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Let's say i have a product A at 100$ with shipping cost at 3$ from supplier X, the same product at 102$ with shipping cost at 2.5$ from supplier Y and the same with different suppliers.

Now let's say i have product B at 200$ with shipping cost at 1$ from supplier Z, the same product at 203$ with shipping cost at 2$ with supplier Y and the same with different suppliers.

I want to order both A and B products and i want to calculate an optimal cost. For example, the input of my program will be multiple products and the output will be like example

I am not familiar with simplex or any linear algorithms at all. How hard is to solve such a problem, can you give me any advice ?

Thanos M
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    just find minimum of (cost+shipping cost) for each product and keep track of the seller for which you got the minimum! what's wrong with that? – Abhishek Keshri Oct 22 '18 at 14:02
  • Because that way i need to order the products from differenct sellers and the shipping cost will be high. For example lets say i want to buy a pc from amazon part by part. I want to buy a specific cpu, specific gpu, specific ram etc. Now considering that there are many suppliers for the same product what is the lowest price combination for a product. – Thanos M Oct 22 '18 at 14:09
  • okay, I got what you want. Please improve your question as it can be easily misinterpreted. – Abhishek Keshri Oct 22 '18 at 14:11
  • and what will be the shipping cost in case when, sc of A = x and sc of B = y for the same seller. will it be x+y or max(x, y) or min(x, y) or ........ – Abhishek Keshri Oct 22 '18 at 14:12
  • For example product A price : 102 , shipping 5 and supplier X , product A price : 105, shipping 4.5 and supplier Y, product B price : 50, shipping 3 and supplier Z, product B : price : 50,3, shiping : 5 and supplier X. Its better to buy product B from supplier X even if the cost is higher because both products will be send from the same supplier with one shipping cost instead of two. – Thanos M Oct 22 '18 at 14:17
  • yeah and what that "shipping cost" will be? is the shipping cost same for each product for a specific seller? – Abhishek Keshri Oct 22 '18 at 14:20
  • The same shipping cost yes – Thanos M Oct 22 '18 at 14:33
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    This is sometimes called the **supplier selection problem**. It becomes more interesting with some discounting schemes (e.g. you get 10% discount if you spend more than $1000). Not unusual to see MIP (mixed integer programming) models for this problem. – Erwin Kalvelagen Oct 22 '18 at 17:52

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