A branch-and-bound methodology within algebraic modelling systems

Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\sc Minto} is an example of a system which offers the possibility to incorporate user-provided directives (written in {\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical programming models. The aim of this paper is to present a branch-and-bound methodology for particular combinatorial structures to be embedded inside an algebraic modelling language. One advantage is the increased scope of application. Another advantage is that directives are more easily implemented at the modelling level than at the programming level

Coalitional Bargaining Equilibria

This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems.

Federal and State Regulation of Cable Television: An Analysis of the New FCC Rules

Denna uppsats behandlar projektering av ett småhus i form av framställande av system och konstruktionsritningar som följer Boverkets byggregler. Den innefattar även val av material för utvalda delar av småhuset där hänsyn tagits till väsentliga parametrar. För att framställa godkända ritningar har beräkningar utförts för att kunna bestämma tillräckliga dimensioner på ventilation, värme, sanitet och konstruktion. Slutligen har även en kostnadskalkyl utförts för att analysera totalkostnad och driftskostnader för småhuset. Detta är fördjupningsdelen i ett arbete som också innefattar projektering och dimensionering av ett småhus.

Classified Stable Matching

We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences over the other side. An institute classifies the applicants based on their research areas (or any other criterion), and, for each class, it sets a lower bound and an upper bound on the number of applicants it would hire in that class. The objective is to find a stable matching from which no group of participants has reason to deviate. Moreover, the matching should respect the upper/lower bounds of the classes. In the first part of the paper, we study classified stable matching problems whose classifications belong to a fixed set of ``order types.'' We show that if the set consists entirely of downward forests, there is a polynomial-time algorithm; otherwise, it is NP-complete to decide the existence of a stable matching. In the second part, we investigate the problem using a polyhedral approach. Suppose that all classifications are laminar families and there is no lower bound. We propose a set of linear inequalities to describe stable matching polytope and prove that it is integral. This integrality allows us to find various optimal stable matchings using Ellipsoid algorithm. A further ramification of our result is the description of the stable matching polytope for the many-to-many (unclassified) stable matching problem. This answers an open question posed by Sethuraman, Teo and Qian

Train-scheduling optimization model for railway networks with multiplatform stations

This paper focuses on optimizing the schedule of trains on railway networks composed of busy complex stations. A mathematical formulation of this problem is provided as a Mixed Integer Linear Program (MILP). However, the creation of an optimal new timetable is an NP-hard problem; therefore, the MILP can be solved for easy cases, computation time being impractical for more complex examples. In these cases, a heuristic approach is provided that makes use of genetic algorithms to find a good solution jointly with heuristic techniques to generate an initial population. The algorithm was applied to a number of problem instances producing feasible, though not optimal, solutions in several seconds on a laptop, and compared to other proposals. Some improvements are suggested to obtain better results and further improve computation time. Rail transport is recognized as a sustainable and energy-efficient means of transport. Moreover, each freight train can take a large number of trucks off the roads, making them safer. Studies in this field can help to make railways more attractive to travelers by reducing operative cost, and increasing the number of services and their punctuality. To improve the transit system and service, it is necessary to build optimal train scheduling. There is an interest from the industry in automating the scheduling process. Fast computerized train scheduling, moreover, can be used to explore the effects of alternative draft timetables, operating policies, station layouts, and random delays or failures.Postprint (published version