Restrict number of items in Bin Packing

[UNS]

Hi Guys - i'm following the bin packing example from the docs here : https://developers.google.com/optimization/bin/bin_packing

I want to add another condition here that restricts the number of items that can be put in a bin. 

Currently, I achieve it in the way stated below - but I'm not sure if this is the right way to do it. The code is reproduced below

def main(store_weights, bin_capacity, max_items,print_suppress=True):

    

    data = create_data_model(store_weights, bin_capacity, max_items)

    # Create the mip solver with the CBC backend.

    solver = pywraplp.Solver('simple_mip_program', pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)

    

    # Variables

    # x[i, j] = 1 if item i is packed in bin j.

    x = {}

    for i in data['items']:

        for j in data['bins']:

            x[(i, j)] = solver.IntVar(0, 1, 'x_%i_%i' % (i, j))

    # y[j] = 1 if bin j is used.

    y = {}

    for j in data['bins']:

        y[j] = solver.IntVar(0, 1, 'y[%i]' % j)

The above is exactly like the example in the docs. 

The part below is where I've made changes:data['max_items'] is the maximum number of items you can put in a bin.Below, I add it alongside the other constraints:

 # Constraints

    # Each item must be in exactly one bin.

    for i in data['items']:

        solver.Add(sum(x[i, j] for j in data['bins']) == 1)

    # The amount packed in each bin cannot exceed its capacity.

    for j in data['bins']:

        solver.Add(

                sum(x[(i, j)] * data['weights'][i] for i in data['items']) <= y[j] *

                data['bin_capacity'])

    

    # Cannot have more than data['max_items'] items in a bin

    for j in data['bins']:

        bin_count = 0

        for i in data['items']:

            bin_count += x[i, j]

        solver.Add(bin_count <= data['max_items'])

        

    

    # Objective: minimize the number of bins used.

    solver.Minimize(solver.Sum([y[j] for j in data['bins']]))

The rest of it just as in the docs example.

Do you guys think this is the correct way to restrict the number of items in a bin? Do you think this is causing any issues that I'm not considering? The output seems to restrict the number of items to data['max_items'] but I'm not sure if this is the right approach.

Thanks in advance!

[Laurent Perron]

This is fine.

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

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