We show that the simplex method with Dantzig's pivoting rule may require an exponential number of iterations over two highly degenerate instances. The feasible region of the first instance is a full dimensional simplex, and a single point for the second one. In addition, the entries of the constraint matrix, the right-hand-side vector, and the cost vector are {0,1,2}-valued. Those instances, with few vertices and small input data length, illustrate the impact of degeneracy on simplex methods.

This paper deals with the ratio of the distances to the first and second nearest facilities. The ratio represents the reliability of facility location when the nearest facility is closed and customers are serviced by the second nearest facility. The distribution of the ratio is derived for grid and random patterns of facilities. Distance is measured as the Euclidean and rectilinear distances. The distribution shows how the ratio is distributed in a study region, and will supply building blocks for facility location models with closing of facilities. The distribution of the ratio of the road network distances is also calculated for actual facility location.

A Latin square is a complete assignment of [n]={1,...,n} to an n × n grid such that, in each row and in each column, each value in [n] appears exactly once. A symmetric Latin square (SLS) is a Latin square that is symmetric in the matrix sense. In what we call the constrained SLS construction (CSLSC) problem, we are given a subset F of [n]³ and are asked to construct an SLS so that, whenever (i,j,k)∈ F, the symbol k is not assigned to the cell (i,j). This paper has two contributions for this problem. One is proposal of an efficient local search algorithm for the maximization version of the problem. The maximization problem asks to fill as many cells with symbols as possible under the constraint on F. In our local search, the neighborhood is defined by p-swap, i.e., dropping exactly p symbols and then assigning any number of symbols to empty cells. For p∈{1,2}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^p+1) time. The other contribution is to show its practical value for the CSLSC problem. For randomly generated instances, our iterated local search algorithm frequently constructs a larger partial SLS than state-of-the-art solvers such as IBM ILOG CPLEX, LocalSolver and WCSP.

This paper proposes an approach to estimate an optimal software rejuvenation schedule minimizing an expected total software cost per unit time. Based on a non-parametric predictive inference (NPI) approach, we derive the upper and lower bounds of the predictive expected software cost via the predictive survival function from system failure time data, and characterize an adaptive cost-based software rejuvenation policy, from the system failure time data with a right-censored observation. In simulation experiments, it is shown that our NPI-based approach is quite useful to predict the optimal software rejuvenation time.

We consider a multiagent network model consisting of nodes and edges as cities and their links to neighbors, respectively. Each network node has an agent and priced goods and the agent can buy or sell goods in the neighborhood. Though every node may not have an equal price, we show the prices will reach an equilibrium by iterating buy and sell operations. First, we present a protocol model in which each buying agent makes a bid to the lowest priced goods in the neighborhood; and each selling agent selects the highest bid, if any. Second, we derive a sufficient condition which stabilizes price in our model. We also show the equilibrium price can be derived from the total funds and the total goods for any network. This is a special case of the Fisher's quantity equation, thus we can confirm the correctness of our model. We then examine the best bidding strategy is available to our protocol. Third, we analyze stabilization time for path and cycle networks. Finally, we perform simulation experiments for estimating the stabilization time, the number of bidders and the effects of spreading funds. Our model is suitable for investigating the effects of network topologies on price stabilization.