Search results for "integer programming"
showing 10 items of 69 documents
Min-max control of uncertain multi-inventory systems with multiplicative uncertainties
2001
In this note, we consider production-distribution systems with buffer and capacity constraints. For such systems, we assume that the model is not known exactly. More precisely, the entries of the matrix representing the system structure may be affine functions of some uncertain time-varying parameters that take values within assigned bounds. We give stabilizability conditions that can be checked, in principle, by solving a min-max problem on the surface of the state-space (buffer level space) unit ball. Then, we consider a special case in which each uncertain parameter affects a single column of the system matrix and is independent of all the other ones. In this case, we propose a mixed int…
An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows
2008
This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality init…
Perceived-Value-driven Optimization of Energy Consumption in Smart Homes
2020
Residential energy consumption has been rising rapidly during the last few decades. Several research efforts have been made to reduce residential energy consumption, including demand response and smart residential environments. However, recent research has shown that these approaches may actually cause an increase in the overall consumption, due to the complex psychological processes that occur when human users interact with these energy management systems. In this article, using an interdisciplinary approach, we introduce a perceived-value driven framework for energy management in smart residential environments that considers how users perceive values of different appliances and how the us…
A hierarchic approach to production planning and scheduling of a flexible manufacturing system
1999
Abstract The paper deals with the problem of improving the machine utilization of a flexible manufacturing cell. Limited tool magazine space of the machines turns out to be a relevant bottleneck. A hierarchic approach for this problem is proposed. At the upper level, sets of parts that can be concurrently processed (batches) are determined. At the lower levels, batches are sequenced, linked, and scheduled. Methods taken from the literature are used for the solution of the latter subproblems, and an original mixed integer programming model is formulated to determine batches. The proposed methods are discussed on the basis of computational experience carried out on real instances.
Optimal Usage of Multiple Network Connections
2008
In the future mobile networks, a mobile terminal is able to select the best suitable network for each data transmission. The selection of a network connection to be used has been under a lot of study. In this paper, we consider a more extensive case in which we do not select a network connection but use several network connections simultaneously to transfer data. When data is transferred using multiple network connections, a network connection has to be selected for each component of the data. We have modelled this problem as a multiobjective optimization problem and developed a heuristic to solve the problem fast in a static network environment. In this paper, we discuss solving the proble…
A branch-and-cut algorithm for the Orienteering Arc Routing Problem
2016
[EN] In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP),in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route.In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds…
Two-phase branch-and-cut for the mixed capacitated general routing problem
2015
The Mixed Capacitated General Routing Problem (MCGRP) is defined over a mixed graph, for which some vertices must be visited and some links must be traversed at least once. The problem consists of determining a set of least-cost vehicle routes that satisfy this requirement and respect the vehicle capacity. Few papers have been devoted to the MCGRP, in spite of interesting real-world applications, prevalent in school bus routing, mail delivery, and waste collection. This paper presents a new mathematical model for the MCGRP based on two-index variables. The approach proposed for the solution is a two-phase branch-and-cut algorithm, which uses an aggregate formulation to develop an effective …
Mixed integer optimal compensation: Decompositions and mean-field approximations
2012
Mixed integer optimal compensation deals with optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent s…
A branch and bound algorithm for the maximum diversity problem
2010
This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the MDP. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium-sized instances (with 50 elements) as well as some large-sized instances (with 100 elements). We compare our method with the best previous line…
Formulations for an inventory routing problem
2014
In this paper, we present and compare formulations for the inventory routing problem (IRP) where the demand of customers has to be served, over a discrete time horizon, by capacitated vehicles starting and ending their routes at a depot. The objective of the IRP is the minimization of the sum of inventory and transportation costs. The formulations include known and new mathematical programming formulations. Valid inequalities are also presented. The formulations are tested on a large set of benchmark instances. One of the most significant conclusions is that the formulations that use vehicle-indexed variables are superior to the more compact, aggregate formulations.