We study three optimization problems in which non-renewable resources are used to execute tasks in parallel. Problems differentiate by the assumptions of whether a resource can be shared between several tasks or not, ...
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We study three optimization problems in which non-renewable resources are used to execute tasks in parallel. Problems differentiate by the assumptions of whether a resource can be shared between several tasks or not, or whether resource sharing between the tasks is limited. We present very efficient solution procedures for two of these problems and prove that the third problem is NP-hard in the strong sense and that it can be solved efficiently for special cases. Applications include optimal resource allocation problems in labor-intensive cellular manufacturing and in parallel task computing.
The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown ...
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The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources. (C) 2009 Elsevier B.V. All rights reserved.
The SPERT problem was defined, in a game theory framework, as the fair allocation of the slack or float among the activities in a PERT network previous to the execution of the project. Previous approaches tackle with ...
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The SPERT problem was defined, in a game theory framework, as the fair allocation of the slack or float among the activities in a PERT network previous to the execution of the project. Previous approaches tackle with this problem imposing that the durations of the activities are deterministic. In this paper, we extend the SPERT problem into a stochastic framework defining a new solution that tries also to maintain the good performance of some other approaches that have been defined for the deterministic case. Afterward, we present a polynomial algorithm for this new solution that also could be used for the calculation of other approaches founded in the deterministic SPERT literature.
This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) levels. The objective is to minimize the cycle time or, equivalently, to maximize the throughput, under the condition that...
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This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) levels. The objective is to minimize the cycle time or, equivalently, to maximize the throughput, under the condition that the WIP level is bounded from above by a given integer number. We present several strongly polynomial algorithms for the 2-cyclic robotic flowshop scheduling problems for various WIP levels. (C) 2010 Wiley Periodicals, Inc. Naval Research Logistics 58: 1-16, 2011
Suppose that in a coalition formation game each participant has a preference list of the other participants and she prefers a set S to a set T if and only if she prefers the worst participant of S to the worst partici...
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Suppose that in a coalition formation game each participant has a preference list of the other participants and she prefers a set S to a set T if and only if she prefers the worst participant of S to the worst participant of T. We consider three definitions of stability. In the case of no indifferences stable partitions cannot contain very large sets and their existence can be decided polynomially. However, in the presence of ties one of the existence problems is NP-complete, the other is polynomial and the existence of a polynomial algorithm for the third one is still open. (C) 2003 Elsevier B.V. All rights reserved.
This paper discusses self-concordant functions on smooth manifolds. In Euclidean space, such functions are utilized extensively as barrier functions in interior-point methods for polynomial time optimization algorithm...
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This paper discusses self-concordant functions on smooth manifolds. In Euclidean space, such functions are utilized extensively as barrier functions in interior-point methods for polynomial time optimization algorithms. Here, the self-concordant function is carefully defined on a differential manifold in such a way that the properties of self-concordant functions in Euclidean space are preserved. A Newton decrement is defined and analyzed for this class of functions. Based on this, a damped Newton algorithm is proposed for the optimization of self-concordant functions. Under reasonable technical assumptions such as geodesic completeness of the manifold, this algorithm is guaranteed to fall in any given small neighborhood of the optimal solution in a finite number of steps. The existence and uniqueness of the optimal solution is also proved in this paper. Hence, the optimal solution is a global one. Furthermore, it ensures a quadratic convergence within a neighborhood of the minimal point. This neighborhood can be specified in terms of the Newton decrement. The computational complexity bound of the proposed approach is also given explicitly. This complexity bound is shown to be of the order O(- In(epsilon)), where epsilon is the desired precision. Some interesting optimization problems are given to illustrate the proposed concept and algorithm.
A graph is point determining if distinct vertices have distinct neighbourhoods. A realization of a point. determining graph H is a point determining graph G such that each vertex-removed subgraph G - x which is point ...
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A graph is point determining if distinct vertices have distinct neighbourhoods. A realization of a point. determining graph H is a point determining graph G such that each vertex-removed subgraph G - x which is point determining, is isomorphic to H. We study the fine structure of point determining graphs, and conclude that every point determining graph has at most two realizations. A full homomorphism of a graph G to a graph H is a vertex mapping f such that for distinct vertices u and v of G, we have u v an edge of G if and only if f (u)f (v) is an edge of H. For a fixed graph H, a full H-colouring of G is a full homomorphism of G to H. A minimal H-obstruction is a graph G which does not admit a full H-colouring, such that each proper induced subgraph of G admits a full H-colouring. We analyse minimal H-obstructions using our results on point determining graphs. We connect the two problems by proving that if H has k vertices, then a graph with k + I vertices is a minimal H-obstruction if and only if it is a realization of H. We conclude that every minimal H-obstruction has at most k + I vertices, and there are at most two minimal H-obstructions with k + I vertices. We also consider full homomorphisms to graphs H in which loops are allowed. If H has f loops and k vertices without loops, then every minimal H-obstruction has at most (k + 1)(e + 1) vertices, and, when both k and e are positive, there is at most one minimal H-obstruction with (k + 1)(f + 1) vertices. In particular, this yields a finite forbidden subgraph characterization of full H-colourability, for any graph H with loops allowed. (c) 2007 Elsevier B.V. All rights reserved.
Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C-1, ... , C-k} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The w...
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Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C-1, ... , C-k} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C-i vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.
A no-wait robotic cell is an automated flow shop in which a robot is used to move the parts from a machine to the next. Parts are not allowed to wait. We analyze the complexity of the part sequencing problem in a robo...
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A no-wait robotic cell is an automated flow shop in which a robot is used to move the parts from a machine to the next. Parts are not allowed to wait. We analyze the complexity of the part sequencing problem in a robotic cell with three machines, for different periodical patterns of robot moves, when the objective is productivity maximization. (C) 2000 Elsevier Science B.V. All rights reserved.
We present a sequential dual-simplex algorithm for the linear problem which has the same complexity as the algorithms of Balinski [3,4] and Goldfarb [8]: O( n 2 ) pivots, O( n 2 log n + nm ) time. Our algorithm works ...
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We present a sequential dual-simplex algorithm for the linear problem which has the same complexity as the algorithms of Balinski [3,4] and Goldfarb [8]: O( n 2 ) pivots, O( n 2 log n + nm ) time. Our algorithm works with the (dual) strongly feasible trees and can handle rectangular systems quite naturally.
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