Duality theorem for a generalized Fermat-Weber problem

The classical Fermat-Weber problem is to minimize the sum of the distances from a point in a plane tok given points in the plane. This problem was generalized by Witzgall ton-dimensional space and to allow for a general norm, not necessarily symmetric; he found a dual for this problem. The authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the Fermat-Weber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As applications, a dual is found for the multi-facility location problem and a nonlinear dual is obtained for a linear programming problem with a priori bounds for the variables. When the norms concerned are continuously differentiable, formulas are obtained for retrieving the solution for each primal problem from the solution of its dual.     

An approximation algorithm for the location of dairy enterprises under time constraints

The facility location problem constitutes a major part of the strategic planning of a dairy enterprise. The decision making process for such a long term investment is rather complicated, with many of the issues involved belonging to the NP – Hard class of algorithms and therefore the challenge for operational researchers who attempt to mathematically model the problem is significant. A number of models have appeared in the last few years in an attempt to find a solution to the problem. This paper introduces a model pertaining to saturated and competitive markets, which include a high investment risk as well as a small margin for incorrect decisions of the newcomers. Time is a crucial element, especially for sensitive products with a limited life span cycle. An approximation algorithm is used and the solution is then compared with the optimal one. Emphasis was given to the running time of the software program, both in the designing and the implementation of the algorithm.     

Hybrid biobjective evolutionary algorithms for the design of a hospital waste management network

Colombian environmental authorities are exploring new alternatives for improving the disposal of hospital waste generated in the Department of Boyacá (Colombia). To design this hospital waste management network we propose a biobjective obnoxious facility location problem (BOOFLP) that deals with the existing tradeoff between a low-cost operating network and the negative effect on the population living near the waste management facilities. To solve the BOOFLP we propose a hybrid approach that combines a multiobjective evolutionary algorithm (NSGA II) with a mixed-integer program. The algorithms are compared against the Noninferior Set Estimation (NISE) method and tested on data from Boyacá’s hospital waste management network and publicly available instances.     

Simulation of Oxford University Gun Tunnel performance using a quasi-one-dimensional model

The performance of the Oxford University Gun Tunnel has been estimated using a quasi-one-dimensional simulation of the facility gas dynamics. The modelling of the actual facility area variations so as to adequately simulate both shock reflection and flow discharge processes has been considered in some detail. Test gas stagnation pressure and temperature histories are compared with measurements at two different operating conditions – one with nitrogen and the other with carbon dioxide as the test gas. It is demonstrated that both the simulated pressures and temperatures are typically within 3% of the experimental measurements. Received 18 June 2001 / Accepted 15 January 2002     

The stochastic location model with risk pooling

In this paper, we present a stochastic version of the location model with risk pooling (LMRP) that optimizes location, inventory, and allocation decisions under random parameters described by discrete scenarios. The goal of our model (called the stochastic LMRP, or SLMRP) is to find solutions that minimize the expected total cost (including location, transportation, and inventory costs) of the system across all scenarios. The location model explicitly handles the economies of scale and risk-pooling effects that result from consolidating inventory sites. The SLMRP framework can also be used to solve multi-commodity and multi-period problems.     

A fast swap-based local search procedure for location problems

We present a new implementation of a widely used swap-based local search procedure for the p-median problem, proposed in 1968 by Teitz and Bart. Our method produces the same output as the best alternatives described in the literature and, even though its worst-case complexity is similar, it can be significantly faster in practice: speedups of up to three orders of magnitude were observed. We also show that our method can be easily adapted to handle the facility location problem and to implement related procedures, such as path-relinking and tabu search. R. F. Werneck: The results presented in this paper were obtained while this author was a summer intern at AT&T Labs Research.     

On finding widest empty curved corridors

An -siphon of width w is the locus of points in the plane that are at the same distance w from a 1-corner polygonal chain C such that is the interior angle of C. Given a set P of n points in the plane and a fixed angle , we want to compute the widest empty -siphon that splits P into two non-empty sets. We present an efficient O(nlog³n)-time algorithm for computing the widest oriented -siphon through P such that the orientation of a half-line of C is known. We also propose an O(n³log²n)-time algorithm for the widest arbitrarily-oriented version and an Θ(nlogn)-time algorithm for the widest arbitrarily-oriented -siphon anchored at a given point.     

Prepositioning supplies in preparation for disasters

In this paper, we examine the decision of where to preposition supplies in preparation for a disaster, such as a hurricane or terrorist attack, and how much to preposition at a location. If supplies are located closer to the disaster, it can allow for faster delivery of supplies after the disaster. As a result of being closer, though, the supplies may be in a risky location if the disaster occurs. Considering these risks, we derive equations for determining the optimal stocking quantity and the total expected costs associated with delivering to a demand point from a supply point. We provide a sensitivity analysis to show how different parameters impact stocking levels and costs. We show how our cost model can be used to select the single best supply point location from a discrete set of choices and how it can be embedded within existing location algorithms to choose multiple supply points. Our computational experiments involve a variety of relationships between distance and risk and show how these can impact location decisions and stocking levels.     

Design of regional production networks for second generation synthetic bio-fuel - A case study in Northern Germany

In the medium-term, second generation synthetic bio-diesel will make an important contribution to sustainable mobility. However, attributed to political, technical, and market related uncertainties, it is still not clear which interest groups will invest in production capacities and which technologies will be used. Hence, a multi-period MIP-model is presented for integrated location, capacity and technology planning for the design of production networks for second generation synthetic bio-diesel. The approach is applied to the region of Niedersachsen, Germany. Principle network configurations are developed for this region considering different scenarios and different risk attitudes of interest groups. As results of the investigation, recommendations are drawn regarding advantageous plant concepts, as well as strategies for the capacity installation. Finally, recommendations for political decision makers as well as for potential investors are deduced.     

An epsilon-free approach for finding the most efficient unit in DEA

Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition.