We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a constant number k. It costs f i to open facility i, and c ij for facility i to serve one unit of demand from client j. The objective is to open at most k facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs.In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated k-facility location problem. Then, we show that the capacitated k-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated k-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening cost.
Emergency Medical Service (EMS) systems worldwide are complex systems, characterised by significant variation in service providers, care pathways, patient case-mix and quality care indicators. Analysing and improving them is therefore challenging. Since EMS systems differ between countries, it is difficult to provide generic rules and approaches for EMS planning. Nevertheless, the common goal for all service providers is to offer medical assistance to patients with serious injuries or illnesses as quickly as possible. This paper presents an overview of logistical problems arising for EMS providers, demonstrating how some of these problems are related and intertwined. For each individual planning problem, a description as well as a concise literature overview of solution approaches considered is given. A summary table classifies the literature according to the problems addressed and connects it to the proposed taxonomy.
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