Case11B3-Location-Allocation Analysis of Hospitals-Part 3 Implement MAEP

Chapter 11 Linear and Quadratic Programming and Applications in Examining Wasteful Commuting and Allocating Healthcare Providers

This chapter introduces two popular methods in optimization, linear program ming (LP) and quadratic programming (QP). QP is perhaps the simplest form of non-linear programming (NLP). LP and QP seek to maximize or minimize an objective function subject to a set of constraints. LP has both the objective and the constraints in linear functions. QP has a quadratic objective function, but its constraints remain linear. This chapter uses case studies to illustrate their applications in spatial planning and location-allocation analysis.

Case Study 11B: Location-Allocation Analysis of Hospitals in Rural China

Case study 11B uses various location-allocation problems to plan healthcare providers in a rural county in China. In addition to illustrate some classic location-allocation models such as the p -median problem, the maximum covering location problem (MCLP), and the minimax problem that belong to the family of integer linear programming (ILP) problems, case study 11B also introduces a new location-allocation problem termed “ Maximal Accessibility Equality Problem (MAEP) ” and demonstrates how the problem is solved by QP. The MAEP seeks to minimize inequality in accessibility of facilities across geographic areas, and by extension, across population groups, and has great potential in applications in both private and public sectors.

This case study is developed from the work reported in Luo et al. (2017). The planning problem is where to build three new hospitals and how large for each. The study area is a rural county Xiantao in Hubei Province of China. A sequential decision-making approach, termed “two-step optimization for spatial accessibility improvement (2SO4SAI) ”, is conceptualized to solve the problem.

The case study is implemented in three parts. Part 1 prepares the data. Part 2 finds the best locations to site the new hospitals by emphasizing accessibility as proximity to the nearest hospitals. Part 3 adjusts their capacities for minimal inequality in accessibility measured by the 2SFCA method. Part 2 strikes a balance among the solutions by three classic location-allocation models ( p -median, MCLP, and minimax problems), and Part 3 solves a QP problem.

The data folder Xiantao includes:
1. Supply point feature class Hosp41.zip includes 41 existing hospitals with a field CHCI (comprehensive hospital capacity index) representing their capacities, and HospAll.zip adds 3 newly sited hospitals to Hosp41 as a result from Part 2.

2. Demand point feature class Village.zip contains 647 villages with a field Popu indicating their population sizes.

3. Feature dataset Road.zip represents the major road network.

4. Two base layers include Xiantao.zip for the study area boundary and Township.zip for the township administrative boundaries (each township includes multiple villages).

5. Intermediate results include (1) a distance table ODhosp41.csv from 647 villages to extant 41 hospitals, and (2) another distance table ODvillage. csv from 647 villages to four candidate hospital sites.

Part 1: Data Preparation
Part 2: Location Optimization for Site Selection
Part 3: Implementing the MAEP to Derive Capacities for Sited New Hospitals

Computational Methods and GIS Applications in Social Science - KNIME Lab Manual
Lingbo Liu, Fahui Wang

External resources

• Github for Workbook Issue Report
• Github for Geospatial Analytics