A bi-objective programming model for designing compact and balanced territories in commercial districting

Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil

“…With transportation and logistics applications in an urban distribution service in a part of the city of São Paulo, Brazil, Novaes et al [26] also investigated Voronoi diagrams, but in association with continuous approximation models, for solving the locationdistricting problem by minimizing total daily delivery costs and balancing the distribution effort among vehicles. Salazar-Aguilar et al [30] applied the ϵ-constraint method for handling the beverage distribution in the city of Monterrey, Mexico, as a multi-objective problem with respect to the number of customers and sales volume. Shirabe [31] applied a single-objective map algebra based heuristic for solving MILP models of several illustrative instances of the wellknown school bus problem.…”

“…A wrong partitioning will certainly result in an unbalanced health service and might cause extensive flow of patients from one microregion to another for the sole purpose of a required procedure not available in the patient's home microregion, and thus it may increase cost and reduce quality. [25] Salt spreading operations Antwerp, Belgium MO H MHP Bergey et al [5] Electrical power districting Republic of Ghana MO MH GA Bozkaya et al [6] Electoral problem Edmonton, Canada SO MH TS Galvão et al [19] Delivery problem São Paulo, Brazil MO H WVD Tavares-Pereira et al [32] Public transportation Paris, France MO MH GA Haugland et al [20] Routing problem Benchmark instances SO MH TS Datta et al [14] Land-use management Southern Portugal MO MH GA Ricca and Simeone [28] Electoral problem Italian regions MO MH LS Ricca et al [27] Electoral problem Italian regions MO H WVD Novaes et al [26] Delivery problem São Paulo, Brazil MO H VD Salazar-Aguilar et al [30] Distribution problem Monterrey, Mexico MO EX ϵ-constraint Shirabe [31] School bus transportation Sweden SO H Map algebra Contreras et al [8] Combined facility location and network design Benchmark instances SO EX MILP Knight et al [21] Locating emergency medical services Wales SO MH GA Datta et al [15] Census tracts London, Ontario, Canada MO MH GA Datta et al [13] Healthcare East England MO MH GA Lin et al [23] Determination of resource levels in surgical services Benchmark instances MO MH GA Benzarti et al [4] Home healthcare France MO EX MILP Ríos-Mercado and López-Pérez [29] Distribution problem Monterrey, Mexico SO EX MILP Assis et al [1] Power meter reading São Paulo, Brazil MO MH GRASP Li et al [22] Urban land use Southern California, USA SO EX MILP Liu et al [24] Periodic vehicle routing problem The Parana State has a total area of 199,314.85 km 2 and its population (close to 11 million inhabitants) is around 5% of the total Brazilian population. The health services in Parana are offered through a public system managed by the government and also complemented by private companies, but the latter are paid services affordable only by a section of the population.…”

Spatial Aspects of Census Districting

“…In general, spatial partitioning problem can be described as decomposing of a large space into smaller subspaces subject to some desired criteria in order to ease of monitoring, planning and management (Salazar-Aguilar et al, 2011). If the original space is composed of a large number of basic spatial units (BSU), then spatial partitioning is aggregating or grouping of these units into larger zones (Figure 1) (Bozkaya et al, 2003;Macmillan, 2001;Salazar-Aguilar et al, 2010;Shirabe, 2005;Yamada, 2009).…”

“…It has a significant influence on census districting procedure; because the points of a circular district are more accessible for the census officers, and thus the length of the traversed path will be smaller. Among several estimations proposed for measuring the compactness of geometrical shapes (Salazar-Aguilar et al, 2011;Svec et al, 2007;Young, 1988), here the perimeter to area test (P2A) is used (Ralphs et al, 2009):…”

Subdividing trade area of cigarette retail stores based on big data analytics

“…Due to the sales activity of retail store usually has a certain geographical zone, it has a relatively stable micro district area [4]. And due to the different merchandise, traffic factors, geographical location and business scale, the size and form of micro trade areas varies greatly [5].Trade area analysis is an important topic of marketing campaigns, for cigarette marketing, it is very important in guiding the rationalization layout of tobacco retail store, providing the basis of strategy formulation of cigarette launch, and so on. In cigarette industry, the trade area of cigarette retailers is divided into 42 categories with town, rural area, large, medium and small scale 7 formats.…”