Skip To Content

Location-allocation analysis layer

What is Location-Allocation?

Location is often considered the most important factor leading to the success of a private- or public-sector organization. Private-sector organizations can profit from a good location, whether a small coffee shop with a local clientele or a multinational network of factories with distribution centers and a worldwide chain of retail outlets. Location can help keep fixed and overhead costs low and accessibility high. Public-sector facilities, such as schools, hospitals, libraries, fire stations, and emergency response services (ERS) centers, can provide high-quality service to the community at a low cost when a good location is chosen.

Choosing the best fire station facilities

Given facilities that provide goods and services and a set of demand points that consume them, the goal of location-allocation is to locate the facilities in a way that supplies the demand points most efficiently. As the name suggests, location-allocation is a twofold problem that simultaneously locates facilities and allocates demand points to the facilities.

Initially, it may appear that all location-allocation analyses solve the same problem, but the best location is not the same for all types of facilities. For instance, the best location for an ERS center is different than the best location for a manufacturing plant. The next two examples demonstrate how the goals of location-allocation problems vary according to the type of facility being located.

Example 1: Locating an ERS center

When someone calls for an ambulance, we trust it will come to their aid almost instantly; the emergency response time depends considerably on the distance between the ambulance and the patient. Typically, the goal for determining the best sites for ERS centers is to make it possible for ambulances to reach the most people within a defined time frame. The specific question may be: Where should three ERS facilities be placed so the greatest number of people in the community can be reached within four minutes?

Example 2: Locating a manufacturing plant

Many retail outlets receive their goods from manufacturing plants. Whether producing automobiles, appliances, or packaged food, a manufacturing plant can spend a large percentage of its budget on transportation. Location-allocation can answer the following question: Where should the manufacturing plant be located to minimize overall transportation costs?

Location-allocation problem types

Location-Allocation analysis layer offers seven different problem types to answer specific kinds of questions, including questions like those posed in the two examples above. The seven problem types are the following:

  • Minimize Weighted Impedance (P-Median)
  • Maximize Coverage
  • Maximize Coverage and Minimize Facilities
  • Maximize Attendance
  • Maximize Market Share
  • Target Market Share
  • Maximize Capacitated Coverage

The following describes the location allocation analysis layer, its analysis properties, and its feature classes.

Facilities feature class

This network analysis class stores the network locations used as the candidate locations from which the actual locations will be chosen from in location-allocation analyses.

When a new location-allocation analysis layer is created, the Facilities class is empty. It is populated only when network locations are added into it. A minimum of one facility and one demand point is necessary to solve the analysis.

Facilities: Input fields

Input fieldDescription

ObjectID

The system-managed ID field.

Shape

The geometry field indicating the geographic location of the network analysis object.

Name

The name of the network analysis object.

FacilityType

This property specifies whether the facility is a candidate, required, competitor, or chosen facility. It is constrained by a domain of values, which is referenced by the integer value in parentheses in the following list:

  • Candidate (0)—A candidate facility is a facility that may be part of the solution.
  • Required (1)—A required facility is a facility that must be part of the solution.
  • Competitor (2)—A competitor facility is specific to the Maximize Market Share and Target Market Share problem types. It is a facility that represents your rivals and will remove demand from the problem.
  • Chosen (3)—Once the location-allocation solver determines that a candidate facility is part of the solution, the solver changes the FacilityType value from Candidate to Chosen. If the FacilityType is set to Chosen before solving, the facility is treated as a candidate facility at solve time.

Weight

The relative weighting of the facility, which is used to rate the attractiveness, desirability, or bias of one facility compared to another.

For example, a value of 2.0 could capture the preference of customers who prefer, at a ratio of 2 to 1, shopping in one facility over another facility. Example factors that potentially affect facility weight include square footage, neighborhood, and age of the building. Weight values other than 1 are only honored by the Maximize Market Share and Target Market Share problem types.

Capacity

The Capacity property is specific to the Maximize Capacitated Coverage problem type; the other problem types ignore Capacity.

This property specifies how much weighted demand the facility is capable of supplying. Excess demand won't be allocated to a facility even if that demand is within the facility's impedance cutoff.

Any value assigned to this facility property overrides the network analysis layer's default capacity.

Network location fields

  • SourceID
  • SourceOID
  • PosAlong
  • SideOfEdge
  • SnapX
  • SnapY
  • SnapZ
  • DistanceToNetworkInMeters

Together, these properties describe the point on the network where the object is located.

CurbApproach

The CurbApproach property specifies which direction of travel is possible when arriving at or departing from the facility. Because the shortest path between two points can change with the direction of travel permitted when arriving at the destination, this property is used when generating impedances between demand points and facilities.

This field is constrained by a domain of values and is set by default to Either side of vehicle (0), indicating the facility can be visited from either the right or left side of the vehicle. Other options include Right side of vehicle (1) or Left side of vehicle (2) if the vehicle should arrive at or depart the facility from a specific direction. The last CurbApproach option, No U-Turns (3), functions the same as Either side of vehicle for location-allocation analyses.

Facilities: Input/output fields

Input/Output fieldDescription

Status

This field is constrained by a domain of values, which are listed below (their coded values are shown in parentheses).

  • OK (0)—The origin is valid.
  • Not located (1)—The origin location on the network dataset can't be determined.
  • Network element not located (2)—The network element identified by the origin network location fields can't be found. This can occur when a network element where the origin should be was deleted and the network location was not recalculated.

After running the analysis, the status can be modified to one of the following status values:

  • OK (0)—The network location was successfully evaluated.
  • Element not traversable (3)—The network element that the origin is on is not traversable. This can occur when the network element is restricted by a restriction attribute.
  • Invalid field values (4)—One or more of the origin field values fall outside the analysis layer's coded or range domains. For example, a negative number may exist where positive numbers are required.
  • Not reached (5)—The origin can't be reached by the solver.
  • Not located on closest (7)—The closest network location to the origin is not traversable because of a restriction or barrier, so the origin has been located on the closest traversable network feature instead.

Facilities: Output fields

Output fieldDescription

DemandCount

This field contains a count of demand points allocated to the facility. A nonzero value means the facility was chosen as part of the solution.

DemandWeight

This field contains a sum of the effective weight from all demand points allocated to the facility. The value is a sum of all the Weight values from the demand points allocated to the facility. In the case of the maximize attendance and market share problem types, the value is an apportioned sum of the Weight field values, since these problem types allow demand to decay with distance or be split among many facilities.

Total_[Cost]

(for instance Total_Miles, where Miles is the travel cost)

This field contains a sum of network costs between the facility and each of the demand points allocated to the facility. The [Impedance] portion of the field name is replaced with the network attribute name, for example, Total_Meters, where Meters is the name of the network attribute.

TotalWeighted_[Cost]

(for instance, TotalWeighted_Miles, where Miles is the travel cost)

This field stores the cumulative weighted cost for a facility. The weighted cost for a demand point is its weight multiplied by the least-cost path between the facility and the demand point. The weighted cost for a facility is the sum of all the weighted costs of demand points allocated to the facility. For example, if a demand point with a weight of two is allocated to a facility 10 miles away, the TotalWeighted_Miles value is 20 (2 x 10). If another demand point with a weight of three is allocated to the same facility and is 5 miles away, the TotalWeighted_Miles value increases to 35 (3 x 5 + 20).

Demand Points feature class

This sublayer stores demand points that are part of a given location-allocation analysis layer. A demand point is typically a location that represents the people or things requiring the goods and services your facilities provide. A demand point could be a ZIP Code centroid weighted by the number of people residing within it or by the expected consumption generated by those people. Demand points could also represent business customers. If you supply businesses with a high turnover of inventory, they would be weighted more heavily than those with a low turnover rate.

Demand points can override the distance cutoff for the location-allocation problem type. This is useful if some demand points have different needs or behavior. For instance, when prepositioning ambulances, it may be acceptable to reach everyone within four minutes, except for areas with a high-density of elderly people, such as senior centers, which require a faster response time of two minutes.

Demand Points: Input fields

Input fieldDescription

ObjectID

The system-managed ID field.

Shape

The geometry field indicating the geographic location of the network analysis object.

Name

The name of the network analysis object.

GroupName

The name of the group the demand point is part of. This property is ignored for the Maximize Capacitated Coverage, Target Market Share, and Maximize Market Share problem types.

If demand points share a group name, the solver allocates all members of the group to the same facility.

Minimize distance without group names
Minimizing distance without grouped demand points
Minimize distance with group names
Minimizing distance with grouped demand points. In this example, the yellow demand points have the same GroupName value, so they are allocated to the same facility.

If constraints, such as a cutoff distance, prevent any of the demand points in the group from reaching the same facility, none of the demand points are allocated.

Weight

The relative weighting of the demand point. A value of 2.0 means the demand point is twice as important as one with a weight of 1.0.

ImpedanceTransformation

Any value assigned to this demand point property overrides the network analysis layer's impedance transformation value.

ImpedanceParameter

Any value assigned to this demand point property overrides the network analysis layer's impedance parameter value.

Cutoff_[Cost]

(for instance Cutoff_Miles, where Miles is the travel cost)

Any value assigned to this demand point property overrides the network analysis layer's Cutoff value.

Network location fields

  • SourceID
  • SourceOID
  • PosAlong
  • SideOfEdge
  • SnapX
  • SnapY
  • SnapZ
  • DistanceToNetworkInMeters

Together, these properties describe the point on the network where the object is located.

CurbApproach

The CurbApproach property specifies which direction of travel is possible when arriving at or departing from the demand point. Because the shortest path between two points can change with the direction of travel that is permitted when arriving at the destination, this property is used when generating impedances between demand points and facilities.

This field is constrained by a domain of values and is set by default to Either side of vehicle (0), indicating the demand point can be visited from either the right or left side of the vehicle. Other options include Right side of vehicle (1) or Left side of vehicle (2) if the vehicle should arrive at or depart the demand point from a specific direction. The last option, No U-Turns (3), functions the same as Either side of vehicle for location-allocation analyses.

Demand Points: Input/output fields

Input/output fieldDescription

Status

As an input field, it indicates the status information about the demand point.

This field is constrained by a domain of values, which are listed below (their coded values are shown in parentheses).

  • OK (0)—The demand point is valid.
  • Not located (1)—The demand point location on the network dataset can't be determined.
  • Network element not located (2)—The network element identified by the demand point network location fields can't be found. This can occur when a network element where the demand point should be was deleted and the network location was not recalculated.

After running the analysis, the status can be modified to one of the following status values:

  • OK (0)—The network location was successfully evaluated.
  • Element not traversable (3)—The network element that the demand point is on is not traversable. This can occur when the network element is restricted by a restriction attribute.
  • Invalid field values (4)—One or more of the demand point field values fall outside the analysis layer's coded or range domains. For example, a negative number may exist where positive numbers are required.
  • Not reached (5)—The demand point can't be reached by the solver.
  • Not located on closest (7)—The closest network location to the demand point is not traversable because of a restriction or barrier, so the demand point has been located on the closest traversable network feature instead.

Demand Points: Output fields

Output fieldDescription

FacilityID

The ObjectID of the facility the demand point was allocated to.

If the value is null, the demand point was not allocated to a facility, or it was allocated to more than one facility; the latter is only possible in the market share problem types.

AllocatedWeight

This is the amount of demand allocated to chosen and required facilities. The value excludes demand allocated to competing facilities. The value can have three interpretations:

  • A null value indicates the demand point wasn't assigned to any facility. This can result, for example, if the demand point is outside all impedance cutoffs or the demand point is on a restricted network element.
  • A zero value indicates the demand point is only assigned to competing facilities.
  • A positive, nonzero value indicates how much demand is assigned to your chosen and required facilities.

Lines feature class

The Lines class is an output-only network analysis class containing line features generated by the solver during the solve operation. It contains line features that connect demand points to the facilities to which they are allocated. If a demand point is allocated to more than one facility, it has one line for each facility to which it is allocated. If a demand point is not allocated to any facility, it won't have any corresponding lines. Location-allocation output in the Lines feature class can either be represented on the map as straight lines or not displayed in the map at all; either way, the analysis always considers the shortest network path between the facility and the demand point; thus, the cost-related attributes reflect network costs, not straight-line distances. The reason the actual shape of the network paths are not output is that they are rarely needed in location-allocation, and generating the shape of the paths would require a substantial increase in the solve time and potentially exhaust your system's resources, especially for large problems.

Lines: Output fields

Output fieldDescription

ObjectID

The system-managed ID field.

Shape

The geometry field indicating the geographic location of the network analysis object.

If the Output Geometry Linear Shape Type property of the analysis layer is set to No Lines, no shape is returned. Setting the Output Geometry Linear Shape Type property to Straight Lines returns straight lines that connect each demand-point or facility pair.

Name

The name of the line. Names are formatted so the facility name and the demand point name are listed in the order they are visited. When the travel direction of the network analysis layer is set to Away from Facilities, the name format is [facility name] - [demand point name]; it is [demand point name] - [facility name] when the property is set to Towards Facilities.

FacilityID

The unique ID of the facility with which the line is associated. A line is always associated with one facility and one demand point.

DemandID

The unique ID of the demand point with which the line is associated. A line is always associated with one facility and one demand point.

Weight

The weight assigned from the connected demand point (DemandID) to the connect facility (FacilityID).

TotalWeighted_[Cost]

(for instance, TotalWeighted_Miles, where Milesis the travel cost)

The weighted cost of traveling between the facility and the demand point. This is the Total_[Cost] value multiplied by the weight of the demand point allocated to the facility.

The active cost attribute will have an accompanying Total_[Cost] field, but the accumulated cost attributes won't. If you need to calculate weighted impedance for accumulated attributes, you can multiply the values from the Weight and appropriate Total_[Cost] fields.

Note that though the lines have either straight or null geometries, the impedance always refers to network costs, not straight-line distances.

Total_[Cost]

(for instance Total_Miles, where Miles is the travel cost)

The network cost of traveling between the facility and the demand point. All accumulated attributes, as well as the active cost attribute, will have an accompanying Total_[Cost] field.

Note that though the lines have either straight or null geometries, the cost always refers to network costs, not straight-line distances.

Location-allocation analysis layer properties

The following subsections list parameters that you can set on the analysis layer. They are found on the Location-Allocation tab, which is available only if your Location-allocation layer or one of its sublayers is selected in the Contents pane.

Location-Allocation tab

Run

Click Run Run, after you load input features and set analysis properties, to solve the location-allocation analysis.

Import Facilities

Import Facilities Import Facilities is in the Input Data group. Click it to load features from another data source, such as a point feature layer, into the Facilities feature class.

Import Demand Points

Import Demand Points Import Demand Points is in the Input Data group. Click it to load features from another data source, such as a point feature layer, into the Demand Points feature class.

Import Barriers

Import Barriers Import Barriers is in the Input Data group. Click it to load features from another data source, such as another feature layer, into one of the barriers feature classes (point barriers, line barriers, polygon barriers).

Mode

The Mode drop-down arrow allows you to choose a travel mode, which is a group of settings that together model the movement of pedestrians, cars, trucks, or other travel mode. The choices available in the drop-down menu depend on the travel modes configured on the network data source that the network analysis layer is referencing.

Direction

Your location-allocation analysis can accumulate travel time or other cost in the direction away from or toward the facility.

  • Away from Facility—The direction of travel is from the facility to the demand point.
    Away from facility
  • Towards Facility—The direction of travel is from the demand point to the facility.
    Towards facility

On a network with one-way restrictions and different travel times based on direction of travel, changing the travel direction can produce different results. The direction you should choose depends on the nature of your analysis. To optimize the location of an ERS center where emergency response vehicles will travel to the location of the emergency (the demand points), the Away from Facilities option would be the most appropriate choice. Alternatively, to locate a retail store, Towards Facilities would be a better choice because you want to attract your demand to the store.

Cutoff

When calculating the least-cost path from a facility to a demand point, the location-allocation solver will stop searching for demand points that lie beyond this impedance cutoff. No demand points beyond this limit will be found for that facility. The units you should use for the cutoff value are shown next to the Mode drop-down arrow.

Facilities

You can specify the number of facilities to find entering a value for Facilities.

Note:

The value in Facilities cannot be specified for two of the problem types that determine the number of facilities needed. These are the Maximize Coverage and Minimize facilities and the Target Market Share problem types.

Type

The Type drop-down gallery in the Problem Type group allows you to specify the problem type solved by the location-allocation solver.

Problem typeDescription

Minimize Weighted Impedance (P-Median)

Facilities are located such that the sum of all weighted costs between demand points and solution facilities is minimized. The arrows in the graphic below highlight the fact that allocation is based on distance among all demand points.

Minimize Weighted Impedance (P-Median) problem type
Minimize Weighted Impedance (P-Median) chooses facilities such that the sum of weighted impedances (demand allocated to a facility multiplied by the impedance to the facility) is minimized.

This problem type is traditionally used to locate warehouses, because it can reduce the overall transportation costs of delivering goods to outlets. Since Minimize Weighted Impedance (P-Median) reduces the overall distance the public needs to travel to reach the chosen facilities, the minimize impedance problem without an impedance cutoff is ordinarily regarded as more equitable than other problem types for locating some public-sector facilities such as libraries, regional airports, museums, department of motor vehicles offices, and health clinics.

The following list describes how the minimize weighted impedance problem type handles demand:

  • If an impedance cutoff is set, any demand outside all the facilities' impedance cutoffs is not allocated.
  • A demand point inside the impedance cutoff of one facility has all its demand weight allocated to that facility.
  • A demand point inside the impedance cutoff of two or more facilities has all its demand weight allocated to the nearest facility only.

Maximize Coverage

Facilities are located such that as many demand points as possible are allocated to solution facilities within the impedance cutoff.

Maximize Coverage problem type
Maximize Coverage chooses facilities such that as much demand as possible is covered by the impedance cutoff of facilities. In this graphic, the solver was directed to choose three facilities.

Maximize Coverage is frequently used to locate fire stations, police stations, and ERS centers, because emergency services are often required to arrive at all demand points within a specified response time. Note that it is important for all organizations, and critical for emergency services, to have accurate and precise data so analysis results correctly model real-world results.

Pizza delivery businesses, as opposed to eat-in pizzerias, try to locate stores where they can cover the most people within a certain drive time. People who order pizzas for delivery don't typically worry about how far away the pizzeria is; they are mainly concerned with the pizza arriving within an advertised time window. Therefore, a pizza-delivery business would subtract pizza-preparation time from their advertised delivery time and solve a maximize coverage problem to choose the candidate facility that would capture the most potential customers in the coverage area. (Potential customers of eat-in pizzerias are more affected by distance, since they need to travel to the restaurant; thus, the attendance maximizing or market share problem types would better suit eat-in restaurants.)

The following list describes how the Maximize Coverage problem handles demand:

  • Any demand point outside all the facilities' impedance cutoffs is not allocated.
  • A demand point inside the impedance cutoff of one facility has all its demand weight allocated to that facility.
  • A demand point inside the impedance cutoff of two or more facilities has all its demand weight allocated to the nearest facility only.

Maximize Capacitated Coverage

Facilities are located such that as many demand points as possible are allocated to solution facilities within the impedance cutoff; additionally, the weighted demand allocated to a facility can't exceed the facility's capacity.Maximize Capacitated Coverage problem type

Maximize Capacitated Coverage chooses facilities such that all or the greatest amount of demand can be served without exceeding the capacity of any facility. In this graphic, each facility has a capacity of one, and the solver was directed to choose three facilities. Although the demand point on the bottom of the map is within the impedance cutoff of a facility, it's not allocated, because doing so would surpass a facility's capacity.

Maximize Capacitated Coverage behaves like either the Minimize Weighted Impedance (P-Median) or Maximize Coverage problem type but with the added constraint of capacity. (If Cutoff is not set, it behaves like a capacitated version of Minimize Weighted Impedance (P-Median).) You can specify a capacity for a facility by assigning a numeric value to its Capacity property. If a value is not assigned in the Capacity field in the Facilities sublayer for a specific facility, the facility is assigned a capacity from the Capacity property of the Location-Allocation tab.

Cases for Maximize Capacitated Coverage include creating territories that encompass a given number of people or businesses, locating hospitals or other medical facilities with a limited number of beds or patients who can be treated, or locating warehouses whose inventory isn't assumed to be unlimited.

The following list describes how the Maximize Capacitated Coverage problem handles demand:

  • Unlike Maximize Coverage, Maximize Capacitated Coverage doesn't require an impedance cutoff; however, when an impedance cutoff is specified, any demand point outside all the facilities' impedance cutoffs is not allocated.
  • An allocated demand point has all or none of its demand weight assigned to a facility; that is, demand isn't apportioned with this problem type.
  • If the total demand within the impedance cutoff of a facility is greater than the capacity of the facility, only the demand points that maximize total captured demand and minimize total weighted impedance are allocated.
    Note:

    You may notice an apparent inefficiency when a demand point is allocated to a facility that isn't the nearest solution facility. This may occur when demand points have varying weights and when the demand point in question is covered by more than one facility's impedance cutoff (or there are no impedance cutoffs at all). This kind of result indicates the nearest solution facility didn't have adequate capacity for the weighted demand, or the most efficient solution for the entire problem required one or more local inefficiencies. In either case, the solution is correct.

Maximize Coverage and Minimize Facilities

Facilities are located such that as many demand points as possible are allocated to solution facilities within the impedance cutoff; additionally, the number of facilities required to cover demand points is minimized.

Maximize Coverage and Minimize Facilities problem type
Maximize Coverage and Minimize Facilities chooses facilities such that as many demand points as possible are within the impedance cutoff of facilities. Additionally, the number of facilities required to cover all demand points is minimized. In this graphic, the solver was able to cover all demand points with only two facilities.

Maximize Coverage and Minimize Facilities is the same as Maximize Coverage but with the exception of the number of facilities to locate, which in this case is determined by the solver. When the cost of building facilities is not a limiting factor, the same kinds of organizations that use Maximize Coverage (emergency response, for instance) use Maximize Coverage and Minimize Facilities so all possible demand points will be covered. Maximize Coverage and Minimize Facilities is also used to choose school bus stops when students are required to walk a certain distance before another school bus stop is provided closer to the student's residence.

The following list describes how the Maximize Coverage and Minimize Facilities problem handles demand:

  • Any demand point outside all the facilities' impedance cutoffs is not allocated.
  • A demand point inside the impedance cutoff of one facility has all its demand weight allocated to that facility.
  • A demand point inside the impedance cutoff of two or more facilities has all its demand weight allocated to the nearest facility only.

Maximize Attendance

Facilities are chosen such that as much demand weight as possible is allocated to facilities while assuming the demand weight decreases in relation to the distance between the facility and the demand point.

Maximize Attendance problem type
Maximize Attendance chooses facilities such that as much demand weight as possible is allocated to facilities while assuming the demand weight decreases with distance. The demand points, represented by pie charts in this graphic, show how much of their total demand is captured by the facility.

Specialty stores that have little or no competition benefit from this problem type, but it may also be beneficial to general retailers and restaurants that don't have the data on competitors necessary to perform market share problem types. Some businesses that might benefit from this problem type include coffee shops, fitness centers, dental and medical offices, bowling alleys, and electronics stores. Public transit bus stops are often chosen with the help of Maximize Attendance. Maximize Attendance assumes that the farther people have to travel to reach your facility, the less likely they are to use it. This is reflected in how the amount of demand allocated to facilities diminishes with distance. You specify the distance decay with the impedance transformation.

The following list describes how the Maximize Attendance problem handles demand:

  • Demand outside the impedance cutoff of all facilities is not allocated to any facility.
  • When a demand point is inside the impedance cutoff of one facility, its demand weight is partially allocated according to the cutoff and impedance transformation. The demand points in the graphic above have pie charts to represent the ratio of their total demand weight captured by the chosen facility.
  • The weight of a demand point covered by more than one facility's impedance cutoff is allocated only to the nearest facility.

Maximize Market Share

A specific number of facilities are chosen such that the allocated demand is maximized in the presence of competitors. The goal is to capture as much of the total market share as possible with a given number of facilities, which you specify. The total market share is the sum of all demand weight for valid demand points.

Maximize Market Share problem type
Maximize Market Share chooses facilities such that the largest amount of allocated demand is captured in the presence of competitors. You specify the number of facilities you want it to choose.

The market share problem types require the most data because, along with knowing your own facilities' weight, you also need to know that of your competitors' facilities. The same types of facilities that use the Maximize Attendance problem type can also use market share problem types given that they have comprehensive information that includes competitor data. Large discount stores typically use Maximize Market Share to locate a finite set of new stores. The market share problem types use a Huff model, which is also known as a gravity model or spatial interaction.

The following list describes how the Maximize Market Share problem handles demand:

  • Demand outside the impedance cutoff of all facilities is not allocated to any facility.

  • A demand point inside the impedance cutoff of one facility has all its demand weight allocated to that facility.

  • A demand point inside the impedance cutoff of two or more facilities has all its demand weight allocated to the facilities that cover it; furthermore, the weight is split among the facilities proportionally to the facilities' attractiveness (facility weight) and inversely proportional to the distance between the facility and demand point. Given equal facility weights, this means more demand weight is assigned to near facilities than far facilities. This behavior is demonstrated in the Maximize Market Share graphic above. Assume the three facilities (squares) have equivalent weights and note that one of the six demand points (circles) is within the impedance cutoff of two competing facilities and has its demand split between the facilities. The demand point near the center of the graphic is covered by both the facility on the left and the facility in the center. Since the demand point is closer to the facility on the left, more of the demand is allocated to that facility.

    The demand point on the lower right did not have any of its demand allocated. The nearest facility to that demand point was not chosen to be part of the solution because the Facilities property was set to 1.

  • The total market share, which can be used to calculate the captured market share, is the sum of the weight of all demand points located on the network; unlocated demand points do not contribute to the total market share and should be relocated on the network if they are to be counted.

Target Market Share

Target Market Share chooses the minimum number of facilities necessary to capture a specific percentage of the total market share in the presence of competitors. The total market share is the sum of all demand weight for valid demand points. You set the percent of the market share you want to reach and let the solver choose the fewest number of facilities necessary to meet that threshold.

Target Market Share problem type
Target Market Share works in the presence of competitors and tries to choose the fewest facilities necessary to capture the market share you specify.

The market share problem types require the most data because, along with knowing your own facilities' weight, you also need to know that of your competitors' facilities. The same types of facilities that use the Maximize Attendance problem type can also use market share problem types given that they have comprehensive information that includes competitor data.

Large discount stores typically use the Target Market Share problem type when they want to know how much expansion would be required to reach a certain level of the market share or see what strategy would be needed just to maintain their current market share given the introduction of new competing facilities. The results often represent what stores would like to do if budgets weren't a concern. In other cases where budget is a concern, stores revert to the Maximize Market Share problem and capture as much of the market share as possible with a limited number of facilities.

The following list describes how the Target Market Share problem handles demand:

  • The total market share, which is used in calculating the captured market share, is the sum of the weight of all demand points located on the network; unlocated demand points do not contribute to the total market share and should be relocated on the network if they are to be counted.
  • Demand outside the impedance cutoff of all facilities is not allocated to any facility.
  • A demand point inside the impedance cutoff of one facility has all its demand weight allocated to that facility.
  • A demand point inside the impedance cutoff of two or more facilities has all its demand weight allocated to the facilities that cover it; furthermore, the weight is split among the facilities proportionally to the facilities' attractiveness (facility weight) and inversely proportional to the distance between the facility and demand point. Given equal facility weights, this means more demand weight is assigned to near facilities than far facilities. This behavior is demonstrated in the Target Market Share graphic above. Assume the three facilities (squares) have equivalent weights and note that two of the six demand points (circles) are within the impedance cutoffs of two different facilities and have their demand split between the facilities. The demand point near the center of the graphic is covered by both the facility on the left and the facility in the center. Since the demand point is closer to the facility on the left, more of the demand is allocated to that facility.

    Another demand point has its weight evenly split between the facility on the left and the facility on the right because it is equidistant to both facilities.

f(cost, β)

This property, the decay function type (impedance transformation), sets the equation for transforming the network cost between facilities and demand points. This property, coupled with the decay function parameter value (β), specifies how severely the network impedance between facilities and demand points influences the solver's choice of facilities.

Applying a transformation can equalize the overall distances that demand points must travel to reach their nearest facility. Libraries and health clinics are concerned with equity of service, so they often locate facilities using a Minimize Weighted Impedance (P-Median) problem type with a Power decay function type and decay function parameter value of 2.0. This way, a minority of faraway patrons or patients is not burdened with comparatively excessive travel distances.

Some stores gather data on where their customers live; as they collect data, the effect distance has on customer behavior is revealed. One benefit of the data is that stores can establish and calibrate decay functions, which can lead to better site selections in the future.

Accurately fitting a decay function and parameter to describe your priorities or model the behavior of your demand points requires careful study, including research on topics like the Huff model and distance decay. The first step, however, is understanding how costs are transformed. In the following list of transformation options, d refers to demand points and f, facilities. So impedancedf is the shortest-path network impedance between demand point d and facility f, and costdf is the transformed network impedance between the facility and demand point. Beta (β) denotes the decay function parameter.

Decay function typeDescription

Linear

costdf = β * impedancedf

Note:

When you set the f(cost, β) property to Linear, the decay function parameter is always internally set to 1, since changing the value of a parameter on a linear transformation doesn't affect the solver's results.

Power

costdf = impedancedfβ

Exponential

costdf = e(β * impedancedf)

Exponential transformations are commonly used in conjunction with an impedance cutoff.

The next set of graphics and tables use Minimize Weighted Impedance (P-Median) to demonstrate the potential effects of using different decay function types and parameters.

Sample problem to demonstrate the effects of decay functions
A sample problem setup uses 2-mile edges with demand points on the ends and candidate facilities in the middle of the edges.

A linear decay function type always uses a parameter value of 1, so the cost is unchanged, and facility B minimizes that cost.

FacilityTotal cost (Linear)Solution facility

A

3+3+5=11

B

7+1+1=9

Facility B is chosen.

Comparison of costs using a linear decay function type
Sample problem to demonstrate the effects of decay functions
Facility B has a lower total transformed cost than facility A when a linear decay function is used.

A power decay function type with a parameter of 2 amplifies longer distances enough that facility A minimizes cost instead.

FacilityTotal cost (Power transformation, β = 2)Solution facility

A

32+32+52=43

Facility A is chosen.

B

72+12+12=51

Comparison of costs using a power decay function type with a parameter of 2.0
Sample problem to demonstrate the effects of decay functions
Facility A has a lower total transformed cost than facility B when a squared power transformation is used.

An exponential decay function type with an impedance parameter of 0.02 will favor nearby demand points, so facility B is the solution facility in this case. (The graphic is omitted, since it would look the same as the linear decay function graphic.)

FacilityTotal cost (Exponential transformation, β = 0.02)Solution facility

A

e0.02*3+e0.02*3+e0.02*5=3.23

B

e0.02*7+e0.02*1+e0.02*1=3.19

Facility B is chosen.

Comparison of costs using an exponential transformation with a parameter of 0.02

β

This property, the decay function parameter value (impedance parameter), allows you to set a parameter, β, for use with the f(cost, β) property. However, when f(cost, β) is set to Linear, this parameter value is ignored, and a value of 1 is used instead. See the f(cost, β) property (above) for more information.

Tip:

Demand points have an ImpedanceParameter property, which, if set, overrides the β property of the analysis layer. You might determine that the decay function parameter should be different for urban and rural residents. You can model this by setting the impedance transformation for the analysis layer to match that of rural residents and setting the impedance transformation for the demand points in urban areas to match that of urbanites.

Market

This property is specific to the Target Market Share problem type. It is the percentage of the total demand weight that you want your solution facilities to capture. The solver chooses the minimum number of facilities required to capture the target market share specified by this numeric value.

Capacity

This property is specific to the Maximize Capacitated Coverage problem type. It is the capacity assigned to all facilities in the analysis. You can override the default capacity on a per-capacity basis by specifying a value in the facility's Capacity field in the Facilities sublayer.

Type

The Type drop-down list is in the Arrive/Depart Time group and is enabled when the cost units are time based. It allows you to choose how to enter a time value. The main reason for setting a specific time and date is to solve the analysis using dynamic traffic conditions, such as from live and predicted traffic flows, if your network data source incorporates that information.

  • Not Using Time Not Using Time—Regardless of whether the network data source includes traffic data, the results are based on static travel times—the travel times on a street don't fluctuate throughout the day. The Time and Date text boxes are disabled.

  • Custom Time & Date Custom Time & Date—You specify the time as a time of day and calendar date. The Time and Date text boxes are enabled for you to enter this information.

  • Today Today—You specify a time, and the day is assumed to be the current date. The Time text box is enabled for you to enter the time of day, and the Date text box is set to Today and is disabled so it can't be changed.

  • Current Date & Time Current Date & Time—When you run the analysis, the time and date are set to the current time and date. This is useful if your network data source is configured with traffic data and you need to know what areas can be reached if drivers departed now. The Time text box is set to Now, and the Date text box is set to Today; both are disabled so they can't be changed.

  • Day of Week Day of Week—You specify a time of day and day of the week. The Time and Date text boxes are enabled for you to enter this information. Set the day of the week by typing one of the following values into the Date text box:

    • Sunday
    • Monday
    • Tuesday
    • Wednesday
    • Thursday
    • Friday
    • Saturday

Output Geometry Linear Shape Type

This control allows you to choose how the output will display in the map. The location-allocation analysis will always solve least-cost paths along the network, but these network paths cannot be displayed in the map. You can choose to represent the output as a straight line if you want to visualize the results in the map, or you can choose to not display any lines at all if you are only interested in the output fields in the Facilities, Demand Points, and Lines class tables.