alkosto-wait-optimizer

name	alkosto-wait-optimizer
description	Estimate optimal waiting time for Alkosto's "every 25/50 customers" promotion using either checkout-flow observations or winner announcement timestamps. Use when the user asks how long to wait, wants a probability-based cutoff, or needs a fast in-store decision rule with uncertainty handling.

Alkosto Wait Optimizer

Use this skill to estimate how long to wait for the next promotion winner event.

Workflow

1. Choose one mode:

• purchase_rate: user observed purchases per minute in one or more lanes.
• winner_timestamps: user logged winner announcement times.

2. Set threshold K:

• K = 25 for Monday-Friday.
• K = 50 for Saturday/Sunday/holiday.

3. Compute and return:

• Mean interval between winner events.
• Expected wait from "now".
• Practical wait cutoff (optimal_wait_minutes).
• Probability of a winner event within cutoff.
• "Re-measure" rule if no event happens before cutoff.

4. If user provides time_value_per_minute and expected_bonus_value, include expected-value vs time-cost guidance.

Mode A: purchase_rate

Collect:

• observed_purchases
• observed_minutes
• observed_lanes
• Optional: total_open_lanes
• model: global or per_lane

Formulas:

• lambda_obs = observed_purchases / observed_minutes
• If global and total_open_lanes exists: lambda_est = lambda_obs * (total_open_lanes / observed_lanes)
• If per_lane: lambda_est = lambda_obs / observed_lanes
• Conservative rate: lambda_cons = lambda_est * (1 - confidence_buffer)
• Winner interval: T = K / lambda_cons
• If arrival is random in cycle: E(wait_to_next) = T / 2
• Default cutoff: optimal_wait = min(max_wait_minutes, target_hit_probability * T)

Decision rule:

• If no winner event by optimal_wait, re-measure for 2 minutes and recalculate.

Mode B: winner_timestamps

Collect:

• Ordered timestamps (HH:MM[:SS] or ISO datetimes).
• Optional elapsed_since_last_winner_minutes.

Compute:

• Intervals: delta_i = t_i - t_(i-1)
• mu = mean(delta_i)
• sigma = stdev(delta_i)
• cv = sigma / mu

Cadence model:

• cv < 0.4: regular
• 0.4 <= cv <= 0.7: mixed
• cv > 0.7: random

Wait estimate:

• regular: remaining ~ max(mu - elapsed, 0)
• random (exponential): use P(event <= W) = 1 - exp(-W / mu), and W_target = -mu * ln(1 - target_hit_probability)
• mixed: average regular and random estimates.

Decision rule:

• If no event by optimal_wait, capture 2-3 more timestamps and recalculate.

Script

Use scripts/calc_wait.py for deterministic calculations:

python3 scripts/calc_wait.py --input-json '{"mode":"purchase_rate","is_weekend_or_holiday":true,"model":"global","observed_purchases":5,"observed_minutes":2,"observed_lanes":5,"total_open_lanes":15}'

python3 scripts/calc_wait.py --input-json '{"mode":"winner_timestamps","winner_timestamps":["12:10:15","12:27:40","12:46:05","13:02:20"],"elapsed_since_last_winner_minutes":6}'

Return concise outputs and state assumptions clearly when data is sparse.