre approche bat celle de nos concurrents, consistant à des modèles d’apprentissage automatique plus simples entraînés à partir des statistiques du solveur, ainsi que la politique par défaut de SCIP, un solveur open-source compétitif, sur trois familles NP-dures: des problèmes de recherche de stables de taille maximum, de flots de réseau multicommodité à charge fixe, et de satisfiabilité maximum.In computer science, solving NP-hard problems in a reasonable time is of great importance, such as in supply chain optimization, scheduling, routing, multiple biological sequence align- ment, inference in probabilistic graphical models, and even some problems in cryptography. In practice, we model many of them as a mixed integer linear optimization problem, which we solve using the branch and bound framework. An algorithm of this style divides a search space to explore it recursively (branch) and obtains optimality bounds by solving linear relaxations in such sub-spaces (bound). To specify an algorithm, one must set several pa- rameters, such as how to explore search spaces, how to divide a search space once it has been explored, or how to tighten these linear relaxations. These policies can significantly influence resolution performance. This work focuses on a novel method for deriving a search policy, that is, a rule for select- ing the next sub-space to explore given a current partitioning, using deep machine learning. First, we collect data summarizing which subspaces contain the optimum, and which do not. By representing these sub-spaces as bipartite graphs encoding their characteristics, we train a graph neural network to determine the probability that a subspace contains the optimal so- lution by supervised learning. The choice of such design is particularly useful as the machine learning model can automatically adapt to problems of different sizes without modifications. We show that our approach beats the one of our competitors, consisting of simpler machine learning models trained from solver statistics, as well as the default policy of SCIP, a state- of-the-art open-source solver, on three NP-hard benchmarks: generalized independent set, fixed-charge multicommodity network flow, and maximum satisfiability problems