Multicriteria tour planning for mobile healthcare facilities in a developing country

A multiobjective combinatorial optimization (MOCO) formulation for the following location-routing problem in healthcare management is given: For a mobile healthcare facility, a closed tour with stops selected from a given set of population nodes has to be found. Tours are evaluated according to three criteria: (i) An economic efficiency criterion related to the tour length, (ii) the criterion of average distances to the nearest tour stops corresponding to p-median location problem formulations, and (iii) a coverage criterion measuring the percentage of the population unable to reach a tour stop within a predefined maximum distance. Three algorithms to compute approximations to the set of Pareto-efficient solutions of the described MOCO problem are developed. The first uses the P-ACO technique, and the second and the third use the VEGA and the MOGA variant of multiobjective genetic algorithms, respectively. Computational experiments for the Thiès region in Senegal were carried out to evaluate the three approaches on real-world problem instances.     

Efficient computation of 2-medians in a tree network with positive/negative weights

We consider a variant of the classical two median facility location problem on a tree in which vertices are allowed to have positive or negative weights. This problem was proposed by Burkard et al. in 2000 (R.E. Burkard, E. Çela, H. Dollani, 2-medians in trees with pos/neg-weights, Discrete Appl. Math. 105 (2000) 51-71). who looked at two objectives, finding the total minimum weighted distance (MWD) and the total weighted minimum distance (WMD). Their approach finds an optimal solution in O(n²) time and O(n³) time, respectively, with better performance for special trees such as paths and stars. We propose here an O(nlogn) algorithm for the MWD problem on trees of arbitrary shape. We also briefly discuss the WMD case and argue that it can be solved in time. However, a systematic exposition of the later case cannot be contained in this paper.     

Weber problems with mixed distances and regional demand

We consider a location problem where the distribution of the existing facilities is described by a probability distribution and the transportation cost is given by a combination of transportation cost in a network and continuous distance. The motivation is that in many cases transportation cost is partly given by the cost of travel in a transportation network whereas the access to the network and the travel from the exit of the network to the new facility is given by a continuous distance.      

Solving a Huff-like competitive location and design model for profit maximization in the plane

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximise the profit obtained for the chain. Several types of constraints and costs are considered.     

An exact algorithm for solving the bilevel facility interdiction and fortification problem

We present an exact approach for solving the $r$-interdiction median problem with fortification. Our approach consists of solving a greedy heuristic and a set cover problem iteratively that guarantees to find an optimal solution upon termination. The greedy heuristic obtains a feasible solution to the problem, and the set cover problem is solved to verify optimality of the solution and to provide a direction for improvement if not optimal. We demonstrate the performance of the algorithm in a computational study.     

An approximation algorithm for dissecting a rectangle into rectangles with specified areas

Given a rectangle R with area α and a set of n positive reals A={a₁,a₂,…,a_n} with ∑_ai∈Aa_i=α, we consider the problem of dissecting R into n rectangles r_i with area so that the set R of resulting rectangles minimizes an objective function such as the sum of the perimeters of the rectangles in R, the maximum perimeter of the rectangles in R, and the maximum aspect ratio of the rectangles in R, where we call the problems with these objective functions PERI-SUM, PERI-MAX and ASPECT-RATIO, respectively. We propose an O(nlogn) time algorithm that finds a dissection R of R that is a 1.25-approximate solution to PERI-SUM, a -approximate solution to PERI-MAX, and has an aspect ratio at most , where ρ(R) denotes the aspect ratio of R.     

An efficient solution method for Weber problems with barriers based on genetic algorithms

In this paper we consider the problem of locating one new facility with respect to a given set of existing facilities in the plane and in the presence of convex polyhedral barriers. It is assumed that a barrier is a region where neither facility location nor travelling are permitted. The resulting non-convex optimization problem can be reduced to a finite series of convex subproblems, which can be solved by the Weiszfeld algorithm in case of the Weber objective function and Euclidean distances. A solution method is presented that, by iteratively executing a genetic algorithm for the selection of subproblems, quickly finds a solution of the global problem. Visibility arguments are used to reduce the number of subproblems that need to be considered, and numerical examples are presented.     

A survey of recent research on location-routing problems

The design of distribution systems raises hard combinatorial optimization problems. For instance, facility location problems must be solved at the strategic decision level to place factories and warehouses, while vehicle routes must be built at the tactical or operational levels to supply customers. In fact, location and routing decisions are interdependent and studies have shown that the overall system cost may be excessive if they are tackled separately. The location-routing problem (LRP) integrates the two kinds of decisions. Given a set of potential depots with opening costs, a fleet of identical vehicles and a set of customers with known demands, the classical LRP consists in opening a subset of depots, assigning customers to them and determining vehicle routes, to minimize a total cost including the cost of open depots, the fixed costs of vehicles used, and the total cost of the routes. Since the last comprehensive survey on the LRP, published by Nagy and Salhi (2007), the number of articles devoted to this problem has grown quickly, calling a review of new research works. This paper analyzes the recent literature (72 articles) on the standard LRP and new extensions such as several distribution echelons, multiple objectives or uncertain data. Results of state-of-the-art metaheuristics are also compared on standard sets of instances for the classical LRP, the two-echelon LRP and the truck and trailer problem.     

Optimal location with equitable loads

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn ³) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented.