An approach to uncertainty in emergency service systems via scenarios and fuzzy values

When a service system is being designed, its resistance to randomly occurring detrimental events is often assessed. Several approaches can be used to include the influence of the events in the design process. This contribution deals with two such approaches. The first approach is based on making the system resistant to a finite set of scenarios. The second approach takes input data as fuzzy values and seeks a design solution where the objective function value belongs to a fuzzy set of good objective function values at the maximal level of satisfaction. Each approach models uncertainty in a different way and we will focus on studying the impact of the used uncertainty model on the resulting min-sum optimal emergency service system design, which is characterized by a deployment of a limited number of service centers in a serviced geographical region

Min-max optimal public service system design

This paper deals with designing a fair public service system. To achieve fairness, various schemes are be applied. The strongest criterion in the process is minimization of disutility of the worst situated users and then optimization of disutility of the better situated users under the condition that disutility of the worst situated users does not worsen, otherwise called lexicographical minimization. Focusing on the first step, this paper endeavours to find an effective solution to the weighted p-median problem based on radial formulation. Attempts at solving real instances when using a location-allocation model often fail due to enormous computational time or huge memory demands. Radial formulation can be implemented using commercial optimisation software. The main goal of this study is to show that the suitability solving of the min-max optimal public service system design can save computational time

EXPLOITATION OF COMERCIAL IP-SOLVER FOR LOCATION PROBLEM SOLVING

V dopravních systémech se setkáváme s úlohou umisťování obslužných středisek tak, aby náklady na obsluhu objektů sítě byly co nejmenší. Obecně jsou tyto úlohy modelovány prostředky celočíselného lineárního programování. To obvykle znamená, že exaktní algoritmus pro úlohy praktického rozsahu vyžaduje pro získání optimálního řešení příliš velkou výpočetní dobu. Přesto však existuje třída umisťovacích úloh, tzv. pokrývací úlohy, které jsou řešitelné i komerčními softwarovými prostředky v krátké době. V tomto příspěvku ukážeme postup, jak umisťovací úlohy převést na úlohy pokrývací. V závěru příspěvku bude publikovaná i krátká výpočetní studie obsahující porovnání výkonnosti komerčního optimalizačního softwaru s exaktní metodou pro daný typ úlohy.The service system design problem with an objective to minimize the cost of customer service can be often met in transportation systems. In general, these problems are modeled by means of integer linear programming. It usually follows that an exact algorithm needs too long computational time to find an optimal solution. In spite of it, there exists a class of location problems, so-called covering problems, which are solvable even by commercial software in a short time. In this contribution, we demonstrate the approach of reformulation the location problem to the covering one. At the end of this contribution, there is published a short numerical study, which contains a efficiency comparison between a commercial software and an exact method for this type of problem

A two‐phase method for the capacitated facility problem of compact customer sub‐sets

The cost optimal design of the majority of distribution and servicing systems consists of decisions on a number and on the locations of facilities from which customers’ demands are satisfied; however, there are severe difficulties in solving exact procedures because the underlying mathematical model is NP‐hard. These decisions should respect some additional conditions as a limited capacity of located facilities. The objective is to minimize the overall costs of the system and to satisfy all customers’ demands. In this paper, we enrich the set of constraints by a new requirement called sub‐pool compactness. This property of customer subset influences the quality of vehicle routes subsequently formed in a sub‐set of customers served by the same facility. This paper formulates the problem of the enriched capacitated facility location considering compactness condition, formalizes and studies the property of compactness and suggests the compound method solving this problem. First published online: 27 Oct 201

Kernel-like Search for Robust Emergency System Designing

Emergency service system, which satisfies randomly emerging demands of public for necessary treatment, is determined by deployment of limited number of service centers at positions from a given set of possible locations. The objective is to minimize average response time of the nearest ambulance vehicle usually located at a service center. The robust service system is designed to comply with specified scenarios by minimizing the maximal value of the above mentioned objective functions corresponding to the particular scenarios, which represent consequences of random failures in the road network. The detrimental events may correspond to congestion, disruptions or blockages of roads. The robust emergency system design problem can be modeled by means of mathematical programming. The model includes scenarios and the associated link-up constraints, which connect average response time connected with individual scenarios to the general objective function, which is maximum of these objective functions. The min-max link-up constraints and the cardinality of the scenario set represent an undesirable burden in any solving process used for design solution. Within this paper, we present a kernel-like search algorithm, which tries to replace the solving process of the huge problem above by a series of smaller problems, which deal with either small subset of scenarios or reduced set of possible center locations

An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the p-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm

Min-max optimization and the radial approach to the public service system design with generalized utility

The paper deals with the min-max public service system design, where the generalized utility is considered. In contrast to the formulations presented in the literature, the generalized utility defined for a public service system assumes that the user’s utility comes generally from more than one located service center and the individual contributions from relevant centers are weighted by reduction coefficients depending on a center order. Given that commercial IP-solvers often fail due to enormous computational times or extreme memory demands when resolving this issue, we suggested and compared several approaches based on a bisection process with the purpose of developing an effective max-min approach to the public service system design with a generalized utility

User-fair designing emergency service systems

The usual approach to emergency system design consists in deploying a given number of service centers to minimize the disutility perceived by an average user, what is called “min-sum” or “system approach”. As a user in emergency tries to obtain service from the nearest service center, the min-sum optimal deployment may cause such partitioning of the users’ set into clusters serviced by one center that population of users is unequally distributed among centers. Within this paper, we focus on user-fair design of emergency service systems, where the fair approach is not applied on the individual users, but on the clusters serviced by one center. The fairer deployment should prevent the users to some extent from frequent occurrence of the situation, when the nearest service center to a current demand location is occupied by servicing some previously raised demand. In such case, the current demand must be assigned to a more distant center. To achieve fairer design of emergency system, we present four approaches to the design problem together with their implementation and comparison using numerical experiments performed with several real-sized benchmarks