Abstract
There is a substantial theoretical literature on the location of retail facilities in space assuming that the spatial demand curve is known, or that the ideal data needed to estimate such a curve is available. This study shows how to implement a formal location analysis for a retail activity (postal services) when all that is known is revenue of currently operating facilities. Further complications, such as the delivery of retail services through two different types of outlets are also accommodated by the method. In the end, it is possible to implement a formal business model for the delivery of retail postal services that allows the user to simulate the consequences of dramatic changes in the way that those services are supplied to the public.
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Notes
- 1.
The retail postal store is commonly known as a main post office, branch, or station. It provides a full range of postal services.
- 2.
For facilities that are connected to the Point Of Sale (POS) system, a window is a register that is generating significant amounts of revenue. The ability to observe revenue generation at the individual register level is a major advantage in the calibration of cost functions. This will be discussed in some detail below.
- 3.
Employees who staff windows have other duties. Some of these are directly related to revenue generation, handling incoming mail. Others may involve sorting mail for delivery. These issues will be discussed later in this chapter.
- 4.
- 5.
- 6.
There are technical reasons for this result that need not concern us here.
- 7.
The emphasis here is on operating inputs and operating costs, and general and administrative costs are ignored.
- 8.
- 9.
The analysis relies on the assumption that the non-register activities of employees observed in the data do not vary systematically with the number of windows. Estimation of equations designed to explain the number of retail employees consistently revealed that the number of windows is the dominant factor determining employment. To the extent that this is not true, some adjustment of the relation between size and labor cost attributed to revenue generation is needed.
- 10.
Equation (10.15) relates to the function in (10.3) as L = h(w) = φ(WA)χ/A
- 11.
- 12.
At the same time, USPS has standards for labor productivity that relate window operating time to revenue. Taken together, these standards would allow one to work backwards from retail revenue expectations for each facility to the size of facility needed to meet those expectations.
- 13.
The possibility of a corner solution at r = 0 is not important here. As a practical matter, solutions for sufficiently small radius are not feasible because they would imply operation with fractional windows and employees. There is a minimum size of feasible facility due to the need to have at least one window and retail worker.
- 14.
A variety of efforts to customize the estimation to differences in local characteristics that might influence transportation costs have demonstrated some promise but are not discussed here in order to focus on the main elements of the calibration effort.
- 15.
The index I P is 0 when there is 0 private mail employment in the service area of the facility, 1 if employment is between > 0 and < 10, 2 if employment is at least 10 and < 20, 3 if employment is at least 20 and < 30, etc. Similarly, the I C index is 0 if there are 0 competitors in the service area, 1 if there is 1 competitor, 2 if there are 2 competitors, 3 if there are 3–5 competitors, and 4 if there are 5 or more competitors.
- 16.
This equation was estimated using 21,898 observations with F(11, 21,886) = 38,000. The t-ratios of the estimated coefficients were all larger than 4.0.
- 17.
It would also be useful to consider the precise shape of the market area.
- 18.
The cost function used in the model is based on x-efficiency in that it takes the current rules and procedures for operating postal stores as given. The term “technical efficiency” used here is based on x-efficiency. It may be that different work rules or ways of deploying labor and capital, perhaps on-line retail aids, could raise output per facility. These innovations are not considered here, although they could be added to the model easily by recalibrating the cost functions.
- 19.
The pattern of revenue per window was also tested for the two high demand weeks, and the small increase in revenue per window with number of windows was observed.
- 20.
A further check on the calibration of revenue per window was done by using data from the USPS Window Operations Survey (WOS) for FY 2008. The USPS has a standard for time per transaction that determines the hours “earned” at a facility window. At facilities reporting actual hours equal to earned hours, the average annual revenue per hour of actual window operation was computed and, when this was multiplied by annual hours per window, the average annual revenue per full time window in operation at these facilities was found to be $ 642,720, well above the $ 400,000 set as efficient revenue per window in this model calibration. Evidently the standard for technically efficient window operation adopted for calibrating the cost function is not particularly rigorous compared to USPS standards for earned hours.
- 21.
This does not mean that the employees in 1 month were the same as those in another month. The employee counts were based on a single week in each month. It does mean that the number of retail workers counted in each of the 3 months was constant.
- 22.
The 3423 also reflects the number of facilities with sufficiently complete data to be used in computation of characteristics of the actual condition of facilities in this group.
- 23.
Specifically, average facility size for those facilities with < 20,000 square feet is 7000 square feet. Larger facilities likely include significant mail processing and/or vehicle storage and maintenance activities.
- 24.
Note that predicted revenue at a radius of 4.5 miles is much larger than actual revenue. This illustrates the difficulty of applying the demand model to large diverse areas and also may point to a further problem in revenue generation in low demand density area.
- 25.
The CPU should not be confused with stamps sold on consignment by a range of ordinary retailers who do not provide mailing services.
- 26.
There is a substantial annual birth and death rate for CPUs both due to economic forces and changes in the business model of the retailer hosting the operation.
- 27.
One complication was the case in which a CPU appeared to fall within the geographic market area of more than one postal store. In this case, the CPU was shared out to the market area proportionally based on distance from each of the postal stores.
- 28.
Of course market size falls significantly with density ranging from 5.2 miles at the lowest density to 1.4 miles for the highest density areas. The share of revenue going to the CPU also increases with market radius based on the second parameter in the CPU revenue equation.
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Yezer, A., Gillula, J. (2015). Modeling the Location of Retail Facilities: An Application to the Postal Service. In: Eiselt, H., Marianov, V. (eds) Applications of Location Analysis. International Series in Operations Research & Management Science, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-20282-2_10
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