经过进一步的阅读和尝试，我提出了一个函数，可以提取由一个主管监督的所有项目的向量：

func_find_supervisor_projects <- function(proj) {
  #Find project supervisor
  super <- df_proj_info %>%
    filter(Project==proj) %>%
    select(Supervisor)
  #Find all projects supervised by supervisor
  p1 <- df_proj_info %>%
    filter(Supervisor %in% super) %>%
    select(Project)`enter code here`
  p1<-unlist(p1)
  p1<-as.vector(p1,'numeric')
}

然后，这被用于过滤模型变量X，对每个管理器的所有分配进行计数，并将其约束为小于管理器的容量。以下是修改后的模型：

model <- MIPModel() %>%
  
  # 1 iff student i is assigned to project j
  add_variable(x[i, j], i = 1:n, j = 1:m, type = "binary") %>%
  
  # maximize the preferences
  set_objective(sum_over(funcWeight(i, j) * x[i, j], i = 1:n, j = 1:m),"min") %>%
  
  # we cannot exceed the capacity of a project
  add_constraint(sum_over(x[i, j], i = 1:n) <= df_proj_info$Proj.Cap[j], j = 1:m) %>%
  
  # we cannot exceed the supervisor capacity
  add_constraint(sum_over(x[i, j1], i = 1:n, j1 = func_find_supervisor_projects(j)) <= df_proj_info$Super.Cap[j], j = 1:m) %>%
  
  # each student needs to be assigned to one project
  add_constraint(sum_over(x[i, j], j = 1:m) == 1, i = 1:n)enter code here

可能有更优雅的解决方案，但它正在为我的目的工作。
下面是修改后的完整代码：

library(purrr)
library(dplyr)
library(ompr)
library(ompr.roi)
library(ROI.plugin.glpk)

#Create model data
n <- 15    #Students
m <- 6    #Projects
o <- 4    #Supervisors

proj_capacity <- rep.int(4, m) # all have equal capacities
proj_info <- matrix(c(1:6,1,1,2,2,3,4,proj_capacity,4,4,4,4,4,4),6,4, dimnames = list(c(1,2,3,4,5,6), c("Project","Supervisor","Proj.Cap","Super.Cap")))

df_proj_info <- as.data.frame(proj_info)

set.seed(1234)
preference_data <- lapply(seq_len(n), function(x) sample(seq_len(m), 3))

##Functions

#Function that extracts vector for preferences of a single student
preferences <- function(student) preference_data[[student]]
preferences(1)

# Function that assigns each project a weight according to a student's choices
# if the project is not among the preferences, the weight is 10000
funcWeight <- function(student, project) {
  p <- which(as.numeric(project) == preferences(as.numeric(student)))
  as.integer(if (length(p) == 0) {
    10000
  } else {
    p
  })
}

#Function to create vector of all projects with same supervisor
func_find_supervisor_projects <- function(proj) {
  #Find project supervisor
  super <- df_proj_info %>%
    filter(Project==proj) %>%
    select(Supervisor)
  #Find all projects supervised by supervisor
  p1 <- df_proj_info %>%
    filter(Supervisor %in% super) %>%
    select(Project)
  p1<-unlist(p1)
  p1<-as.vector(p1,'numeric')
}

#Build model
model <- MIPModel() %>%
  
  # 1 iff student i is assigned to project j
  add_variable(x[i, j], i = 1:n, j = 1:m, type = "binary") %>%
  
  # maximize the preferences
  set_objective(sum_over(funcWeight(i, j) * x[i, j], i = 1:n, j = 1:m),"min") %>%
  
  # we cannot exceed the capacity of a project
  add_constraint(sum_over(x[i, j], i = 1:n) <= df_proj_info$Proj.Cap[j], j = 1:m) %>%
  
  # we cannot exceed the supervisor capacity
  add_constraint(sum_over(x[i, j1], i = 1:n, j1 = func_find_supervisor_projects(j)) <= df_proj_info$Super.Cap[j], j = 1:m) %>%
  
  # each student needs to be assigned to one project
  add_constraint(sum_over(x[i, j], j = 1:m) == 1, i = 1:n)

 

#Model definition
model

#Solve model
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))

#Extract Student-Project pairs
df_matching <- result %>% 
  get_solution(x[i,j]) %>%
  filter(value > .9) %>%  
  select(i, j) %>% 
  rowwise() %>% 
  mutate(weight = funcWeight(as.numeric(i), as.numeric(j)), 
         preferences = paste0(preferences(as.numeric(i)), collapse = ",")) %>% ungroup

##Decode pairs
#And merge with Student-Project pairs info
df_proj_allocation<-merge(df_matching,df_proj_info, by.x=c("j"), by.y=c("Project"),all.x=TRUE)
df_proj_allocation<-df_proj_allocation %>%
  rename(
    Student=i,
    Project=j
  )

head(df_proj_allocation)