Question

I’m trying to put together a system to suggest consumable kits based on a requested quantity. The challenge I’m running into is that the kits have volume/bulk discounts, so it may be cheaper for the customer to order a larger quantity because the price may be less. For example, let’s say the available kits are:

• 25 widgets for $15
• 10 widgets for $7
• 5 widgets for $4
• 1 widget for $1

Right now, for a requested quantity of 74, my algorithm will suggest 2 x 25, 2 x 10, and 4 x 1 = $48. It would be cheaper however for the customer to just order 3 x 25 = $45.

Any thoughts on how to tackle this? I’m coding in C#.

Thanks!

Answer 1

That looks like standard DP (dynamic programming).

// bestPrice is array of best prices for each amount
// initially it's [0, INFINITY, INFINITY, INFINITY, ...]

for (int i = 0; i <= 74; ++i) {
    for (Pack pack : packs) {
        // if (i + pack.amount) can be achieved with smaller price, do it
        int newPrice = bestPrice[i] + pack.price;
        if (newPrice < bestPrice[i + pack.amount]) {
            bestPrice[i + pack.amount] = newPrice;
        }
    }
}

The answer is min(bestPrice[74], bestPrice[74 + 1], ... bestPrice[74 + 25 - 1]). Overhead 25 - 1 is obviously enough, because otherwise you would remove one pack and amount would still be >= 74.

Some links on the topic:
http://en.wikipedia.org/wiki/Dynamic_programming
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=dynProg

edit
You can find optimal solution if you modify it a little. Add lastPack array, so lastPack[i] is the size of the package you used to achieve amount i. I guess, you can figure out how to update pseudo-code above.

Once algorithm is finished, you can get solution like this

int total = 74;
while (total > 0) {
    // package of size lastPack[total] was used to get amount 'total'
    // do whatever you want with this number here

    total -= lastPack[total];
}