Decision-making in Strategic Management of the Public Service System

Let us assume that a certain organization financially supports service centers of public interest, sports, cultural, educational, or other. These centers provide the requirements of customers, who are residents. The organization wants to use its funds efficiently so that the public service system achieves maximum usefulness and fairness to the population. With various possible criteria, we will consider the availability of the inhabitant to the service center and the distance of each inhabitant to the service center to be the main ones. If the management of the organization had an audit carried out after a few years of operation, it would show that some centers are not sufficiently used, and others not used in terms of capacity. The population of the nearest center is low, and the center is a little used. There would be a possibility to cancel or relocate the service center. On the other hand, some centers do not have sufficient capacity because their services are used by many inhabitants at an acceptable distance. There would be a solution to increase the number of service centers. It is still about using funds efficiently. To resource the unused centers or not to provide services to residents because of the insufficient capacity? This work deals with the optimization of system by the redistribution of the originally located service centers. I assumed that each center has one or more stations that provide service with a given capacity. Then the service system design task can be modeled as a capacity-limited location task. The XPRESSIVE optimization setting can be used for its implementation. Numerical experiments were performed by using the real data of the Slovak emergency service

THE CAPACITATED FACILITY LOCATION PROBLEM FOR A VAGUE CONSTRAINTS

Úloha optimálne umiestniť strediská obsluhy s obmedzenou obslužnou schopnosťou tak, aby zabezpečovali požiadavky všetkých zákazníkov pri minimálnych relevantných nákladoch je kapacitne obmedzená umiestňovacia úloha. Vzhľadom na dlhodobý charakter navrhovaného obslužného systému, limitujúce kapacity stredísk, ktoré predstavujú ich obslužnú schopnosť za určité vopred dané odbobie, niesú deterministicky dané. Využitím fuzzy logiky ich možno aproximovať fuzzy množinou a popísať funkciou príslušnosti neznámej hodnoty do tejto množiny. Potom treba stanoviť neznáme reálne objemy kapacít stredísk tak, aby navrhnutý systém dosiahol čo najvyššiu mieru splnenia kapacitných podmienok s čo najnižšími finančnými nákladmi.The main objective of the thesis is to devise and implement the algorithmic solution of the problem of optimal location of set of facilities so that all customer’s demands will be satisfied and the relevant costs are minimal. This optimization task can be modelled by capacitated facility location problem, which is the special class of integer linear programming problems. When a distribution system is to be designed, limits on terminal capability often must be taken into account. In capacitated location problems, the capacity of a facility as an upper limit of its ability to satisfy a given volume of demands cannot be precisely determined in most of practical applications. This circumstance evokes an idea to employ fuzzy approach for handling of the capacities and to utilize the fuzzy description in capacity constraint relaxation

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

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

Fair facility allocation in emergency service system

The request of equal accessibility must be respected to some extent when dealing with problems of designing or rebuilding of emergency service systems. Not only the disutility of the average user but also the disutility of the worst situated user must be taken into consideration. Respecting this principle is called fairness of system design. Unfairness can be mitigated to a certain extent by an appropriate fair allocation of additional facilities among the centres. In this article, two criteria of collective fairness are defined in the connection with the facility allocation problem. To solve the problems, we suggest a series of fast algorithms for solving of the allocation problem. This article extends the family of the original solving techniques based on branch-and-bound principle by newly suggested techniques, which exploit either dynamic programming principle or convexity and monotony of decreasing nonlinearities in objective functions. The resulting algorithms were tested and compared performing numerical experiments with real-sized problem instances. The new proposed algorithms outperform the original approach. The suggested methods are able to solve general min-sum and min-max problems, in which a limited number of facilities should be assigned to individual members from a finite set of providers

Load balancing location of emergency medical service stations

When we want to design a successful and efficient emergency medical system, the crucial task is to determine the number of ambulances operating in a given region and the deployment of stations where the ambulances are kept. In the Slovak Republic, the number and locations of stations are specified by the Ministry of Health for the whole state territory. In the Czech Republic, the network of stations is established by the local authority for each administrative region. Due to geographical and population diversity, there are significant differences in population served by individual ambulances. Assuming that the number of ambulances is given, we want to investigate whether a different location of the ambulances might result in a more even distribution of their workload and, consequently, shorter response time. The problem is modelled as a capacitated p-median problem and solved using mathematical programming. The capacitated p-median problem is known to be NP-complete. As a consequence, it cannot be solved to optimality even for moderate-sized problem instances. However, we face a large-scale problem instance consisting of almost 3,000 demand nodes. Therefore heuristic approaches need to be used to get a sufficiently good solution in an acceptable time. Two decomposition mathematical heuristics are described in the paper and a new heuristic method based on previously developed approaches is presented. A redeployment of existing EMS stations in the Slovak Republic is calculated using these methods. The results are compared mutually and with the current deployment. The benefits and limitations of the presented methodology are discussed