Retail Site Selection & Spatial Economics
Reilly Retail Breaking-Point & Huff Gravity Formula
Delimit city trade-area boundaries via Converse-Reilly Breaking Point D_B = D_AB / (1 + SQRT(Pop_A / Pop_B)) and compute Huff (1964) probabilistic store patronage shares.
Progress from hard retail trade-area borders (Reilly) to overlapping shopper probabilities (Huff)!
Retail real-estate site-selection teams rely on two complementary spatial gravity models. First, Paul Converse’s (1949) reformulation of William J. Reilly’s (1931) Law of Retail Gravitation locates the 50/50 Trade-Area Breaking Point between City A (Pop_A) and smaller City B (Pop_B) separated by highway distance D_AB at distance from B equal to D_B = D_AB / (1 + SQRT(Pop_A / Pop_B))! Second, David Huff (1964) replaced hard geographic borders with overlapping consumer choice probabilities: a census tract at travel times d_j to stores of floor space S_j visits Store 1 with probability P_1 = (S_1 / d_1^lambda) / SUM_j(S_j / d_j^lambda)!
Verify both models on exact integers! First, for Metro_A Pop_A = 360,000 (B2), Town_B Pop_B = 90,000 (B3, ratio = 4 -> SQRT = 2), and Highway_Distance D_AB = 30.0 km (B4): Town B’s trade-area boundary extends D_B = 30 / (1 + 2) = 10.00 km toward A (giving Metro A 20.00 km!). Second, for a neighborhood choosing between Flagship_Store_1 (S_1 = 60,000 sqft in B5, travel time d_1 = 4 min in B6) and Local_Store_2 (S_2 = 10,000 sqft in B7, d_2 = 2 min in B8) under distance-decay exponent lambda = 2.0 (B9): Store 1 attraction is 60,000 / 16 = 3,750, Store 2 attraction is 10,000 / 4 = 2,500, and Huff Patronage Share is 3,750 / 6,250 = 0.6000 (60.00% capture)!
| Spatial Retail Metric | Formula | Verified Output |
|---|---|---|
| Reilly Breaking Point from Town B (D_B) | 30 / (1 + SQRT(360,000 / 90,000)) | 10.00 km (Metro A = 20.00 km) |
| Flagship Store 1 Gravity Utility (U_1) | 60,000 / (4^2) | 3,750.00 |
| Local Store 2 Gravity Utility (U_2) | 10,000 / (2^2) | 2,500.00 |
| Huff Store 1 Patronage Share (P_1) | 3,750 / (3,750 + 2,500) | 0.6000 (60.00% Market Share) |
Converse-Reilly Trade-Area Breaking Point Distance from B Formula
Validate Pop_A > 0, Pop_B > 0, and inter-city distance D_AB > 0.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Gravity Input", ROUND(B4 / (1 + SQRT(B2 / B3)), 2))Huff (1964) Probabilistic Store Patronage Capture Formula
Validate store sizes S_j > 0, travel times d_j > 0, and friction-of-distance parameter lambda > 0.
=LET(s_1, B5, d_1, B6, s_2, B7, d_2, B8, lm_d, B9, IF(OR(s_1 <= 0, d_1 <= 0, s_2 <= 0, d_2 <= 0, lm_d <= 0), "Invalid Gravity Input", LET(u_1, s_1 / (d_1 ^ lm_d), u_2, s_2 / (d_2 ^ lm_d), ROUND(u_1 / (u_1 + u_2), 4))))Try the example
Use the original values or change them to test your understanding.