def prob_3():
T, C, e_c, t, p_mu, p_var = problem_data.hw5_p3_data()
n = C + 1
m = 2
p = 1
f = get_f(n, m, p)
g = get_g(n, m, T, p_mu, e_c)
v_final = get_v_final(n)
w_dist = np.array([1])
# part a
pol_a, v_a = utils_mdp.value(f, g, v_final, w_dist, T, g_is_time_dependent=True)
utils_io.label('5.3a')
print_cost(v_a, 'part a')
job_times = get_schedule(pol_a)
p_mu_normal = get_underlying_normal_mu(p_mu, p_var)
p_var_normal = get_underlying_normal_var(p_mu, p_var)
plot_cost_histogram(job_times, p_mu, p_var, e_c)
# part b
price_grid_dim = 10
price_grid = get_prices_over_grid(price_grid_dim, p_mu_normal, p_var_normal)
g_w_known = get_g_w_known(n, m, T, price_grid, p_mu, e_c)
price_grid_dist = np.ones(len(price_grid)) / len(price_grid)
f_w_known = f.repeat(price_grid_dim).reshape([n, m, price_grid_dim, 1])
pol_b, v_b = utils_mdp.value_info_pat(f_w_known, g_w_known, v_final, price_grid_dist, w_dist, T, g_is_time_dependent=True)
utils_io.label('5.3b')
print_cost(v_b, 'part b')
plot_cost_histogram_real_time(pol_b, price_grid, e_c)
def prob_1():
d_t_dist, p_fixed, p_whole, p_disc, u_disc, s_lin, s_quad, p_rev, p_unmet, p_sal, T, C, D, q_0 = problem_data.hw5_p1_data()
n = C + 2 # 0, 1, ..., C plus a dummy state
m = C + 1 # 0, 1, ..., C
p = len(d_t_dist)
f = get_f(n, m, p)
g_order = get_g_order(n, m, p_fixed, p_whole, p_disc, u_disc) # n by m
g_store = get_g_store(n, s_lin, s_quad) # n
g_rev = get_g_rev(n, m, p, p_rev) # n by m by p
g_unmet = get_g_unmet(n, m, p, p_unmet)
g_sal = get_g_sal(n, p_sal)
g_total = get_g_total(g_order, g_store, g_rev, g_unmet)
pol, v = utils_mdp.value(f, g_total, g_sal, d_t_dist, T, g_is_w_dependent=True)
utils_io.label('5.1a')
print 'j_star: ', v[q_0, 0]
# part b; yes the optimal policy converges; for all but the last two time periods it is optimal to buy 7 when x = 0,
# buy 5 when x = 1, and buy 0 otherwise
ax = pd.DataFrame(pol).T.plot(title='5.1b: Optimal Policy for various current inventory values (most = 0)', legend=True)
ax.set_xlabel('time')
ax.set_ylabel('Number of items to buy')
plt.ion()
part_c(pol, g_order, g_store, g_rev, g_unmet, g_sal, q_0, d_t_dist)
