Search results for "Mathematical optimization"
showing 10 items of 1300 documents
On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach
2011
In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.
Impulsively-controlled systems and reverse dwell time: A linear programming approach
2015
We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for th…
A Branch-and-Cut method for the Capacitated Location-Routing Problem
2011
International audience; Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5–10 potential depots and 20–88 …
A computational study of LP-based heuristic algorithms for two-dimensional guillotine cutting stock problems
2002
In this paper we develop and compare several heuristic methods for solving the general two-dimensional cutting stock problem. We follow the Gilmore-Gomory column generation scheme in which at each iteration a new cutting pattern is obtained as the solution of a subproblem on one stock sheet. For solving this subproblem, in addition to classical dynamic programming, we have developed three heuristic procedures of increasing complexity, based on GRASP and Tabu Search techniques, producing solutions differing in quality and in time requirements. In order to obtain integer solutions from the fractional solutions of the Gilmore-Gomory process, we compare three rounding procedures, rounding up, t…
In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem
2015
Recently, Bode and Irnich [Bode C, Irnich S (2012) Cut-first branch-and-price-second for the capacitated arc-routing problem. Oper. Res. 60(5):1167–1182] presented a cut-first branch-and-price-second algorithm for solving the capacitated arc-routing problem (CARP). The fundamental difference to other approaches for exactly solving the CARP is that the entire algorithm works directly on the typically sparse underlying graph representing the street network. This enables the use of highly efficient dynamic programming-based pricing algorithms to solve the column-generation subproblem also known as the pricing problem. The contribution of this paper is the in-depth analysis of the CARP pricing…
The Capacitated Arc Routing Problem: Lower bounds
1992
In this paper, we consider the Capacitated Arc Routing Problem (CARP), in which a fleet of vehicles, based on a specified vertex (the depot) and with a known capacity Q, must service a subset of the edges of a graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity. New lower bounds are developed for this problem, producing at least as good results as the already existing ones. Three of the proposed lower bounds are obtained from the resolution of a minimum cost perfect matching problem. The fourth one takes into account the vehicle capacity and is computed using a dynamic programming algorithm. Computational results, in which these bounds…
Effective Handling of Dynamic Time Windows and Its Application to Solving the Dial-a-Ride Problem
2015
A dynamic time window relates to two operations that must be executed within a given time meaning that the difference between the points in time when the two operations are performed is bounded from above. The most prevalent context of dynamic time windows is when precedence is given for the two operations so that it is a priori specified that one operation must take place before the other. A prominent vehicle routing problem with dynamic time windows and precedence is the dial-a-ride problem (DARP), where user-specified transportation requests from origin to destination points must be serviced. The paper presents a new branch-and-cut-and-price solution approach for the DARP, the prototypi…
Discrete frequency models for inventory management – an introduction
2001
Abstract The paper deals with the problem of devising a periodic replenishment policy when orders must be periodic, but only a given, discrete set of order frequencies can be used. The multi-item, instantaneous replenishment case with known demand is studied. In particular, staggering policies somehow arranging replenishments not to come at the same time instants are considered. The paper is composed of three parts: first, a taxonomy of several versions of the discrete frequency problem is proposed, according to different elements; in the second part, a general mixed integer programming model is proposed which is able to capture the peculiarities of the whole spectrum of this kind of proble…
Solving multiobjective optimization problems with decision uncertainty: an interactive approach
2018
We propose an interactive approach to support a decision maker to find a most preferred robust solution to multiobjective optimization problems with decision uncertainty. A new robustness measure that is understandable for the decision maker is incorporated as an additional objective in the problem formulation. The proposed interactive approach utilizes elements of the synchronous NIMBUS method and is aimed at supporting the decision maker to consider the objective function values and the robustness of a solution simultaneously. In the interactive approach, we offer different alternatives for the decision maker to express her/his preferences related to the robustness of a solution. To conso…
A branch & bound algorithm for cutting and packing irregularly shaped pieces
2013
Abstract Cutting and packing problems involving irregular shapes, usually known as Nesting Problems, are common in industries ranging from clothing and footwear to furniture and shipbuilding. Research publications on these problems are relatively scarce compared with other cutting and packing problems with rectangular shapes, and are focused mostly on heuristic approaches. In this paper we make a systematic study of the problem and develop an exact Branch & Bound Algorithm. The initial existing mixed integer formulations are reviewed, tested and used as a starting point to develop a new and more efficient formulation. We also study several branching strategies, lower bounds and procedures f…