The diff-convex (DC) problem of perturbed spatial median and the Weiszfeld algorithm in a framework for incomplete data is studied, and some level set theorems for general DC problems are provided. These results are then applied to study certain multiobjective formulations of clustering problems, and to yield a new algorithm for solving the multisource Weber problem.

A resource investment problem is a project-scheduling problem in which the availability levels of the resources are considered as decision variables and the goal is to find a schedule, and resource requirement levels, such that some objective function optimizes. In this paper, we consider a resource investment problem in which the goal is to maximize the net present value of the project cash fl...

The multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane in order to minimize the total transportation cost for satisfying the demand of n xed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial...

A resource investment problem is a project-scheduling problem in which the availability levels of the resources are considered decision variables and the goal is to find a schedule and resource requirement levels such that some objective function optimizes. In this paper, we consider a resource investment problem in which the goal is to maximize the net present value of the project cash flows. ...

The multisource Weber problem is to locate simultaneously mn facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solut...

In this paper, we consider the continuous Fermat-Weber problem, where the customers are continuously (uniformly) distributed along the boundary of a convex polygon. We derive the closed-form expression for finding the average distance from a given point to the continuously distributed customers along the boundary. A Weiszfeld-type procedure is proposed for this model, which is shown to be linea...

AJ1STRACT In this paper we apply Galois theoretic algebraic methods to certain fundamental geometric optimization problems whose recognition versions are not even known to be in the class NP. In particular we show that the classic Weber problem, the Line-restricted' Weber probe lem and the 3-Dimension version of this problem are in general not solvable by radicals over the field of rationals. O...

in this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. the constraints are the warehouse capacity and the batch forms of the order placements. the first objective of this problem is to find the order quantities such that the expected ...