# Product allocation to vendor according to their demand

Company X has 3 types of products and due to the limited availability of raw materials, the production of products are also limited.

They have partnered with Store A for them to sell their products. Store A has 5 branches with different amount of demands for each product type but due to the limited number of products available, not all branches will be allocated.

How can I transform this into a LP model where it selects the branch while maximizing profits? Or if this doesn't make sense, how should I improve my problem?

Product Type Profits (USD/piece) Available Supply
1 1589 1456
2 4798 1274
3 974 1789
Branch Type 1 Demand Type 2 Demand Type 3 Demand
1 90 78 140
2 204 50 145
3 78 40 60
4 548 648 105
5 789 500 500

I only came up with the parameters and decision variable so far.

v = index of vendors/sellers, v= 1,2,...m

Ni = minimum # of product type i for vendor/seller v

Ov = maximum # of product type i for vendor/seller v

Decision variable:

Wiv = # of allocated product type i to product for vendor/seller v

**Will update this one with the LP model I formulated as soon as I'm done.

• Welcome to OR.SE! I suggest that you edit your post and show us your work. What have you done so far and where are you stuck? That way you can get better help.
– EhsanK
Dec 3 '21 at 3:57
• I suspect you are missing some critical information. If the profit is independent of the branch where the product is sold and there are no missing constraints, you would just allocate your entire supply of products 1 and 2 to branches in an arbitrary fashion (since total demand exceeds supply), and allocate to each branch its entire demand for product 3 (since total demand is less than supply). There is no need for (or value to using) an LP. Dec 3 '21 at 16:21
• @sonyeoja, to add the useful comments of Prof. Rubin, Please, be aware that the available supply for the first and the second products is less than the demand in the warehouse and for the third is vise versa. It means you might have the shortage/stock inventory that will be considered as an inventory control model. Dec 4 '21 at 11:18