Finding the best combinations

Question

I'm looking for the approach to solve the following problem.

Suppose I've this product grid.

table = [{'Products': 'Prod1', 'Unit1': 32, 'Unit2': 32, 'Unit3': 27, 'Unit4': 15 },
         {'Products': 'Prod2', 'Unit1': 35, 'Unit2': 12, 'Unit3': 19, 'Unit4': 29 },
         {'Products': 'Prod3', 'Unit1': 37, 'Unit2': 36, 'Unit3': 36, 'Unit4': 19 },
         {'Products': 'Prod4', 'Unit1': 16, 'Unit2': 15, 'Unit3': 18, 'Unit4': 31 },
         {'Products': 'Prod5', 'Unit1': 14, 'Unit2': 32, 'Unit3': 20, 'Unit4': 33 },
         {'Products': 'Prod6', 'Unit1': 10, 'Unit2': 33, 'Unit3': 28, 'Unit4': 36 },
         {'Products': 'Prod7', 'Unit1': 18, 'Unit2': 22, 'Unit3': 27, 'Unit4': 30 },
         {'Products': 'Prod8', 'Unit1': 11, 'Unit2': 13, 'Unit3': 20, 'Unit4': 26 }]

df = pd.DataFrame(table)

Each value reflects the maximum revenue I'll get by selling this product. Eg Selling 2 units of prod1 , I'll get $32. For each product I can sell maximum of 4 units. And total I can sell maximum of 16 units (4*4). My objective is to maximize the total revenue. In the example given I'll sell the following combinations to maximize my revenue:

{prod1: 2 units (32),
 prod2: 1 unit  (35),
 prod3: 1 unit  (37),
 prod4: 4 units (31),
 prod5: 4 units (33),
 prod6: 4 units (36)}

My question is, how I can formulate it algorithmically?

Answer 1

The trivial solution would be to test all options and determine the option that gives the maximum revenue.

All options can be generated using itertools.product :

from itertools import product
options = product(range(5), repeat=8)

One could either sell 0, 1, 2, 3, or 4 units of each product so I use range(5) as first argument and there are 8 products so I used repeat=8 .

However we don't want to maximize the number of units sold but the revenue when 16 or less units are sold. In this case I use max with a key function. The key-function returns a negative value if there are more than 16 units sold otherwise it checks what revenue is made based on the list of dicts and the number of sold units:

def total_revenue(sales):
    if sum(sales) > 16:  # discard the revenue if more than 16 units are sold.
        return -1
    else: 
        # Sum the revenue based on the sales and the values in the table.
        sum_ = 0
        for idx, num in enumerate(sales):
            if num:
                sum_ += table[idx]['Unit{}'.format(num)]
        return sum_

maximized_revenue = max(options, key=total_revenue)
print(maximized_revenue)
# (1, 1, 1, 4, 2, 2, 1, 4)

This is a tuple, that still needs to be transformed to the desired dictionary:

{'prod{}'.format(idx+1): num for idx, num in enumerate(maximized_revenue)}
# {'prod1': 1,
#  'prod2': 1,
#  'prod3': 1,
#  'prod4': 4,
#  'prod5': 2,
#  'prod6': 2,
#  'prod7': 1,
#  'prod8': 4}

There is still room for improvement because product generates lots of unneccessary values (more than 16 items sold). You could create a custom generator that works like product with the repeat argument but doesn't generate solutions when more than 16 units are already sold.