Methodology

This page explains what the visual computes, the models it rests on, the assumptions it makes and how it was checked, for readers who want to understand a result before they act on it. It describes the approach, not the implementation.

1. The question it answers

Territory design is classically split into two questions (Zoltners & Sinha, 2005): how many salespeople are needed, and which clients each one covers. The visual answers both, in that order, at planning level. Headcount is given per commercial area as a fractional figure — 6.4, not "6 or 7" — so the rounding, and the judgement behind it, stay with you.

2. Workload

Each client's monthly workload is the time spent with it plus the time spent getting to it:

Without visit data every client counts the same, and the result becomes a geographic split of the clients rather than a workload plan. Clients you flag as outliers (isolated clients, by a distance you choose) are left out, for you to decide how to serve them.

3. Travel: a planning estimate

Travel depends on how clients are grouped, and the grouping depends on travel. Planning models break that circle with the continuous approximation of routing (Daganzo, 1984; Ansari et al., 2018): instead of solving a route, they predict its expected length from how many clients there are and how they are spread. The theory goes back to Beardwood, Halton & Hammersley (1959), who showed that the shortest tour through many scattered points grows with the square root of their number times the area they cover.

The visual applies the two classic parts of that approximation to each visit:

• The hop to the next client, from how densely clients are packed around it: short in a town centre, long in the countryside.
• Its share of the day's trip out to the territory and back, shared among the visits that fit in a working day — many in a dense zone, few in a sparse one. The working day follows from the salesperson's monthly hours and working days.

Distances are straight lines multiplied by the road factor you set, and turned into time with the speed you set (one for everyone, or one per client). Published average road-to-straight-line ratios give a starting point — about 1.2 for the United States, 1.3 for India, 1.5 for Mexico and 1.6 for Spain (Ballou, Rahardja & Sakai, 2002; inter-city averages with a wide spread) — but your own ratio, measured on a sample of real trips, is better.

4. Sales-force sizing

The visual applies the workload approach to sales-force sizing (Talley, 1961; Zoltners & Sinha, 2005):

Every client counts: a group of clients too small for a full salesperson — a remote valley, a small island — appears as a fraction of one. Because travel depends on how the area is split, the figure is computed after the territories are built.

5. Commercial areas

Areas are the level at which headcount is decided: a province, a region, a delegation. They follow geography and do not balance hours: an area needing 12 salespeople next to one needing 2 is a correct answer.

• Your own areas. With an Area field, each client goes where your data puts it; the visual never overrides it.
• Automatic areas group nearby clients into the number of areas you ask for, by workload-weighted clustering (in the family of k-means: Lloyd, 1982; Arthur & Vassilvitskii, 2007), so that each area is compact and in one piece.
• Towns and postal codes stay whole. Clients close together are kept in the same area, and with a postal code bound, areas are made of whole postal codes.
• Land borders and islands. An area only joins regions connected by land, so it never reaches across a gulf or the sea; islands and archipelagos get areas of their own.

6. Territories

Inside each area, clients are grouped into territories, one per salesperson, under three rules:

• Never above one salesperson's monthly hours — a hard limit, not a target band. Territories can end short, never long.
• Compact: dense towns are served first and kept together; the balanced partition follows the principle of power diagrams — weighted Voronoi diagrams, whose cells are convex — known to describe balanced clustering (Aurenhammer, 1987; Brieden, Gritzmann & Klemm, 2017), in the tradition of balanced districting (Hess et al., 1965; Hess & Samuels, 1971; Kalcsics, Nickel & Schröder, 2005).
• Never across an area boundary or the sea, and, with a postal code bound, made of whole postal codes, so that a code belongs to one salesperson; only codes with more work than one salesperson are shared.

Each territory has a base, the centre of its workload, from which the day's trip is estimated. Salespeople's home addresses are not used. The same data and parameters always give the same territories.

7. Geography

The visual makes no network requests, so it carries its own map: country borders and first-level regions (states, provinces, departments) for every country, from Natural Earth, simplified to a few kilometres. They are used to place each client in its region, to know which regions share a land border, and to tell islands apart. Natural Earth draws borders as they are controlled on the ground; in disputed regions they may differ from a country's official map.

8. Assumptions and limitations

• No routing and no road network (see the box at the top). Distances are straight lines times the road factor.
• One base per territory, at the centre of its workload, not the salesperson's home.
• Visits are steady and independent: no time windows, weekly patterns or priorities.
• One speed per client (Pro) or one for everyone.
• Areas follow geography, not workload balance.
• Simplified borders decide the region of clients within a few kilometres of a border.
• Size: Power BI limits the memory a visual may use; very large models may not deliver every row.
• A proposal, not a decision: validate a plan with the people who know the territory before acting on it.

9. Validation

Checked on four synthetic datasets of points of sale distributed by population — Spain (40,000 clients, plus a variant with the Balearic and Canary Islands), the United States (30,000), Mexico (20,000) and India (30,000) — including deliberately dirty data (postal codes spanning whole provinces, province labels taken from the nearest city):

10. References

1. Ansari, S., Başdere, M., Li, X., Ouyang, Y., & Smilowitz, K. (2018). Advancements in continuous approximation models for logistics and transportation systems: 1996–2016. Transportation Research Part B, 107, 229–252. doi:10.1016/j.trb.2017.09.019
2. Arthur, D., & Vassilvitskii, S. (2007). k-means++: The advantages of careful seeding. In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '07) (pp. 1027–1035). SIAM.
3. Aurenhammer, F. (1987). Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing, 16(1), 78–96. doi:10.1137/0216006
4. Ballou, R. H., Rahardja, H., & Sakai, N. (2002). Selected country circuity factors for road travel distance estimation. Transportation Research Part A, 36(9), 843–848. doi:10.1016/S0965-8564(01)00044-1
5. Beardwood, J., Halton, J. H., & Hammersley, J. M. (1959). The shortest path through many points. Proceedings of the Cambridge Philosophical Society, 55(4), 299–327. doi:10.1017/S0305004100034095
6. Brieden, A., Gritzmann, P., & Klemm, F. (2017). Constrained clustering via diagrams: A unified theory and its application to electoral district design. European Journal of Operational Research, 263(1), 18–34. doi:10.1016/j.ejor.2017.04.018
7. Daganzo, C. F. (1984). The distance traveled to visit N points with a maximum of C stops per vehicle: An analytic model and an application. Transportation Science, 18(4), 331–350. doi:10.1287/trsc.18.4.331
8. Hess, S. W., Weaver, J. B., Siegfeldt, H. J., Whelan, J. N., & Zitlau, P. A. (1965). Nonpartisan political redistricting by computer. Operations Research, 13(6), 998–1006. doi:10.1287/opre.13.6.998
9. Hess, S. W., & Samuels, S. A. (1971). Experiences with a sales districting model: Criteria and implementation. Management Science, 18(4, Part II), P41–P54. doi:10.1287/mnsc.18.4.P41
10. Kalcsics, J., Nickel, S., & Schröder, M. (2005). Towards a unified territorial design approach — Applications, algorithms and GIS integration. TOP, 13(1), 1–56. doi:10.1007/BF02578982
11. Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129–137. doi:10.1109/TIT.1982.1056489
12. Talley, W. J. (1961). How to design sales territories. Journal of Marketing, 25(3), 7–13. doi:10.1177/002224296102500302
13. Zoltners, A. A., & Sinha, P. (2005). The 2004 ISMS Practice Prize winner—Sales territory design: Thirty years of modeling and implementation. Marketing Science, 24(3), 313–331. doi:10.1287/mksc.1050.0133

11. Data and software credits

• Natural Earth — country and first-level region boundaries. Public domain. Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com.
• Leaflet — map rendering. BSD-2-Clause licence, © Volodymyr Agafonkin.
• Delaunator — triangulation. ISC licence, © Mapbox; author Vladimir Agafonkin.