Python Pulp using with Matrices

I am still very new to Python, after years and years of Matlab. I am trying to use Pulp to set up an integer linear program.

Given an array of numbers:

{P[i]:i=1...N}

I want to maximize:

sum( x_i P_i )

subject to the constraints

A x <= b
A_eq x = b_eq

and with bounds (vector based 开发者_StackOverflow中文版bounds)

LB <= x <= UB

In pulp however, I don't see how to do vector declarations properly. I was using:

RANGE = range(numpy.size(P))
x = pulp.LpVariable.dicts("x", LB_ind, UB_ind, "Integer")

where I can only enter individual bounds (so only 1 number).

prob = pulp.LpProblem("Test", pulp.LpMaximize)
prob += pulp.lpSum([Prices[i]*Dispatch[i] for i in RANGE])

and for the constraints, do I really have to do this line per line? It seems that I am missing something. I would appreciate some help. The documentation discusses a short example. The number of variables in my case is a few thousand.

You can set the lowBound and upBound on variables after the initialization. You can create an array of variables with

LB[i] <= x[i] <= UB[i]

with the following code.

x = pulp.LpVariable.dicts("x", RANGE,  cat="Integer")
for i in x.viewkeys():
     x[i].lowBound = LB_ind[i]
     x[i].upBound = UB_ind[i]

The second parameter to LpVariable.dict is the index set of the decision variables, not their lower bounds.

For the first question, you can do it like this in some other problem.

students = range(96)
group = range(24)

var = lp.LpVariable.dicts("if_i_in_group_j", ((i, j) for i in students for j in group),cat='binary')