Let us denote a⊕ b=max(a; b) and a⊗ b= a+ b for a; b∈R=R ∪ {−∞} and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n(m + n log n)) algorithm for 8nding all essential terms of the max-algebraic characteristic polynomial of an n × n matrix over R with m 8nite elements. In the cases when all terms are essential, this algorithm also solv...

The referee assignment problem in sports scheduling is addressed for the First Division of the Chilean professional football league using integer linear programming. Various criteria that enhance the transparency and objectivity of the assignment process are considered. As well as better balances in the number of matches each referee must officiate, the frequency each is assigned to a given tea...

We present a review of the various integer linear programming (ILP) formulations that have been proposed for the routing and wavelength assignment problem in WDM optical networks with a unified and simplified notation under asymmetrical assumptions on the traffic. We show that all formulations proposed under asymmetrical traffic assumptions, both link and path formulations, are equivalent in te...

The design of state observer for a linear discrete or continuous time uncertain system based on circularly regional pole assignment is studied. Taking use of algebraic Riccati equations and linear matrix inequalities, necessary and sufficient conditions for the existence of the state observer based on circularly regional pole assignment is proposed and the formulation of the gain matrix of the ...

The linear bottleneck assignment problem (LBAP), which is a variation of the classical assignment problem, seeks to minimize the longest completion time rather than the sum of the completion times when a number of jobs are to be assigned to the same number of workers. If the completion times are not certain, then it is said to be a fuzzy LBAP. Here we propose a new algorithm to solve fuzzy LBAP...

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...

In many applications it is necessary to find a minimum weight assignment that satisfies one or several additional resource constraints. For example, consider the problem of assigning persons to jobs where each assignment utilizes at least two scarce resources and the resource utilization is dependent on the person and the type of task. A practical situation where the above might occur is a slau...

We present a polynomial time improvement of the linear channel pin assignment LCPA algorithms presented by Cai and Wong in 1990. We solve the LCPA problem according to minimum channel density under a special priority schedule subject to vertical constraints and ux. The priority driven linear channel pin assignment algorithm (PDCPA) reduces the channel height by an average of 17 % without increa...

We study the tradeoff between efficiency and service quality in tandem systems. We reward efficiency by assuming that a revenue is earned each time a job is completed, and we penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, genera...

Analysis of random instances of optimization problems is instrumental for understanding of the behavior and properties of problem’s solutions, feasible region, optimal values, especially in large-scale cases. A class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems, and many important problems ...