15 research outputs found
Throughput Rate Optimization in High Multiplicity Sequencing Problems
Mixed model assembly systems assemble products (parts) of differenttypes in certain prespecified quantities. A minimal part set is a smallestpossible set of product type quantities, to be called the multiplicities,in which the numbers of assembled products of the various types are inthe desired ratios. It is common practice to repeatedly assemble minimalpart sets, and in such a way that the products of each of the minimalpart sets are assembled in the same sequence. Little is known howeverregarding the resulting throughput rate, in particular in comparison to thethroughput rates attainable by other input strategies. This paper investigatesthroughput and balancing issues in repetitive manufacturing environments.It considers sequencing problems that occur in this setting andhow the repetition strategy influences throughput. We model the problemsas a generalization of the traveling salesman problem and derive ourresults in this general setting. Our analysis uses well known concepts fromscheduling theory and combinatorial optimization.Economics ;
Many-visits vehicle routing problems
We consider constrained routing problems where each city is to be visited possibly many times. Two algorithms are given having complexities which are exponentials in the number of cities, but not i the number of visits. I addition, a critria is proposed for classifying algorithms for general many-visits routhing/scheduling problems.Consideramos problemas de roteamento com restrições, onde cada cidade deve ser visitada, possivelmente, várias vezes. Descrevemos dois algoritmos cujas complexidades são expressões exponenciais no número de cidades, porém não no número de visitas. Além disso, propomos um critério de classificação de algoritmos para problemas gerais de scheduling/roteamento com múltiplas visitas
The Minimum Backlog Problem
We study the minimum backlog problem (MBP). This online problem arises, e.g.,
in the context of sensor networks. We focus on two main variants of MBP.
The discrete MBP is a 2-person game played on a graph . The player
is initially located at a vertex of the graph. In each time step, the adversary
pours a total of one unit of water into cups that are located on the vertices
of the graph, arbitrarily distributing the water among the cups. The player
then moves from her current vertex to an adjacent vertex and empties the cup at
that vertex. The player's objective is to minimize the backlog, i.e., the
maximum amount of water in any cup at any time.
The geometric MBP is a continuous-time version of the MBP: the cups are
points in the two-dimensional plane, the adversary pours water continuously at
a constant rate, and the player moves in the plane with unit speed. Again, the
player's objective is to minimize the backlog.
We show that the competitive ratio of any algorithm for the MBP has a lower
bound of , where is the diameter of the graph (for the discrete
MBP) or the diameter of the point set (for the geometric MBP). Therefore we
focus on determining a strategy for the player that guarantees a uniform upper
bound on the absolute value of the backlog.
For the absolute value of the backlog there is a trivial lower bound of
, and the deamortization analysis of Dietz and Sleator gives an
upper bound of for cups. Our main result is a tight upper
bound for the geometric MBP: we show that there is a strategy for the player
that guarantees a backlog of , independently of the number of cups.Comment: 1+16 pages, 3 figure
Maximum Scatter TSP in Doubling Metrics
We study the problem of finding a tour of points in which every edge is
long. More precisely, we wish to find a tour that visits every point exactly
once, maximizing the length of the shortest edge in the tour. The problem is
known as Maximum Scatter TSP, and was introduced by Arkin et al. (SODA 1997),
motivated by applications in manufacturing and medical imaging. Arkin et al.
gave a -approximation for the metric version of the problem and showed
that this is the best possible ratio achievable in polynomial time (assuming ). Arkin et al. raised the question of whether a better approximation
ratio can be obtained in the Euclidean plane.
We answer this question in the affirmative in a more general setting, by
giving a -approximation algorithm for -dimensional doubling
metrics, with running time , where . As a corollary we obtain (i) an
efficient polynomial-time approximation scheme (EPTAS) for all constant
dimensions , (ii) a polynomial-time approximation scheme (PTAS) for
dimension , for a sufficiently large constant , and (iii)
a PTAS for constant and . Furthermore, we
show the dependence on in our approximation scheme to be essentially
optimal, unless Satisfiability can be solved in subexponential time
Throughput rate optimization in high multiplicity sequencing problems
Mixed model assembly systems assemble products (parts) of different types in certain prespecified quantities. A minimal part set is a small-est possible set of product type quantities, to be called the multiplicities, in which the numbers of assembled products of the various types are in the desired ratios. It is common practice to repeatedly assemble minimal part sets, and in such a way that the products of each of the minimal part sets are assembled in the same sequence. Little is known however regarding the resulting throughput rate, in particular in comparison to the throughput rates attainable by other input strategies. This paper inves-tigates throughput and balancing issues in repetitive manufacturing envi-ronments. It considers sequencing problems that occur in this setting and how the repetition strategy influences throughput. We model the prob-lems as a generalization of the traveling salesman problem and derive our results in this general setting. Our analysis uses well known concepts from scheduling theory and combinatorial optimization