Search results for "Integer"
showing 10 items of 250 documents
The multiple vehicle pickup and delivery problem with LIFO constraints
2015
Abstract This paper approaches a pickup and delivery problem with multiple vehicles in which LIFO conditions are imposed when performing loading and unloading operations and the route durations cannot exceed a given limit. We propose two mixed integer formulations of this problem and a heuristic procedure that uses tabu search in a multi-start framework. The first formulation is a compact one, that is, the number of variables and constraints is polynomial in the number of requests, while the second one contains an exponential number of constraints and is used as the basis of a branch-and-cut algorithm. The performances of the proposed solution methods are evaluated through an extensive comp…
Feasibility of finite and infinite paths in data dependent programs
2005
This paper considers the feasibility of finite and infinite paths in programs in two simple programming languages. The language LBASE allows to express the dependencies of real time systems on integer data, the language LTIM can model quantitative timing constraints in r.t.s. specifications. It is proven that the problem of whether a given LBASE or LTIM program has an infinite feasible path (i.e. whether it can exhibit an infinite behaviour) is decidable. The possibilities to characterise the sets of all feasible finite and infinite paths in LBASE and LTIM programs are also discussed. The infinite feasible path existence problem is proven decidable also for the language LTIBA which has both…
Partially Renewable Resources
2014
In recent years, in the field of project scheduling the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this chapter we define this type of resource, describe an integer linear formulation and present some examples of conditions appearing in real problems which can be modeled using partially renewable resources. Then we introduce some preprocessing procedures to identify infe…
A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem
2015
Abstract In the Synchronized Pickup and Delivery Problem (SPDP), user-specified transportation requests from origin to destination points have to be serviced by a fleet of homogeneous vehicles. The task is to find a set of minimum-cost routes satisfying pairing and precedence, capacities, and time windows. Additionally, temporal synchronization constraints couple the service times at the pickup and delivery locations of the customer requests in the following way: a request has to be delivered within prespecified minimum and maximum time lags (called ride times) after it has been picked up. The presence of these ride-time constraints severely complicates the subproblem of the natural column-…
Integer Preemption Problems
2014
A fundamental assumption in the basic RCPSP is that activities in progress are non-preemptable. Some papers reveal the potential benefits of allowing activity interruptions in the schedule when the objective is the makespan minimization. In this chapter we consider the Maxnint_PRCPSP in which it is assumed that activities can be interrupted at any integer time instant with no cost incurred, that each activity can be split into a maximum number of parts, and that each part has a minimum duration established. We show how some procedures developed for the RCPSP can be adapted to work with the Maxnint_PRCPSP and we introduce some procedures specifically designed for this problem. Furthermore, p…
Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem
2012
This paper presents the first full-fledged branch-and-price (bap) algorithm for the capacitated arc-routing problem (CARP). Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent symmetry, dense underlying networks, or a formulation where edge flows in a potential solution do not allow the reconstruction of unique CARP tours. The proposed algorithm circumvents all these drawbacks by taking the beneficial ingredients from existing CARP methods and combining them in a new way. The first step is the solution of the one-index formulation of the CARP in order to produce strong cut…
Counting and equidistribution in Heisenberg groups
2014
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for …
Coprime actions and correspondences of Brauer characters
2017
We prove several results giving substantial evidence in support of the conjectural existence of a Glauberman–Isaacs bijection for Brauer characters under a coprime action. We also discuss related bijections for the McKay conjecture.
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz
2003
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…
Drivetrain design optimization for electrically actuated systems via mixed integer programing
2015
The proposed paper presents a method to optimally select components of a drivetrain for an electrically actuated machine. A simple mathematical model of the machine is established and inequality constraints which determine the choice of drivetrain components are formulated. Elements to be picked (namely, a motor, a gearbox, and a drive) are taken from a discrete set of data provided in the catalogs of industrial motors and drives manufacturers. By solving an optimization problem, a combination of components which both satisfy design requirements and minimize the total drivetrain cost is selected. The operation of the selected drivetrain is verified against the motor loadability curves. In a…