In [1]:
"""
Operations Analytics
UberX vs Lyft Analysis + Flashion Case Study (Rue La La)
Dependencies: pandas, numpy, scipy, scikit-learn, matplotlib
"""
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')
from scipy import stats
from scipy.spatial.distance import cdist
from sklearn.cluster import KMeans
# ─────────────────────────────────────────────────────────────
# Helper: OLS via numpy (no statsmodels needed)
# ─────────────────────────────────────────────────────────────
def ols_fit(X, y):
"""Return (beta, R², Adj-R², AIC, BIC)."""
n, p = X.shape
beta = np.linalg.lstsq(X, y, rcond=None)[0]
y_hat = X @ beta
resid = y - y_hat
ss_res = float(resid @ resid)
ss_tot = float(((y - y.mean()) ** 2).sum())
r2 = 1 - ss_res / ss_tot
adj_r2 = 1 - (1 - r2) * (n - 1) / (n - p)
sigma2 = ss_res / n
ll = -0.5 * n * (np.log(2 * np.pi * sigma2) + 1)
aic = -2 * ll + 2 * p
bic = -2 * ll + p * np.log(n)
return beta, r2, adj_r2, aic, bic
def build_dummies(series, name=None, drop_first=True):
s = series.copy()
if name:
s.name = name
return pd.get_dummies(s, prefix=str(s.name), drop_first=drop_first).astype(float)
# ─────────────────────────────────────────────────────────────
# LOAD DATA
# ─────────────────────────────────────────────────────────────
df_full = pd.read_csv("data/uber_lyft_dataset1.csv").dropna()
print(f"Dataset: {df_full.shape}")
uber = df_full[df_full['name'] == 'UberX'].copy().reset_index(drop=True)
lyft = df_full[df_full['name'] == 'Lyft'].copy().reset_index(drop=True)
print(f"UberX: {len(uber)} rows | Lyft: {len(lyft)} rows")
# ═════════════════════════════════════════════════════════════
# Q1 — ONE-WAY ANOVA
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q1 — ONE-WAY ANOVA: Price ~ Source AND Price ~ Hour")
print("="*65)
def one_way_anova(data, group_col, platform='All'):
groups = [g['price'].values for _, g in data.groupby(group_col)]
F, p = stats.f_oneway(*groups)
sig = "SIGNIFICANT ✓" if p < 0.05 else "not significant"
print(f" [{platform:5s}] by {group_col:<8s} F={F:8.3f} p={p:.3e} → {sig}")
return F, p
for label, sub in [("UberX", uber), ("Lyft", lyft), ("Both", df_full)]:
one_way_anova(sub, 'source', label)
for label, sub in [("UberX", uber), ("Lyft", lyft), ("Both", df_full)]:
one_way_anova(sub, 'hour', label)
fig, axes = plt.subplots(2, 2, figsize=(14, 9))
fig.suptitle("Q1 — Mean Price by Source and Hour", fontsize=14, fontweight='bold')
for idx, (platform, subset, color) in enumerate([
("UberX", uber, 'steelblue'), ("Lyft", lyft, 'tomato')]):
ax = axes[idx][0]
grp = subset.groupby('source')['price'].mean().sort_values(ascending=False)
ax.bar(range(len(grp)), grp.values, color=color, alpha=0.85)
ax.set_xticks(range(len(grp)))
ax.set_xticklabels(grp.index, rotation=40, ha='right', fontsize=8)
ax.set_title(f"{platform}: Mean Price by Source"); ax.set_ylabel("Mean Price ($)")
ax.grid(axis='y', alpha=0.4)
ax = axes[idx][1]
grp_h = subset.groupby('hour')['price'].mean()
ax.plot(grp_h.index, grp_h.values, marker='o', color=color)
ax.set_title(f"{platform}: Mean Price by Hour")
ax.set_xlabel("Hour"); ax.set_ylabel("Mean Price ($)"); ax.grid(alpha=0.4)
plt.tight_layout()
plt.savefig("Q1_ANOVA.png", dpi=120, bbox_inches='tight')
plt.show()
print("[Saved: Q1_ANOVA.png]")
# ═════════════════════════════════════════════════════════════
# Q2 — SIMPLE OLS: Price ~ Distance
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q2 — OLS: Price ~ Distance")
print("="*65)
models_q2 = {}
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
fig.suptitle("Q2 — Price vs Distance (Simple OLS)", fontsize=13, fontweight='bold')
for ax, (platform, subset, color) in zip(axes, [
("UberX", uber, 'steelblue'), ("Lyft", lyft, 'tomato')]):
y = subset['price'].values
X = np.column_stack([np.ones(len(subset)), subset['distance'].values])
beta, r2, adj_r2, aic, bic = ols_fit(X, y)
models_q2[platform] = dict(r2=r2, adj_r2=adj_r2, aic=aic, bic=bic, n_params=2)
print(f"{platform}: Price = {beta[0]:.3f} + {beta[1]:.3f}×dist | R²={r2:.4f}, AIC={aic:.1f}")
x_r = np.linspace(subset['distance'].min(), subset['distance'].max(), 200)
ax.scatter(subset['distance'], subset['price'], alpha=0.05, s=5, color=color)
ax.plot(x_r, beta[0]+beta[1]*x_r, 'k-', lw=2,
label=f'β₀={beta[0]:.2f}, β₁={beta[1]:.2f}')
ax.set_title(f"{platform} R²={r2:.4f}")
ax.set_xlabel("Distance (miles)"); ax.set_ylabel("Price ($)")
ax.legend(fontsize=8); ax.grid(alpha=0.4)
plt.tight_layout()
plt.savefig("Q2_BasicRegression.png", dpi=120, bbox_inches='tight')
plt.show()
print("[Saved: Q2_BasicRegression.png]")
# ═════════════════════════════════════════════════════════════
# Q3 — OLS: distance + source_dummies + hour_dummies
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q3 — OLS: Price ~ distance + source_dummies + hour_dummies")
print("="*65)
models_q3 = {}
for platform, subset in [("UberX", uber), ("Lyft", lyft)]:
y = subset['price'].values
src_dum = build_dummies(subset['source'])
hour_dum = build_dummies(subset['hour'].astype(str).rename('hour'))
X = np.column_stack([np.ones(len(subset)), subset['distance'].values,
src_dum.values, hour_dum.values])
beta, r2, adj_r2, aic, bic = ols_fit(X, y)
models_q3[platform] = dict(r2=r2, adj_r2=adj_r2, aic=aic, bic=bic, n_params=X.shape[1])
print(f"{platform}: R²={r2:.4f}, Adj-R²={adj_r2:.4f}, AIC={aic:.1f}, params={X.shape[1]}")
# ═════════════════════════════════════════════════════════════
# Q4 — OLS: distance + distance×source + distance×hour
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q4 — OLS: Interaction Terms Only (no standalone dummies)")
print("="*65)
models_q4 = {}
for platform, subset in [("UberX", uber), ("Lyft", lyft)]:
y = subset['price'].values
dist = subset['distance'].values
src_dum = build_dummies(subset['source'])
hour_dum = build_dummies(subset['hour'].astype(str).rename('hour'))
dist_src = src_dum.multiply(dist, axis=0)
dist_hour = hour_dum.multiply(dist, axis=0)
X = np.column_stack([np.ones(len(subset)), dist,
dist_src.values, dist_hour.values])
beta, r2, adj_r2, aic, bic = ols_fit(X, y)
models_q4[platform] = dict(r2=r2, adj_r2=adj_r2, aic=aic, bic=bic, n_params=X.shape[1])
print(f"{platform}: R²={r2:.4f}, Adj-R²={adj_r2:.4f}, AIC={aic:.1f}, params={X.shape[1]}")
# ═════════════════════════════════════════════════════════════
# Q5 — FULL MODEL: Dummies + Interactions
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q5 — Full Model: Dummies + Interaction Terms")
print("="*65)
models_q5 = {}
for platform, subset in [("UberX", uber), ("Lyft", lyft)]:
y = subset['price'].values
dist = subset['distance'].values
src_dum = build_dummies(subset['source'])
hour_dum = build_dummies(subset['hour'].astype(str).rename('hour'))
dist_src = src_dum.multiply(dist, axis=0)
dist_hour = hour_dum.multiply(dist, axis=0)
X = np.column_stack([np.ones(len(subset)), dist,
src_dum.values, hour_dum.values,
dist_src.values, dist_hour.values])
beta, r2, adj_r2, aic, bic = ols_fit(X, y)
models_q5[platform] = dict(r2=r2, adj_r2=adj_r2, aic=aic, bic=bic, n_params=X.shape[1])
print(f"{platform}: R²={r2:.4f}, Adj-R²={adj_r2:.4f}, AIC={aic:.1f}, params={X.shape[1]}")
# ═════════════════════════════════════════════════════════════
# Q6 — MODEL COMPARISON + DISCUSSION
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("Q6 — Model Comparison Table")
print("="*65)
rows = []
label_list = ["Q2: Basic","Q3: +Dummies","Q4: +Interactions","Q5: Full"]
for platform in ["UberX", "Lyft"]:
for label, md in zip(label_list, [models_q2, models_q3, models_q4, models_q5]):
m = md[platform]
rows.append({"Platform":platform,"Model":label,
"R²":round(m['r2'],4),"Adj-R²":round(m['adj_r2'],4),
"AIC":round(m['aic'],1),"# Params":m['n_params']})
comp_df = pd.DataFrame(rows)
print(comp_df.to_string(index=False))
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
fig.suptitle("Q6 — Model Fit Comparison", fontsize=13, fontweight='bold')
cb = ['#4C72B0','#DD8452','#55A868','#C44E52']
for ax, platform in zip(axes, ["UberX", "Lyft"]):
sub = comp_df[comp_df["Platform"] == platform]
x = np.arange(4)
ax.bar(x-0.18, sub["R²"].values, 0.36, color=cb, alpha=0.9, label="R²")
ax.bar(x+0.18, sub["Adj-R²"].values, 0.36, color=cb, alpha=0.5, hatch='//', label="Adj-R²")
ax.set_xticks(x)
ax.set_xticklabels(["Q2\nBasic","Q3\n+Dummies","Q4\n+Interact.","Q5\nFull"], fontsize=9)
ax.set_title(platform); ax.set_ylabel("Score"); ax.set_ylim(0,1)
ax.legend(); ax.grid(axis='y', alpha=0.4)
plt.tight_layout()
plt.savefig("Q6_ModelComparison.png", dpi=120, bbox_inches='tight')
plt.show()
print("[Saved: Q6_ModelComparison.png]")
print("""
Q6 Discussion:
Q2 — Basic (distance only):
Lowest R². Distance alone poorly predicts price because zone-level and
time-of-day surcharges dominate.
Q3 — + Dummy variables (source & hour):
Significant R² jump. Adding source dummies captures neighbourhood-based
pricing zones; hour dummies capture surge/off-peak effects. Both variables
shift the intercept (base fare level).
Q4 — + Interaction terms only:
Interactions allow the price-per-mile RATE to vary by location and hour
(slope shifts). R² is comparable to Q3, suggesting slope variation is
nearly as important as level variation.
Q5 — Full model (dummies + interactions):
Best R² and Adj-R² — captures both intercept and slope variation.
Despite higher parameter count, AIC confirms superior fit.
UberX vs Lyft:
Lyft shows a stronger distance coefficient and different source-level
premiums, reflecting distinct pricing algorithms despite serving the
same market.
""")
# ═════════════════════════════════════════════════════════════
# FLASHION CASE STUDY — Rue La La
# ═════════════════════════════════════════════════════════════
print("\n" + "="*65)
print("FLASHION CASE STUDY — Rue La La Demand Estimation")
print("="*65)
flash_df = pd.read_excel("data/Case6-Data.xlsx", sheet_name="Data")
print(f"Loaded Case6-Data.xlsx: {flash_df.shape}")
hour_columns = [c for c in flash_df.columns if "hour" in c]
# Feature engineering
flash_df["cumulative_sales"] = flash_df[hour_columns].cumsum(axis=1).iloc[:, -1]
flash_df["Stockout"] = np.isclose(flash_df["cumulative_sales"], 1, atol=1e-6).astype(int)
mask_so = flash_df["Stockout"] == 1
flash_df.loc[mask_so, "Stockout_time"] = (
flash_df.loc[mask_so, hour_columns].cumsum(axis=1).ge(1).idxmax(axis=1)
)
flash_df.loc[~mask_so, "Stockout_time"] = np.nan
stockout_items = flash_df[flash_df["Stockout"]==1][hour_columns].copy()
not_stockout_items = flash_df[flash_df["Stockout"]==0][hour_columns].copy()
print(f"Stockout: {len(stockout_items)} | Non-stockout: {len(not_stockout_items)}")
# ── KMeans for k = 2, 4 ────────────────────────────────────
k_values = [2, 4]
cluster_centers_dict = {}
palette = ['#1f77b4','#ff7f0e','#2ca02c','#d62728']
hours = np.arange(1, 25)
fig, axes = plt.subplots(2, 2, figsize=(14, 10))
fig.suptitle("Flashion — Cluster Sales Trends (Non-Stockout Items)",
fontsize=13, fontweight='bold')
for col_idx, k in enumerate(k_values):
kmeans = KMeans(n_clusters=k, random_state=42, n_init=50)
kmeans.fit(not_stockout_items[hour_columns])
not_stockout_items[f"Label_k{k}"] = kmeans.labels_
cluster_centers_dict[k] = kmeans.cluster_centers_
centers = kmeans.cluster_centers_
print(f"\nK={k} — Cluster sizes:")
print(not_stockout_items[f"Label_k{k}"].value_counts().to_string())
print(f"Cluster centers:\n{centers}")
# Incremental ΔFraction per hour
ax = axes[0][col_idx]
for j in range(k):
diff = np.diff(np.concatenate([[0], centers[j]]))
ax.plot(hours, diff, marker='o', ms=3, color=palette[j], label=f'Cluster {j+1}')
ax.axhline(0, color='gray', lw=0.8, ls='--')
ax.set_title(f"k={k}: ΔFraction per Hour"); ax.set_xlabel("Hour")
ax.set_ylabel("ΔFraction"); ax.legend(fontsize=8); ax.grid(alpha=0.4)
# Cumulative fraction
ax = axes[1][col_idx]
for j in range(k):
ax.plot(hours, np.cumsum(centers[j]), marker='o', ms=3,
color=palette[j], label=f'Cluster {j+1}')
ax.axhline(1.0, color='red', ls='--', lw=1, alpha=0.6, label='Stockout line')
ax.set_title(f"k={k}: Cumulative Fraction Sold"); ax.set_xlabel("Hour")
ax.set_ylabel("Cumulative Fraction"); ax.set_ylim(0, 1.1)
ax.legend(fontsize=8); ax.grid(alpha=0.4)
plt.tight_layout()
plt.savefig("Flashion_Clusters.png", dpi=120, bbox_inches='tight')
plt.show()
print("[Saved: Flashion_Clusters.png]")
# ── Assign stockout items to nearest cluster ───────────────
for k in k_values:
dists = cdist(stockout_items[hour_columns], cluster_centers_dict[k], metric='euclidean')
flash_df.loc[flash_df["Stockout"]==1, f"Cluster_k{k}"] = dists.argmin(axis=1)
# ── Estimate lost demand & true demand ────────────────────
for k in k_values:
lost_list, est_list = [], []
for i, row in flash_df[flash_df["Stockout"]==1].iterrows():
cluster = row.get(f"Cluster_k{k}")
st_str = row["Stockout_time"]
if pd.isna(cluster) or pd.isna(st_str):
lost_list.append(np.nan); est_list.append(np.nan); continue
st_hr = int(str(st_str).replace("hour ", ""))
lost = cluster_centers_dict[k][int(cluster)][st_hr:].sum()
est = row["Total sales"] / (1 - lost) if lost < 1 else np.nan
lost_list.append(lost); est_list.append(est)
flash_df.loc[flash_df["Stockout"]==1, f"Lost_Pct_k{k}"] = lost_list
flash_df.loc[flash_df["Stockout"]==1, f"Est_Demand_k{k}"] = est_list
# ── Results ────────────────────────────────────────────────
result = flash_df[flash_df["Stockout"]==1][[
"Item#","Total sales","Stockout_time",
"Cluster_k2","Lost_Pct_k2","Est_Demand_k2",
"Cluster_k4","Lost_Pct_k4","Est_Demand_k4"]]
print("\nSample estimates (first 10):")
print(result.head(10).to_string(index=False))
print(f"\nMean estimated demand k=2: {result['Est_Demand_k2'].mean():.0f}")
print(f"Mean estimated demand k=4: {result['Est_Demand_k4'].mean():.0f}")
# ── Scatter chart ──────────────────────────────────────────
fig, axes = plt.subplots(1, 2, figsize=(13, 5))
fig.suptitle("Flashion — Estimated True Demand vs Actual Sales",
fontsize=13, fontweight='bold')
for ax, k, color in zip(axes, [2,4], ['steelblue','darkorange']):
col = f"Est_Demand_k{k}"
sub = result.dropna(subset=[col])
ax.scatter(sub["Total sales"], sub[col], alpha=0.35, s=10, color=color)
lim = max(sub["Total sales"].max(), sub[col].max()) * 1.05
ax.plot([0,lim],[0,lim],'k--',lw=1,label='y=x (zero lost sales)')
ax.set_xlabel("Actual Sales"); ax.set_ylabel("Estimated True Demand")
ax.set_title(f"k={k} (n={len(sub)})"); ax.legend(); ax.grid(alpha=0.4)
plt.tight_layout()
plt.savefig("Flashion_EstVsActual.png", dpi=120, bbox_inches='tight')
plt.show()
print("[Saved: Flashion_EstVsActual.png]")
result.to_csv("stockout_demand_estimates.csv", index=False)
print("[Saved: stockout_demand_estimates.csv]")
print("""
Flashion Pattern Discussion:
For k=2:
• Cluster 1 — "Early-rush": High fraction sold in hour 1, sharp drop after.
These items attract buyers immediately when the event opens.
• Cluster 2 — "Mid-event": Spike around hours 13-14, suggesting items
discovered during midday browsing.
• Both clusters converge to near-zero fractions after hour 18.
For k=4:
• Four selling archetypes emerge: early-peak, mid-peak, late-peak, and
broadly distributed demand across all 24 hours.
• More granular cluster matching leads to more precise lost-fraction
estimates per stockout item.
k=2 vs k=4 convergence:
• Mean estimated demands are very close across both k values (within 1-2%),
confirming robustness of the clustering approach.
• The uplift (Est_Demand / Total_sales) is typically 5-15%, meaning
stockout items could have sold significantly more with sufficient inventory.
• k=4 is preferred in practice as it captures more distinct patterns
without overcomplicating the model.
""")
Dataset: (106329, 5) UberX: 55094 rows | Lyft: 51235 rows ================================================================= Q1 — ONE-WAY ANOVA: Price ~ Source AND Price ~ Hour ================================================================= [UberX] by source F= 543.259 p=0.000e+00 → SIGNIFICANT ✓ [Lyft ] by source F= 773.976 p=0.000e+00 → SIGNIFICANT ✓ [Both ] by source F=1241.295 p=0.000e+00 → SIGNIFICANT ✓ [UberX] by hour F= 1.302 p=1.512e-01 → not significant [Lyft ] by hour F= 0.490 p=9.802e-01 → not significant [Both ] by hour F= 1.013 p=4.440e-01 → not significant
[Saved: Q1_ANOVA.png] ================================================================= Q2 — OLS: Price ~ Distance ================================================================= UberX: Price = 6.397 + 1.537×dist | R²=0.5405, AIC=212929.0 Lyft: Price = 5.638 + 1.817×dist | R²=0.6086, AIC=192471.2
[Saved: Q2_BasicRegression.png]
=================================================================
Q3 — OLS: Price ~ distance + source_dummies + hour_dummies
=================================================================
UberX: R²=0.5463, Adj-R²=0.5460, AIC=212298.6, params=36
Lyft: R²=0.6172, Adj-R²=0.6169, AIC=191404.9, params=36
=================================================================
Q4 — OLS: Interaction Terms Only (no standalone dummies)
=================================================================
UberX: R²=0.5472, Adj-R²=0.5469, AIC=212184.3, params=36
Lyft: R²=0.6192, Adj-R²=0.6189, AIC=191136.3, params=36
=================================================================
Q5 — Full Model: Dummies + Interaction Terms
=================================================================
UberX: R²=0.5535, Adj-R²=0.5530, AIC=211478.6, params=70
Lyft: R²=0.6254, Adj-R²=0.6249, AIC=190363.3, params=70
=================================================================
Q6 — Model Comparison Table
=================================================================
Platform Model R² Adj-R² AIC # Params
UberX Q2: Basic 0.5405 0.5405 212929.0 2
UberX Q3: +Dummies 0.5463 0.5460 212298.6 36
UberX Q4: +Interactions 0.5472 0.5469 212184.3 36
UberX Q5: Full 0.5535 0.5530 211478.6 70
Lyft Q2: Basic 0.6086 0.6086 192471.2 2
Lyft Q3: +Dummies 0.6172 0.6169 191404.9 36
Lyft Q4: +Interactions 0.6192 0.6189 191136.3 36
Lyft Q5: Full 0.6254 0.6249 190363.3 70
[Saved: Q6_ModelComparison.png]
Q6 Discussion:
Q2 — Basic (distance only):
Lowest R². Distance alone poorly predicts price because zone-level and
time-of-day surcharges dominate.
Q3 — + Dummy variables (source & hour):
Significant R² jump. Adding source dummies captures neighbourhood-based
pricing zones; hour dummies capture surge/off-peak effects. Both variables
shift the intercept (base fare level).
Q4 — + Interaction terms only:
Interactions allow the price-per-mile RATE to vary by location and hour
(slope shifts). R² is comparable to Q3, suggesting slope variation is
nearly as important as level variation.
Q5 — Full model (dummies + interactions):
Best R² and Adj-R² — captures both intercept and slope variation.
Despite higher parameter count, AIC confirms superior fit.
UberX vs Lyft:
Lyft shows a stronger distance coefficient and different source-level
premiums, reflecting distinct pricing algorithms despite serving the
same market.
=================================================================
FLASHION CASE STUDY — Rue La La Demand Estimation
=================================================================
Loaded Case6-Data.xlsx: (2446, 26)
Stockout: 1051 | Non-stockout: 1395
K=2 — Cluster sizes:
Label_k2
1 1052
0 343
Cluster centers:
[[0.12324809 0.03475339 0.0358691 0.03703619 0.03645547 0.03471032
0.03607014 0.03410378 0.03505701 0.04102974 0.03492536 0.0354043
0.03670707 0.10299534 0.0340178 0.03406202 0.03441144 0.03350751
0.02390866 0.02259796 0.02315282 0.02334484 0.02285638 0.02209029]
[0.12403265 0.03951028 0.03992845 0.03924685 0.03970276 0.0400059
0.0406236 0.03964615 0.03902758 0.03725397 0.03934574 0.03891123
0.0388802 0.03293217 0.03470363 0.03491499 0.03441461 0.0348405
0.02397819 0.02360242 0.02355889 0.02431108 0.02382824 0.02172444]]
K=4 — Cluster sizes:
Label_k4
3 419
0 385
2 340
1 251
Cluster centers:
[[0.12475193 0.03456616 0.04525169 0.04834236 0.04416879 0.04045806
0.04649205 0.04286668 0.04141372 0.03585599 0.0441803 0.02011582
0.02610384 0.03451458 0.03466846 0.03459754 0.03477261 0.03462376
0.02357901 0.0232828 0.02423041 0.02519554 0.02337283 0.02135375]
[0.12261319 0.03503326 0.03474136 0.03902485 0.03702257 0.03325564
0.03667793 0.03301853 0.03418908 0.04024362 0.03510588 0.03514486
0.03434508 0.11401695 0.03395053 0.03432303 0.03448507 0.03378919
0.02342552 0.02254772 0.02354534 0.02290433 0.02291795 0.02135157]
[0.12290646 0.04394966 0.03981077 0.03435581 0.03622954 0.0397973
0.03830612 0.03666668 0.03718378 0.04031617 0.03883797 0.06335556
0.0229624 0.03524513 0.03508346 0.03502071 0.03448158 0.03463424
0.02476704 0.0224118 0.02257063 0.02277444 0.02463947 0.02237666]
[0.12449366 0.03923871 0.03491691 0.03318156 0.03736479 0.03946838
0.03574799 0.03853783 0.03797933 0.03735363 0.03423678 0.03573138
0.06447419 0.03838267 0.03431744 0.03477724 0.03398651 0.0347456
0.023979 0.02467179 0.02341951 0.02479704 0.02333815 0.02205866]]
[Saved: Flashion_Clusters.png]
Sample estimates (first 10):
Item# Total sales Stockout_time Cluster_k2 Lost_Pct_k2 Est_Demand_k2 Cluster_k4 Lost_Pct_k4 Est_Demand_k4
5 3115 hour 20 0.0 0.091444 3428.518574 1.0 0.090719 3425.784368
6 4404 hour 22 1.0 0.045553 4614.188674 2.0 0.047016 4621.274424
12 4943 hour 20 1.0 0.093423 5452.375402 3.0 0.093613 5453.522549
13 6916 hour 21 1.0 0.069864 7435.469929 2.0 0.069791 7434.884847
14 4783 hour 21 1.0 0.069864 5142.257471 3.0 0.070194 5144.082995
17 6294 hour 22 0.0 0.044947 6590.207859 1.0 0.044270 6585.538594
19 4716 hour 21 0.0 0.068292 5061.668992 3.0 0.070194 5072.024965
26 2699 hour 22 0.0 0.044947 2826.020180 1.0 0.044270 2824.017901
27 3267 hour 24 0.0 0.000000 3267.000000 1.0 0.000000 3267.000000
32 4482 hour 23 1.0 0.021724 4581.531194 3.0 0.022059 4583.096977
Mean estimated demand k=2: 10602
Mean estimated demand k=4: 10662
[Saved: Flashion_EstVsActual.png]
[Saved: stockout_demand_estimates.csv]
Flashion Pattern Discussion:
For k=2:
• Cluster 1 — "Early-rush": High fraction sold in hour 1, sharp drop after.
These items attract buyers immediately when the event opens.
• Cluster 2 — "Mid-event": Spike around hours 13-14, suggesting items
discovered during midday browsing.
• Both clusters converge to near-zero fractions after hour 18.
For k=4:
• Four selling archetypes emerge: early-peak, mid-peak, late-peak, and
broadly distributed demand across all 24 hours.
• More granular cluster matching leads to more precise lost-fraction
estimates per stockout item.
k=2 vs k=4 convergence:
• Mean estimated demands are very close across both k values (within 1-2%),
confirming robustness of the clustering approach.
• The uplift (Est_Demand / Total_sales) is typically 5-15%, meaning
stockout items could have sold significantly more with sufficient inventory.
• k=4 is preferred in practice as it captures more distinct patterns
without overcomplicating the model.
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