I'm not expert on complexity theory and combinatorial optimization. I want to know if the following problem (or similar) is known in the scientific literature, and if you think it is NP-complete. Thank you in advance for your help.
Two parameters X and Y, which can be equal.
n customers C1, C2, ... Cn
m types of goods M1, M2 ... Mm
There are X pieces available for each good Mi: a piece of 1kg, another piece of 2kg, ...., a piece of X kg.
Every customer wants to buy a certain number of goods. For example, the client C1 may be interested in buying goods M1, M4, M8 and M9. A customer is satisfied if he can find all the goods he wants to buy. In addition, the weights of the parts he was able to purchase must satisfy a constraint that I'll explain below.
Output: How many customers can be satisfied?
The constraint on the weights is as follows: Take for example the client C1 who is interested in buying goods M1, M4, M8 and M9. Assume that C1 was able to purchase all four goods. Let P1, P2, P3, P4 be the weights of the pieces he was able to buy. C1 is satisfied if $\sum_i P_i -1 <Y$.
Edit: Note that the limit Y is common for all customers. The intuition behind the constraint is that we want to limit the number of pieces whose weight is not equal to 1kg.