Lab Exercise 7

Lab Exercise 7 Location Selection Problems ‘When selecting a location for a new facility, planners need some metric for evaluating how good any particular location is. One of the most widely-used metrics is distance, which most commonly measures the distance from the new location to its customers, its suppliers, or both. Another option is using gravity models that, essentially, measure the total "attractive force" of a potential location to the entire set of customers. In this exercise, we will apply three different models to location selection problems. These models all assume a known set of demand data, which are contained in the "DemandData.xlsx" file. 7.1 Distance Models We'll start with distance models that measure the total distance between a business location and the distribution of expected demand. These models assume that distance is a strong factor in customer choice; travel costs would be incurred when customers travel to the facility, or service providers travel to customers, or a physical product is delivered to customers. In all cases, the goal is to minimize these total travel costs, which vary depending on whether travel is unrestricted or limited to a rectangular road grid. Distance models may be implemented with weighted or unweighted customer demand. In the unweighted models, customers are considered to be undifferentiated and, accordingly, the location with the smallest sum of distances is considered to be the best. In the weighted models, customers are differentiated. For example, some might buy more often, in greater quantities, or more profitable items. The weighted approach is also suitable for aggregate demand, like the total customers in a zip code. The two distance models we consider are: o Euclidean: This model uses the total straight-line distances between all customers and the business location. For a customer at (x. y.) and a potential operation location (xo, ), the distance between them is \/(x, — X0)? + (¥ — ¥0)?. The Euclidean model is appropriate when customers can travel reasonably directly to the business. e Metropolitan model: This model uses the distances between the x- and y-coordinates of each customer-location pair. For a customer at (xc,yc) and a potential operation location (xo, ¥o), the distance between them is simply | x. — xo | + | yc — ¥o |. The metropolitan model is appropriate when all travel is confined to east-west or north-south roads, which is reasonably accurate for many cities in the United States. Additionally, more sophisticated models (not considered here) might also consider travel time variations, alternate travel modes (like walking or using public transportation), or route selection (as the most direct route might not be the fastest). Still, the general principle of choosing the location with the lowest total travel costs remains the same. 7.1.1 Euclidean Models Open the DemandData file to the "Euclidean" worksheet. There are 1200 customer demand data points (which might be derived from past purchase activity, demographic predictors of 139