set_up_constraints

set_up_constraints.py

def set_up_constraints(solver, data_model, x, w, num_products, num_locations):

    # Sum of quantities of each product should be equal to its quantities
    for i in range(num_products):
        solver.Add(solver.Sum([x[i, j] for j in range(num_locations)]) == data_model['products'][i].quantity) 

    # Each location should not have more products than its capacity.
    for j in range(num_locations):
        solver.Add(solver.Sum([x[i, j] for i in range(num_products)]) <= data_model['locations'][j].freeCapacity)

    
    for upr in data_model['unallocated_prod_relationship']:

        i, k = data_model['products'].index(upr.product1), data_model['products'].index(upr.product2)
        quantity_i, quantity_k = data_model['products'][i].quantity, data_model['products'][k].quantity

        for j in range(num_locations):

            freeCapacity_j = data_model['locations'][j].freeCapacity
            min_freeCapJ_quantI = min(freeCapacity_j, quantity_i)
            min_freeCapJ_quantK = min(freeCapacity_j, quantity_k)

            #solver.Add(w[i, j, k, j] >= 0)

            # w[i, j, k, j] >= max(x[i, j])*x[k, j] + x[i, j]*max(x[k, j]) - max(x[i, j])*max(x[k, j]))
            # the max value of x[i,j] = min(freeCapacity_j, quantity_i)
            solver.Add( w[i, j, k, j] >= min_freeCapJ_quantI * x[k, j] +  x[i, j] * min_freeCapJ_quantK 
                       - min_freeCapJ_quantI * min_freeCapJ_quantK )

            # w[i, j, k, j] <= max(x[i, j])*x[k, j] + x[i, j]*min(x[k, j]) - max(x[i, j])*min(x[k, j])
            # the min value of each x[i,j] and x[k,j] is 0. So,
            # w[i, j, k, j] <= max(x[i, j])*x[k, j]
            # the max value of x[i,j] = min(freeCapacity_j, quantity_i)
            solver.Add( w[i, j, k, j] <= min_freeCapJ_quantI * x[k, j] )

            # w[i, j, k, j] <= x[i, j]*max(x[k, j]) + min(x[i, j])*x[k, j] - min(x[i, j])*max(x[k, j])
            # the min value of each x[i,j] and x[k,j] is 0. So,
            # w[i, j, k, j] <= x[i, j]*max(x[k, j])
            # the max value of x[k,j] = min(freeCapacity_j, quantity_k)
            solver.Add( w[i, j, k, j] <= x[i, j] * min_freeCapJ_quantK ) 

# Constraints
set_up_constraints(solver, data_model, x, w, num_products, num_locations)