We are given a set of points pl,...,p. and a symmetric distance matrix (o!ij) giving the distance between pi and pj. We wish to construct a tour that minimizes ~~=1 1(z), where l(i) is

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In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways. 180 In this paper, we consider the problem of scheduling

In this paper, we give a 9.28-approximation algorithm for the minimum latency problem that uses only O(n log n) calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson. A previous algorithm of Goemans and Kleinberg for the minimum latency problem requires an approximation algorithm for the k-MST problem which is called as a black box. Their algorithm can achieve a performance guarantee of 10.77 while making O(n PCST calls (via a k-MST algorithm of Garg), or a performance guarantee of 7.18+ # while using n O(1/#) PCST calls (via a k-MST algorithm of Arora and Karakostas). In order to match our approximation ratio (i.e. setting # = 2.10), the latter version requires n) PCST calls, so our running time bound is faster by a factor of #(n log n). Since PCST can be implemented to run in O(n ) time, the overall running time of our algorithm is O(n log n).

Abstract We give a 7.18-approximation algorithm for the minimum latency problem that uses only O(n log n) calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson.This improves the previous best algorithms in both performance guarantee and running time. A previous algorithm of Goemans and Kleinberg for the minimum latency problem requires anapproximation algorithm for the k-MST problem which is called as a black box for each valueof k. Their algorithm can achieve a performance guarantee of 10.77 while making O(n2 log n)PCST calls (via a k-MST algorithm of Garg), or a performance guarantee of 7.18 + ffl while using nO(1/ffl) PCST calls (via a k-MST algorithm of Arora and Karakostas). In all cases, the runningtime is dominated by the PCST calls. Since the PCST subroutine can be implemented to run in O(n2) time, the overall running time of our algorithm is O(n3 log n).The basic idea for our improvement is that we do not treat the k-MST algorithm as ablack box. This allows us to take advantage of some special situations in which the PCST

this paper, we discuss, from a practical point of view, the e#ectiveness of applying reusable metaheuristics software components to the continuous flow-shop scheduling problem. This includes analyzing the knowledge and e#orts needed to adapt the metaheuristics and analyzing by experiments the trade-o# between running time and solution quality. Our goal is to gain general insights in the e#ectiveness of applying di#erent types of metaheuristics with respect to di#erent demands for solution quality and di#erent amounts of available resources such as knowledge about algorithms, implementation e#orts and running time. In Section 2, we first describe the continuous flow-shop scheduling problem. Then, in Sections 3 and 4, we review di#erent kinds of construction methods and metaheuristics. The implementation is briefly discussed in Section 5. In Section 6, we provide and discuss extensive computational results. Finally, we draw some conclusions and give directions for future research

We give improved approximation algorithms for a variety of latency minimization problems. In particular, we give a 3.59 1-approximation to the minimum latency problem, improving on previous algorithms by a multiplicative factor of 2. Our techniques also give similar improvements for related problems like k-traveling repairmen and its multiple depot variant. We also observe that standard techniques can be used to speed up the previous and this algorithm by a factor of Õ(n). 1

We propose a mixed integer programming formulation for the delivery man problem and derive additional classes of valid inequalities. Computational results are presented for instances of the delivery man problem with time windows. In particular, the quality of the lower bounds obtained from the linear programming relaxation and the effectiveness of the additional inequalities in improving these bounds are studied. 1 Introduction In this paper we study the delivery man problem (DMP) from a polyhedral point of view. This problem is a variant of the well-known traveling salesman problem (TSP) in which the objective is to find a tour starting from a given depot that minimizes the sum of the waiting times of the customers. The DMP can also be interpreted as a single-machine scheduling problem with sequence-dependent processing times in which the total flow time of the jobs has to be minimized. Polyhedral methods have been proven to be very successful for the TSP and many of its extensions. ...

Given a complete directed graph G = (V, E), the traveling repairman problem consists of determining a Hamiltonian circuit minimizing the sum of the waiting times of customers located at the nodes of the graph. In this paper, we propose two new linear integer formulations for TRP and computationally evaluate the strength of their linear programming relaxations. Computational results show the efficiency of the second new formulation considering the LP relaxations gaps and CPU times. The larger instance solved to optimality with the proposed second formulation involves 29 vertices. This compares favorably with a previously published formulation.