1 comment

• Gurobi Staff

I will discuss one type of constraints, because the others can be fixed in the same way.

You are trying to model the constraints

$b_j(t) \leq b_j(t-1) - th_{i+1}(t) + v_i(t)$

Your times $$t$$ are in $$\{1,\dots,10\}$$. First thing that comes up is that you have to start at $$t\geq 2$$, because there is no $$b_j(0)$$.
Your machines are given as $$m \in \{\text{machine }1, \dots, \text{machine }5\}$$. Thus, you have to go to at most machine $$4$$, because there is no $$th_{\text{machine }6}$$(t).
You can model the above constraints as

machines = ['Machine 1', 'Machine 2', 'Machine 3', 'Machine 4', 'Machine 5']time     = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]buffers  = ['b1', 'b2', 'b3', 'b4', 'b5']speeds   = df[df.columns[:-1]].stack().to_dict()k_max    = 40model = gp.Model()thi   = model.addVars(machines, time, name = 'Throughputs')  # The throughputs of the machinesbj    = model.addVars(buffers, time, ub = k_max, name = "Buffers")  # Actual amount of units in buffer iamount_bj_1 = model.addConstrs((bj[b, t] <= bj[b, t-1]                             - thi[machines[m+1],t] + speeds[t, machines[m]]                             for t in time if t>=2 for m in range(len(machines)-1) for b in buffers))model.write("myLP.lp") # write LP file to analyze whether the model looks correct so far

A few remarks:

• It is best to add constraints one by one and check whether the constraints you generated are correct.
This makes debugging easier
• Avoid using indices or names with whitespaces. In your particular case, consider using 'Machine_X' instead of 'Machine X'
• It might be easier to use integer indices $$1,2,3,...$$ for machines instead of strings Machine_1, Machine_2, ...

Best regards,
Jaromił