Solution not found or model is infeasible ( Gurobi in R)

 # Specify the file to read
> # fileName = "example.txt";
> fileName = "small.txt";
> # Read the number of jobs
> nProjects = scan(fileName, skip = 1, nlines =  1);
Read 1 item
> # Read the properties of the jobs
> input = scan(fileName, skip = 3, nlines = nProjects);
Read 30 items
> durations = rep(-1, nProjects);
> weights = rep(-1, nProjects);
> deadlines = rep(-1, nProjects)
> index = 1;
> for(j in 1:nProjects)
+ {
+         durations[j]= input[index];
+         deadlines[j] = input[index + 1];
+         weights[j] = input[index + 2];
+         index = index + 3;
+ }
> rm(index, input, j, fileName)
> deadlines
 [1] 14 13 11 15  7 19 10 20 15 13
> durations
 [1] 10  6  2 10  2  5  2  3  2  9
> weights
 [1] 2 4 4 1 2 2 1 3 4 4
> nProjects
[1] 10
> # Calculate a suitable bigM, possibly a bit larger than the sum of all durations
> bigM = sum(durations)+1
> # Initialize the MIP model
> model <- MIPModel() %>%
+         # Define binary variables for project assignment to employees
+         add_variable(x[i, j], i = 1:2, j = 1:nProjects, type = "binary") %>%  # x[i,j]: 1 if project j is assigned to employee i, otherwise 0
+         # Define binary variables for sequencing of projects
+         add_variable(s[j, k], j = 1:nProjects, k = 1:nProjects, j != k, type = "binary") %>%  # s[j,k]: 1 if project j is before project k, otherwise 0
+         # Define continuous variables for project completion times
+         add_variable(C[j], j = 1:nProjects, type = "continuous", lb = 0, ub = sum(durations)) %>%  # C[j]: Completion time of project j
+         # Define continuous variables for fines
+         add_variable(F[j], j = 1:nProjects, type = "continuous", lb = 0) %>%  # F[j]: Fine for project j if it is late
+         
+         # Set the objective to minimize the sum of fines
+         set_objective(sum_expr(F[j], j = 1:nProjects), "min") %>%  # Minimize the total fines across all projects
+         
+         # Assignment constraint: Each project is assigned to one employee
+         add_constraint(sum_expr(x[i, j], i = 1:2) == 1, j = 1:nProjects) %>%
+         
+         # Sequencing constraints: Ensure proper project ordering and completion time calculation
+         add_constraint(C[k] >= C[j] + durations[j] - bigM * (3 - s[j, k] - x[1, j] - x[1, k]), j = 1:nProjects, k = 1:nProjects, j != k) %>%
+         #add_constraint(C[k] >= C[j] + durations[j] - bigM * (3 - s[j, k] - x[2, j] - x[2, k]), j = 1:nProjects, k = 1:nProjects, j != k) %>%
+         
+         # Completion time initialization: Ensure project starts only after previous project's completion
+         add_constraint(C[j] >= sum_expr(durations[j] * x[i, j], i = 1:2), j = 1:nProjects) %>%
+         
+         # Fine calculation: Calculate fines based on project lateness
+         add_constraint(F[j] >= weights[j] * (C[j] - deadlines[j]), j = 1:nProjects) %>%
+         add_constraint(F[j] >= 0, j = 1:nProjects) %>%
+         
+         # Logical constraint for sequencing: Prevent circular project references
+         add_constraint(s[j, k] + s[k, j] <= 1, j = 1:nProjects, k = 1:nProjects, j != k)
> model
Mixed integer linear optimization problem
Variables:
  Continuous: 20 
  Integer: 0 
  Binary: 110 
Model sense: minimize 
Constraints: 220 
> # Solve the model using Gurobi
> library("gurobi")
> params <- list(OutputFlag=1)    #set solver options
> result <- solve_model(model, with_ROI(solver = "gurobi", params))
Set parameter Username
Academic license - for non-commercial use only - expires 2025-04-05
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: Intel(R) Core(TM) i5-7500 CPU @ 3.40GHz, instruction set [SSE2|AVX|AVX2]
Thread count: 4 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 220 rows, 130 columns and 710 nonzeros
Model fingerprint: 0x0a330f6c
Variable types: 20 continuous, 110 integer (110 binary)
Coefficient statistics:
  Matrix range     [1e+00, 5e+01]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 5e+01]
  RHS range        [1e+00, 2e+02]
Found heuristic solution: objective 0.0000000

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 1: 0 

Optimal solution found (tolerance 1.00e-04)
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap 0.0000%