Maximising the coverage of emergency medical services with time-dependent demand restrictions: a case study in Shanghai Ming Kun Li and Jia Wei Zhang School of Management, Shanghai University, Shanghai, People’s Republic of China ABSTRACT In many Asian cities, periodic changes in the demand for emergency medical services are concerned, but few existing studies have discussed the time-dependent factor in delivering these services. This study proposes a formula for locating emergency medical services, in which factors of varying demand, time-dependence, cost and facility capacity are considered. A real case is investigated in order to understand the impact of time-dependence on decision making. The case study suggests different solutions depending on whether the design is service-oriented or cost-oriented. The analysis also indicates that the limitations on demand complicate the making of decisions to optimise service locations, e.g. more service stations are required. By creating a design for allocating service sites based on demand nodes in a real case, this study provides a framework for analysing the location problem when demand changes. KEYWORDS Emergency medical services; integer programming; location; time-dependent restrictions CONTACT Ming Kun Li [email protected] Received 8 July 2016 1. Introduction staff workloads can be easily detected, as indicated below in the summary of emergency medical services in Shanghai The Shanghai society faces a variety of challenges from 2001 to 2014. As a result, the response time for due to rapid urbanisation. At the end of 2014, the elderly ambulance services in urban cities is getting longer (Qi and population in Shanghai was 28.8% of the total population Jing, 2017). (Shanghai Civil Affairs Bureau, 2015). The growing Along with the increasing demand for medical services, proportion of elderly residents, together with the booming other problems have emerged during the implementation of a number of migrants is placing growing pressure on the more effective service, such as limited resources and changes city’s emergency medical services. A significant growth in in demand. This paper observed that the time-dependent Table 1. Summary of emergency medical services in Shanghai. (source: www.sn120.sh.cn) Year Distance travelled (km) Number of vehicle-times Number of patients 2001 3,684,900 157,400 146,600 2002 4,757,000 192,200 179,800 2003 5,540,600 223,200 207,500 2004 6,237,800 254,000 234,200 2005 6,898,700 297,400 268,300 2006 7,573,300 327,200 290,100 2007 8,251,600 359,000 322,800 2008 9,052,700 396,800 361,900 2009 9,632,700 430,200 396,100 2010 11,330,100 498,700 455,800 2011 - 535,900 487,800 2012 12,016,600 594,500 541,000 2013 12,648,300 628,500 571,900 2014 12,367,700 642,000 584,000 009 © 2019 The Hong Kong Institution of Engineers HKIE Transactions | Volume 26, Number 1, pp.9–19 • https://doi.org/10.33430/V26N1THIE-2016-0029 M K LI AND J W ZHANG aspect of the demand problem is mainly being caused by the dynamic setting of ambulance locations (Gendreau et mobility of citizens. al., 2001; Rajagopalan et al., 2008; Zarandi et al., 2013) To put it simple, a large portion of the population is was considered. Another direction for applying current now choosing to live in the growing suburbs and commute coverage models to real problems is to consider capacitated downtown to work. Thus, the movement of the population facilities (Chung et al., 1983; Current and Storbeck, 1988; has substantially changed the demand for emergency Murray and Gerrard, 1997). Applications of the extended services in different regions of the city at different times. capacitated covering models to real-world problems are Where one medical station might have once been sufficient provided by authors (Yin and Mu, 2012). for communities in a designated region, the fluctuating In recent years, the time-dependent aspect in coverage overall demand for ambulances from a shifting population problems has attracted growing attention. One of the often leads to long response times by medical services. features is that the speed of the ambulance is affected by These shifting population patterns also influence unfavourable traffic conditions during rush hours, and the planning procedures for emergency facility locations. therefore the radius of prompt cover can vary at different So, optimising facility locations for emergency medical times (see arguments on vehicle routing problems in Hill services has become a priority for local government. and Benton, 1992; Malandraki and Daskin, 1992; Ichoua et This study is driven by the time-dependent nature of al., 2003). the demand for emergency medical services. Shackled by This led to the problems of ambulance location and limited budgets and finite land resources, planners have relocation in relation to time-dependent service (Budge et al., to consider many factors such as the city layout, costs, the 2010; Schmid and Doerner, 2010). In medical emergency limited number of candidate sites and the mobility of the logistics, the time window was also an important factor when population, in order to optimise the use of facilities while optimising the number and locations of supply nodes to achieving a satisfactory service level. Consequently, the demand nodes (see a case study by Tuzkaya et al., 2014). allocation problem for emergency medical sites needs to be Some other researchers (Griffin et al., 2008) argued investigated from a variety of different angles to ensure the that the cost of health services and the locations of health optimum allocation of facilities for each demand node. In centres are subject to fluctuations in needs, while some this research, a real case in Shanghai is discussed. recent surveys (Basçar et al., 2012; Farahani et al., 2012) highlighted the fact that the time-dependence aspect of emergency service station location problems were under- 2. Literature review developed areas of academic research. On the one hand, rapid urbanisation in Asia and an The importance of ambulance services in any urban ageing population have resulted in a growing need for society has been explored extensively in the literature. more ambulances and health care services overall, (Loo Many problems are considered such as the location of and Lam, 2012), while is the residential shifts of people has ambulance stations, and the relocation and dispatching of exacerbated the delivery of the services. On the other hand, ambulances. however, we can see from the literature that few studies These problems are connected to each other, but have discussed models and applications for covering solving the facility location problem is the basis for making problems of delivering medical services with time- all the other related decisions (Aringhieri et al., 2017). dependent demand restrictions. Minimising the cost of covering all the demand nodes Therefore, on the basis of some real cases in Asian (Toregas et al., 1971) and covering the largest possible level cities, a formula addressing two time-dependent demand of demand (Church and ReVelle, 1974) are some recognised constraints was considered in this research. A better plan objectives of previous research. Similar objectives have for the location of medical stations was attempted with appeared in studies on determining the locations of fire reference to changing demands during different time stations (Indriasari et al., 2010) and emergency warning periods. sirens (Current and O’Kelly, 1992). Early research work, however, has some major drawbacks, e.g. the assumption of un-capacitated facilities and the 3. Model formulations static condition of demand, largely negate the application of current coverage models. More background on the planning process is introduced To remedy this situation, more attention must be to provide the mathematical formulation. In reality, a new paid to improve the models to reflect real-world problems. plan for facilities is often made from the existing service Hence, some researchers (Hogan and ReVelle 1986; locations and some new potential candidates. The budget Gendreau et al., 1997) considered the Double Standard restricts the number of locations in this plan, and also Model to ensure multiple coverage of each demand node, imposes an upper limit on the capacity of medical emergency while other researchers (Daskin 1983; Batta et al., 1989) services at each site. extended the studies on investigating the availability of In order to facilitate the service process and control the ambulances at different time periods. More recently, the costs, one demand node is assigned to at most one service 010 HKIE Transactions | Volume 26, Number 1, pp.9–19 In order to facilitate the service process and control the costs, one demand node is assigned to at most one service site. The demands of a node correspond to the population, while the demand varies periodically over time. More specifically, it is also affected by work time and leisure time. Authorities will always attempt to improve service levels, and therefore, in this research, maximising the coverage of emergency services within a limited budget, and time-dependent restriction were the major objectives. The problem is formulated as follows: Parameters: N the set of existing and candidate emergency service sites, N 0 the set of existing emergency service sites at the beginning of the plan, i.e. 0 0 0 = jN ∈ N |{ x j = 1 } , where x j denotes the initial status of site j, M the set of demand nodes, ⎧ ,1 if the distance from i to j is not greater than the upper limit of services