We consider a certain T period aggregate production planning model, where the two sources of production are regular and overtime. The model allows for time varying production, holding and backordering costs and includ...
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We consider a certain T period aggregate production planning model, where the two sources of production are regular and overtime. The model allows for time varying production, holding and backordering costs and includes bounds on inventory and backorders. We show that the problem has a rather interesting network structure and exploit this structure to develop a greedy algorithm to solve the problem. The procedure is easy to implement and has a computational complexity of O(T2). We report computational experience with the greedy procedure and demonstrate its superiority to a well known network simplex code, GNET, implemented on the classical network formulation of the problem. [ABSTRACT FROM AUTHOR]
The augmenting chain technique has been applied to solve the maximum stable set problem in the class of line graphs (which coincides with the maximum matching problem) and then has been extended to the class of claw-f...
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The augmenting chain technique has been applied to solve the maximum stable set problem in the class of line graphs (which coincides with the maximum matching problem) and then has been extended to the class of claw-free graphs. In the present paper, we propose a further generalization of this approach. Specifically, we show how to find an augmenting chain in graphs containing no skew star, i.e. a tree with exactly three vertices of degree 1 of distances 1, 2, 3 from the only vertex of degree 3. As a corollary. we prove that the maximum stable set problem is polynomially solvable in a class that strictly contains claw-free graphs, improving several existing results. (C) 2005 Elsevier Inc. All rights reserved.
We consider a P model version of stochastic spanning tree problems with random edge costs. Parameters of underling probability distribution of edge costs are unknown, and so they are estimated by a confidence region f...
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We consider a P model version of stochastic spanning tree problems with random edge costs. Parameters of underling probability distribution of edge costs are unknown, and so they are estimated by a confidence region from statistical data. The problem is first transformed into a deterministic equivalent problem with a minimax type objective function and a confidence region of means and variances, since we assume normal distributions with respect to random edge costs. Our model reflects the situation that the maximum possible damage due to an unknown parameter should be minimized. We show the problem can be reduced to the deterministic equivalent problem of another stochastic spanning tree problem, which is already investigated by us. Thus, we can find an optimal spanning tree of the original problem very efficiently by this reduction.
The stable set problem is to find in a simple graph a maximum subset of pairwise non-adjacent vertices. The problem is known to be NP-hard in general and can be solved in polynomial time on some special classes, like ...
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The stable set problem is to find in a simple graph a maximum subset of pairwise non-adjacent vertices. The problem is known to be NP-hard in general and can be solved in polynomial time on some special classes, like cographs or claw-free graphs. Usually, efficient algorithms assume membership of a given graph in a special class. Robust algorithms apply to any graph G and either solve the problem for G or find in it special forbidden configurations. In the present paper we describe several efficient robust algorithms, extending some known results.
For the nonpreemptive two machine job-shop scheduling problem with a fixed number of jobs and objective functions Sigma f(i) and max f(i), where f(i) are nondecreasing functions of the finish times of jobs i, polynomi...
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For the nonpreemptive two machine job-shop scheduling problem with a fixed number of jobs and objective functions Sigma f(i) and max f(i), where f(i) are nondecreasing functions of the finish times of jobs i, polynomial algorithms are presented. This answers previous open questions about the complexity status of the corresponding problems with objective functions L(max), Sigma w(i) U-i, and Sigma w(i) T-i. We generalize these results by showing that the problem with any regular criterion can be solved in polynomial time.
This paper deals with the deterministic single-item procurement planning problem with batch ordering under the buyback contract. We assume a buyback contract with returns of unused products at the end of each period t...
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Suppose that n independent tasks are to be scheduled without preemption on an unlimited number of parallel machines of two types: inexpensive slow machines and expensive fast machines. Each task requires a given proce...
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Suppose that n independent tasks are to be scheduled without preemption on an unlimited number of parallel machines of two types: inexpensive slow machines and expensive fast machines. Each task requires a given processing time on a slow machine or a given smaller processing time on a fast machine. We make two different feasibility assumptions: (a) each task has a specified processing interval, the length of which is equal to the processing time on a slow machine; (b) each task has a specified starting time. For either problem type, we wish to find a feasible schedule of minimum total machine cost. It is shown that both problems are NP-hard in the strong sense. These results are complemented by polynomial algorithms for some special cases.
In this paper, we propose a new large-update primal-dual interior point algorithm for P-* complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, ...
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In this paper, we propose a new large-update primal-dual interior point algorithm for P-* complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, the new method is based on a class of kernel functions psi(t) = (t(p+1) - 1)/(p + 1) + (t(-q) - 1)/q, p is an element of [0, 1], q > 0. We show that if a strictly feasible starting point is available and the undertaken problem satisfies some conditions, then the new large-update primal-dual interior point algorithm for P-* CPs has O((1 + 2k) root n log n log (n mu(0)/epsilon)) iteration complexity which is currently the best known result for such methods with p = 1 and q = (log n)/2 - 1. (C) 2011 Elsevier B.V. All rights reserved.
We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled ...
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We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled leading to systems of two non-linear equations with two unknowns. In this way we avoid the classical iterative approaches. A simple complexity analysis reveals that the algorithm requires O(s log s) steps, where s is the number of states of the game. The classical Pig and the Piglet (a simple variant of the Pig played with a coin) are examined in detail.
We consider the 1-median problem with euclidean distances with uncertainty in the weights, expressed as possible changes within given bounds and a single budget constraint on the total cost of change. The upgrading (r...
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We consider the 1-median problem with euclidean distances with uncertainty in the weights, expressed as possible changes within given bounds and a single budget constraint on the total cost of change. The upgrading (resp. downgrading) problem consists of minimizing (resp. maximizing) the optimal 1-median objective value over these weight changes. The upgrading problem is shown to belong to the family of continuous single facility location-allocation problems, whereas the downgrading problem reduces to a convex but highly non-differentiable optimization problem. Several structural properties of the optimal solution are proven for both problems, using novel planar partitions, the knapsack Voronoi diagrams, and lead to polynomial time solution algorithms.
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