Abstract. Th e 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 satisfi ed; however, there are severe difficulties in solving exact procedures because the underlying mathematical model is NP-hard. Th ese decisions should respect some additional conditions as a limited capacity of located facilities. Th e 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. Th is property of customer subset infl uences the quality of vehicle routes s ubsequently formed in a sub-set of customers served by the same facility. Th is 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.
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.
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