我正在尝试在 Dynamic room pricing model for hotel revenue management systems 上构建白皮书的实现。如果此链接将来失效，我将在此处粘贴相关部分:
到目前为止，我目前的实现非常严重，因为我真的不完全理解如何求解非线性最大化方程。
# magical lookup table that returns demand based on those inputs
# this will eventually be a db lookup against past years rental activity and not hardcoded to a specific value
def demand(dateFirstNight, duration):
return 1
# magical function that fetches the price we have allocated for a room on this date to existing customers
# this should be a db lookup against previous stays, and not hardcoded to a specific value
def getPrice(date):
return 75
# Typical room base price
# Defined as: Nominal price of the hotel (usually the average historical price)
nominalPrice = 89
# from the white paper, but perhaps needs to be adjusted in the future using the methods they explain
priceElasticity = 2
# this is an adjustable constant it depends how far forward we want to look into the future when optimizing the prices
# likely this will effect how long this will take to run, so it will be a balancing game with regards to accuracy vs runtime
numberOfDays = 30
def roomsAlocated(dateFirstNight, duration)
roomPriceSum = 0.0
for date in range(dateFirstNight, dateFirstNight+duration-1):
roomPriceSum += getPrice(date)
return demand(dateFirstNight, duration) * (roomPriceSum/(nominalPrice*duration))**priceElasticity
def roomsReserved(date):
# find all stays that contain this date, this
def maximizeRevenue(dateFirstNight):
# we are inverting the price sum which is to be maximized because mystic only does minimization
# and when you minimize the inverse you are maximizing!
return (sum([getPrice(date)*roomsReserved(date) for date in range(dateFirstNight, dateFirstNight+numberOfDays)]))**-1
def constraint(x): # Ol - totalNumberOfRoomsInHotel <= 0
return roomsReserved(date) - totalNumberOfRoomsInHotel
from mystic.penalty import quadratic_inequality
@quadratic_inequality(constraint, k=1e4)
def penalty(x):
return 0.0
from mystic.solvers import diffev2
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
bounds = [0,1e4]*numberOfDays
result = diffev2(maximizeRevenue, x0=bounds, penalty=penalty, npop=10, gtol=200, disp=False, full_output=True, itermon=mon, maxiter=M*N*100)
任何熟悉与 mystic 合作的人都可以就如何实现这一点给我一些建议吗？
最佳答案
抱歉，我回答这个问题迟到了，但我认为接受的答案并没有解决完整的问题，而且还错误地解决了它。请注意如何在局部最小化中，解决接近名义价格并不能给出最佳解决方案。
我们首先构建一个 hotel 类:
"""
This file is 'hotel.py'
"""
import math
class hotel(object):
def __init__(self, rooms, price_ave, price_elastic):
self.rooms = rooms
self.price_ave = price_ave
self.price_elastic = price_elastic
def profit(self, P):
# assert len(P) == len(self.rooms)
return sum(j * self._reserved(P, i) for i,j in enumerate(P))
def remaining(self, P): # >= 0
C = self.rooms
# assert len(P) == C
return [C[i] - self._reserved(P, i) for i,j in enumerate(P)]
def _reserved(self, P, day):
max_days = len(self.rooms)
As = range(0, day)
return sum(self._allocated(P, a, L) for a in As
for L in range(day-a+1, max_days+1))
def _allocated(self, P, a, L):
P_nom = self.price_ave
e = self.price_elastic
return math.ceil(self._demand(a, L)*(sum(P[a:a+L])/(P_nom*L))**e)
def _demand(self, a,L): #XXX: fictional non-constant demand function
return abs(1-a)/L + 2*(a**2)/L**2
这是使用
mystic 解决它的一种方法:"""
This file is 'local.py'
"""
n_days = 7
n_rooms = 50
P_nom = 85
P_bounds = 0,None
P_elastic = 2
import hotel
h = hotel.hotel([n_rooms]*n_days, P_nom, P_elastic)
def objective(price, hotel):
return -hotel.profit(price)
def constraint(price, hotel): # <= 0
return -min(hotel.remaining(price))
bounds = [P_bounds]*n_days
guess = [P_nom]*n_days
import mystic as my
@my.penalty.quadratic_inequality(constraint, kwds=dict(hotel=h))
def penalty(x):
return 0.0
# using a local optimizer, starting from the nominal price
solver = my.solvers.fmin
mon = my.monitors.VerboseMonitor(100)
kwds = dict(disp=True, full_output=True, itermon=mon,
args=(h,), xtol=1e-8, ftol=1e-8, maxfun=10000, maxiter=2000)
result = solver(objective, guess, bounds=bounds, penalty=penalty, **kwds)
print([round(i,2) for i in result[0]])
结果:
>$ python local.py
Generation 0 has Chi-Squared: -4930.000000
Generation 100 has Chi-Squared: -22353.444547
Generation 200 has Chi-Squared: -22410.402420
Generation 300 has Chi-Squared: -22411.780268
Generation 400 has Chi-Squared: -22413.908944
Generation 500 has Chi-Squared: -22477.869093
Generation 600 has Chi-Squared: -22480.144244
Generation 700 has Chi-Squared: -22480.280379
Generation 800 has Chi-Squared: -22485.563188
Generation 900 has Chi-Squared: -22485.564265
Generation 1000 has Chi-Squared: -22489.341602
Generation 1100 has Chi-Squared: -22489.345912
Generation 1200 has Chi-Squared: -22489.351219
Generation 1300 has Chi-Squared: -22491.994305
Generation 1400 has Chi-Squared: -22491.994518
Generation 1500 has Chi-Squared: -22492.061127
Generation 1600 has Chi-Squared: -22492.573672
Generation 1700 has Chi-Squared: -22492.573690
Generation 1800 has Chi-Squared: -22492.622064
Generation 1900 has Chi-Squared: -22492.622230
Optimization terminated successfully.
Current function value: -22492.622230
Iterations: 1926
Function evaluations: 3346
STOP("CandidateRelativeTolerance with {'xtol': 1e-08, 'ftol': 1e-08}")
[1.15, 20.42, 20.7, 248.1, 220.56, 41.4, 160.09]
再次使用全局优化器:
"""
This file is 'global.py'
"""
n_days = 7
n_rooms = 50
P_nom = 85
P_bounds = 0,None
P_elastic = 2
import hotel
h = hotel.hotel([n_rooms]*n_days, P_nom, P_elastic)
def objective(price, hotel):
return -hotel.profit(price)
def constraint(price, hotel): # <= 0
return -min(hotel.remaining(price))
bounds = [P_bounds]*n_days
guess = [P_nom]*n_days
import mystic as my
@my.penalty.quadratic_inequality(constraint, kwds=dict(hotel=h))
def penalty(x):
return 0.0
# try again using a global optimizer
solver = my.solvers.diffev
mon = my.monitors.VerboseMonitor(100)
kwds = dict(disp=True, full_output=True, itermon=mon, npop=40,
args=(h,), gtol=250, ftol=1e-8, maxfun=30000, maxiter=2000)
result = solver(objective, bounds, bounds=bounds, penalty=penalty, **kwds)
print([round(i,2) for i in result[0]])
结果:
>$ python global.py
Generation 0 has Chi-Squared: 3684702.124765
Generation 100 has Chi-Squared: -36493.709890
Generation 200 has Chi-Squared: -36650.498677
Generation 300 has Chi-Squared: -36651.722841
Generation 400 has Chi-Squared: -36651.733274
Generation 500 has Chi-Squared: -36651.733322
Generation 600 has Chi-Squared: -36651.733361
Generation 700 has Chi-Squared: -36651.733361
Generation 800 has Chi-Squared: -36651.733361
STOP("ChangeOverGeneration with {'tolerance': 1e-08, 'generations': 250}")
Optimization terminated successfully.
Current function value: -36651.733361
Iterations: 896
Function evaluations: 24237
[861.07, 893.88, 398.68, 471.4, 9.44, 0.0, 244.67]
我认为为了产生更合理的定价，我会将
P_bounds 值更改为更合理的值。关于python - 根据 Python mystic 中的条件最大化总和，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/48088516/