dynamic-pricing-c02.py

T = 24 * 1                              # time step is one hour, flash offering for 1 day 
m = 4                                   # not more than 4 price updates

def logx(x, n):                         # iterative logarithm function
    for i in range(0, n): x = math.log(x) if x > 0 else 0
    return x

def intervals(m, T, scale):             # generate a price schedule vector
    mask = []
    for i in range(1, m):
        mask.extend( np.full(scale * math.ceil(logx(T, m - i)), i - 1) )
    return np.append(mask, np.full(T - len(mask), m - 1))

tau = 0                                 # start time of the current interval
p = h_vec[0]['p_opt']                   # initial price

t_mask = intervals(m, T, 2)
h_vec = demand_hypotheses(...)

hist_d = []
for t in range(0, T - 1):               # simulation loop
    realized_d = sample_actual_demand(p)
    hist_d.append(realized_d)
    
    if( t_mask[t] != t_mask[t + 1] ):   # end of the interval
        interval_mean_d = np.mean( hist_d[tau : t + 1] )
        
        min_dist = float("inf")
        for h in h_vec:                 # search for the best hypothesis
            dist = abs(interval_mean_d - h['d'](p))
            if(dist < min_dist):
                min_error = error
                h_opt = h
                
        p = h_opt['p_opt']              # set price for the next interval
        tau = t + 1                     # switch to the next interval