Using Rejection Methods in a DSS for Production Strategies

In this paper we face the problem arising in an enterprise that must decide whether and when scheduling production orders in order to maximize the production efficiency. In particular we developed an on-line scheduling algorithm able to manage such decisions. Computational results are provided to show the performance of the algorithm

An approximation result for a periodic allocation problem

AbstractIn this paper we study a periodic allocation problem which is a generalization of the dynamic storage allocation problem to the case in which the arrival and departure time of each item is periodically repeated. These problems are equivalent to the interval coloring problem on weighted graphs in which each feasible solution corresponds to an acyclic orientation, and the solution value is equal to the length of the longest weighted path of the oriented graph. Optimal solutions correspond to acyclic orientations having the length of longest weighted path as small as possible. We prove that for the interval coloring problem on a class of circular arc graphs, and hence for a periodic allocation problem, there exists an approximation algorithm that finds a feasible solution whose value is at most two times the optimal

An approximation result for a duo-processor task scheduling problem

We consider the problem of scheduling tasks on a set of dedicated processors, where each task requires a subset of two processors be simultaneously available for a given processing time. The objective is to determine a nonpreemptive schedule with minimum completion time. By means of a graph theoretical formulation, we show that instances with up to 4 processors can be solved in polynomial time. With m = 2s + 1 processors (for s = 2, 3,...) and a minimum of m task types, we prove that the problem is NP-hard. Moreover, for this class of NP-hard instances, a simple O(m) approximation algorithm, whose performance ratio is bounded by 3s/(2s + 1), is given. The bound is shown to be tight

An approximation result for a duo-processor task scheduling problem

We consider the problem of scheduling tasks on a set of dedicated processors, where each task requires a subset of two processors be simultaneously available for a given processing time. The objective is to determine a nonpreemptive schedule with minimum completion time. By means of a graph theoretical formulation, we show that instances with up to 4 processors can be solved in polynomial time. With m = 2s + 1 processors (for s = 2, 3,...) and a minimum of m task types, we prove that the problem is NP-hard. Moreover, for this class of NP-hard instances, a simple O(m) approximation algorithm, whose performance ratio is bounded by 3s/(2s + 1), is given. The bound is shown to be tight