Planar/network/discrete

Planar — demand occurs anywhere in the plane (possibly represented by a deterministic or probabilistic field). Facilities may be located anywhere in the plane; Network — demand and facilities can only be located at network nodes or on links, and travel is restricted to the network; Discrete — nodes are fixed but the cost of travel between nodes is not determined by an underlying network

Tree/graph

Some network problems are amenable to treatment as if the graph is a tree, which can make solution far simpler

Distance metric

We have previously noted (Section 4.4.1) that a variety of metrics can be used in spatial analysis and this applies equally to location problems, notably planar and discrete cases

Facilities

The number of facilities to locate can be pre-specified (e.g. as p) or generated as part of the optimization process (as in the set coverage problem — see below). Problems involving the location of only one facility are often relatively straightforward to solve, and some procedures use this fact to develop heuristics that incrementally increase the number of facilities based on local optimization of the next facility added

Static/dynamic

Most of the problems and techniques described in this chapter are essentially static. Such methods may be applied to some dynamic problems, but in many cases these procedures require extension or alternative approaches to deal with dynamic cases. Examples include: choosing when as well as where to locate the next 1,2… facilities; incorporating dynamic demand and possibly supply into the model; modifying vehicle locations as demand varies by time of day or week (e.g. relocating emergency vehicles on standby based on time of day)

Private/public

The principal issue here relates to the definition of the objective function — can this be done in purely monetary (or equivalent) terms or do social, environmental and other factors require evaluation? Generally all location selection processes are part of a broader decision-making environment (as identified in the PPDAC model, Section 3.3). In public facilities location it is also often possible to dictate allocations whereas for private facilities this is almost never possible, requiring the modeling of allocation (e.g. using spatial interaction models)

Single/multi-objective

In most instances single-objective solutions are sought (e.g. time, distance or cost minimization). However, real-world situations are almost always multi-objective. One approach to this is to compute multiple solutions for variations in parameters that reflect the multiple objectives, and examine the nature and robustness of these solutions. This is not equivalent to true multi-objective analysis but may provide benchmarks and guidance for such problems as part of a broader analytical framework

Unique/diverse service

A unique service is one in which a single (principal) service is being modeled, such as ambulance provision. A diverse service might be a similar problem, but where different categories of ambulance service and associated vehicles and staffing were modeled — for example, full emergency call-out vehicles; individual paramedics on-call; and ambulances for non-emergency usage (e.g. transport of patients, medical supplies etc.)

Elastic/inelastic demand

Most models assume that demand and supply are independent. However, it must be recognized that improved supply frequently increases demand, i.e. that demand is elastic, and that supply may or may not be

Deterministic/adaptive/ stochastic

Many models are deterministic in terms of supply, demand and feasible solutions; others may assume demand is probabilistic and often dynamic, with solutions being sought that are optimal with respect to the inputs, but which are often adaptive reflecting changes in demand, supply and transport dynamics

Capacitated/uncapacitated

Basic models do not consider the capacity of facilities (e.g. warehouses, storage depots, hospitals, vehicles) or links (e.g. transport networks or pipelines) as a constraint. Tools are available that allow for the inclusion of such constraints (an example is provided in Section 7.3.5.1)

Nearest facility/ General demand allocation

Demand is often assumed to be allocated to the nearest facility. In capacitated models this may require that some demand is split between facilities (fractional allocation) — e.g. a retail store may need to be serviced by more than one warehouse, or patients may be sent to more distant hospitals in times of high demand or major emergencies

Hierarchical/single level

Some problems are intrinsically hierarchical, in that products or services are provided from larger centers (e.g. national) to smaller regional centers and on to district and local facilities (or vice versa, upwards flow rather than downwards distribution). This may apply for product or service offerings. In such problems the existence of facilities at one level (up or down) may be a pre-requisite for locating facilities at the next (e.g. large-scale regional hospitals are only provided where at least a certain number of local level medical facilities already exist). A similar example would be the design of a completely new multi-level health infrastructure for a region previously not served with these kinds of facility

Desirable/undesirable

Most location modeling relates to desirable facilities — the distance or cost of travel to or from facilities is to be minimized, according to some criterion. For some facilities, such as waste disposal sites, incinerators, nuclear power plants, etc. the facility location problem becomes more complex because there are often conflicting objectives. For example, the location of waste disposal sites need to be as near as possible to the waste creation points (towns say), but ideally as far away as possible from habitation