An optimal sequential procedure for a multiple selling problem with independent observations

We consider a sequential problem of selling K identical assets over the finite time horizon with a fixed number of offers per time period and no recall of past offers. The objective is to find an optimal sequential procedure which maximizes the total expected revenue. In this paper, we derive an effective number of stoppings for an optimal sequential procedure for the selling problem with independent observations.     

Maximum flow problem in wireless ad hoc networks with directional antennas

Directional antenna offers a variety of benefits for wireless networks, one of which is the increased spatial reuse ratio. This feature gives rise to the improved throughput in resource limited wireless ad hoc networks. In this paper, we formulate the maximum flow problem as an optimization problem in wireless ad hoc networks with switched beam directional antennas constrained by interference. We demonstrate how to solve this optimization problem. It turns out that the proposed method works for both single beam antenna and multi-beam antenna, with minor variation of the constraints.     

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.     

A discrete long-term location–price problem under the assumption of discriminatory pricing: Formulations and parametric analysis

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.     

Global optimization of a nonconvex single facility location problem by sequential unconstrained convex minimization

The problem of maximizing the sum of certain composite functions, where each term is the composition of a convex decreasing function, bounded from below, with a convex function having compact level sets arises in certain single facility location problems with gauge distance functions. We show that this problem is equivalent to a convex maximization problem over a compact convex set and develop a specialized polyhedral annexation procedure to find a global solution for the case when the inside function is a polyhedral norm. As the problem was solved recently only for local solutions, this paper offers an algorithm for finding a global solution. Implementation and testing are not treated in this short communication.An earlier version of this paper appeared in the proceedings of a conference on Recent Advances in Global Optimization, C. Floudas and P. Pardalos, eds., Princeton University Press, 1991.     

A Simple Approach to the Discount Purchase Problem

In this paper we consider the problem of determining the optimal purchase quantity when the supplier offers a discount on large purchases. We propose a simple approach which requires fewer EOQ calculations for determining the lot size.     

Production planning with approved vendor matrices for a hard-disk drive manufacturer

We develop an optimal production schedule for a manufacturer of hard-disk drives that offers its customers the approved vendor matrix (AVM) as a competitive advantage. An AVM allows each customer to pick and choose the various product component vendors for individual or pairs of components constituting their product. The production planning problem faced by the manufacturer is to meet customer demand as precisely as possible while observing the matrix restrictions and also the limited availability of production resources. We formulate this problem as a linear programming model with a large number of variables, and present a solution procedure based on the column generation technique. A special class of the problem is then studied, whereby the number of production setups in each period is limited and discrete. We modify our formulation into a mixed-integer problem, and proceed to develop procedures that can obtain good feasible solutions using linear programming rounding techniques.     

Efficiency and compromise: a bid-offer–counteroffer mechanism with two players

A bid-offer–counteroffer mechanism is proposed to solve a fundamental two-person decision choice problem with two alternatives. It yields a unique subgame perfect equilibrium outcome, and leads to an intuitive overall solution that offers a reconciliation between egalitarianism and utilitarianism. We then investigate the axiomatic foundation of the solution. Furthermore, we compare it with several conventional strategic approaches to this setting.     

Guarantee structures for problems of fair division

We study the problem of fair division in situations where the number of individuals involved may vary while the resources at their disposal remain fixed. We are interested in minimizing the loss that an agent originally present may incur in such circumstances. Given a solution, i.e., a systematic method of solving any division problem in some class, we introduce the notion of its guarantee structure as a measure of the protection it offers to the original agents. We show that the Kalai-Smorodinsky solution offers greater guarantees than any weakly Pareto-optimal and anonymous solution and in particular than the Nash solution.     

Minimization of functionals on the solution of a large-scale discrete ill-posed problem

In this work we study the minimization of a linear functional defined on a set of approximate solutions of a discrete ill-posed problem. The primary application of interest is the computation of confidence intervals for components of the solution of such a problem. We exploit the technique introduced by Eldén in 1990, utilizing a parametric programming reformulation involving the solution of a sequence of quadratically constrained least squares problems. Our iterative method, which uses the connection between Lanczos bidiagonalization and Gauss-type quadrature rules to bound certain matrix functionals, is well-suited for large-scale problems, and offers a significant reduction in matrix-vector product evaluations relative to available methods.