R优化买入卖出 [英] R optimisation buy sell
问题描述
我需要找到优化问题的解决方案.在我的简化示例中，我对明年的价格进行了预测.我的库存最多可以包含25种产品.我每个月可以买卖.我每月不能购买4种以上的产品，也不能出售8种以上的产品.我通过以低于出售的价格购买来寻找利润.是否有包装/功能可以指示何时购买和何时出售?目的是在维持设定条件的同时，使期末的利润最大化(请参见下面的示例).还提供了可能的手动解决方案.在实际应用中，还会有其他条件，例如，我需要在冬季保持一定的库存水平，或者最大买/卖取决于库存水平.例如.如果库存很高，那么您可以出售更多等等.
I need to find a solution to an optimisation problem. In my simplified example, I have a prediction of prices for the next year. I have inventory that can contain max 25 products. I can either sell or buy each month. I cannot buy more than 4 products or sell more than 8 products per month. I am looking for profit by buying for lower price than selling. Is there a package/function that can indicate when to buy and when to sell? The objective is to maximise the profit at the end of the period whilst maintaining set conditions (see the example below). A possible manual solution is provided as well. In the real application, there will be additional conditions such as that I need to maintain a certain level of inventory in winter or that the max buy/sell is dependent on the inventory level. E.g. if the inventory is high then you can sell more etc.
library(tidyverse)
library(lubridate)
df <- tibble(
date = ymd("2020-06-01") + months(0:11),
price = c(12, 11, 12, 13, 16, 17, 18, 17, 18, 16, 17, 13),
total_capacity = 25,
max_units_buy = 4,
max_units_sell = 8)
# date price total_capacity max_units_buy max_units_sell
# 1 2020-06-01 12 25 4 8
# 2 2020-07-01 11 25 4 8
# 3 2020-08-01 12 25 4 8
# 4 2020-09-01 13 25 4 8
# 5 2020-10-01 16 25 4 8
# 6 2020-11-01 17 25 4 8
# 7 2020-12-01 18 25 4 8
# 8 2021-01-01 17 25 4 8
# 9 2021-02-01 18 25 4 8
# 10 2021-03-01 16 25 4 8
# 11 2021-04-01 17 25 4 8
# 12 2021-05-01 13 25 4 8
df_manual_solution <- tibble(
date = ymd("2020-06-01") + months(0:11),
price = c(12, 11, 12, 13, 16, 17, 18, 17, 18, 16, 17, 13),
total_capacity = 25,
max_units_buy = 4,
max_units_sell = 8,
real_buy = c(4, 4, 4, 4, 4, 4, 0, 0, 0, 4, 0, 0),
real_sell = c(0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 4, 0),
inventory_level = cumsum(real_buy) - cumsum(real_sell),
profit_loss = cumsum(real_sell*price) - cumsum(real_buy*price))
# date price total_capacity max_units_buy max_units_sell real_buy real_sell inventory_level profit_loss
# 1 2020-06-01 12 25 4 8 4 0 4 -48
# 2 2020-07-01 11 25 4 8 4 0 8 -92
# 3 2020-08-01 12 25 4 8 4 0 12 -140
# 4 2020-09-01 13 25 4 8 4 0 16 -192
# 5 2020-10-01 16 25 4 8 4 0 20 -256
# 6 2020-11-01 17 25 4 8 4 0 24 -324
# 7 2020-12-01 18 25 4 8 0 8 16 -180
# 8 2021-01-01 17 25 4 8 0 8 8 -44
# 9 2021-02-01 18 25 4 8 0 8 0 100
# 10 2021-03-01 16 25 4 8 4 0 4 36
# 11 2021-04-01 17 25 4 8 0 4 0 104
# 12 2021-05-01 13 25 4 8 0 0 0 104
推荐答案
我相信可以将其建模为小型混合整数编程(MIP)模型.
I believe this can be modeled as a small Mixed Integer Programming (MIP) model.
这是使用CVXR的实现:
Here is an implementation using CVXR:
> library(CVXR)
>
> # data
> price = c(12, 11, 12, 13, 16, 17, 18, 17, 18, 16, 17, 13)
> capacity = 25
> max_units_buy = 4
> max_units_sell = 8
>
> # number of time periods
> NT <- length(price)
>
> # Decision variables
> inv = Variable(NT,integer=T)
> buy = Variable(NT,integer=T)
> sell = Variable(NT,integer=T)
>
> # Lag operator
> L = cbind(rbind(0,diag(NT-1)),0)
>
> # optimization model
> problem <- Problem(Maximize(sum(price*(sell-buy))),
+ list(inv == L %*% inv + buy - sell,
+ inv >= 0, inv <= capacity,
+ buy >= 0, buy <= max_units_buy,
+ sell >= 0, sell <= max_units_sell))
> result <- solve(problem,verbose=T)
GLPK Simplex Optimizer, v4.47
84 rows, 36 columns, 119 non-zeros
* 0: obj = 0.000000000e+000 infeas = 0.000e+000 (12)
* 35: obj = -1.040000000e+002 infeas = 0.000e+000 (0)
OPTIMAL SOLUTION FOUND
GLPK Integer Optimizer, v4.47
84 rows, 36 columns, 119 non-zeros
36 integer variables, none of which are binary
Integer optimization begins...
+ 35: mip = not found yet >= -inf (1; 0)
+ 35: >>>>> -1.040000000e+002 >= -1.040000000e+002 0.0% (1; 0)
+ 35: mip = -1.040000000e+002 >= tree is empty 0.0% (0; 1)
INTEGER OPTIMAL SOLUTION FOUND
> cat("status:",result$status)
status: optimal
> cat("objective:",result$value)
objective: 104
> print(result$getValue(buy))
[,1]
[1,] 4
[2,] 4
[3,] 4
[4,] 4
[5,] 4
[6,] 0
[7,] 0
[8,] 4
[9,] 0
[10,] 4
[11,] 0
[12,] 0
> print(result$getValue(sell))
[,1]
[1,] 0
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 8
[7,] 8
[8,] 0
[9,] 8
[10,] 0
[11,] 4
[12,] 0
> print(result$getValue(inv))
[,1]
[1,] 4
[2,] 8
[3,] 12
[4,] 16
[5,] 20
[6,] 12
[7,] 4
[8,] 8
[9,] 0
[10,] 4
[11,] 0
[12,] 0
>
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