# How can I have minimum amount of resources wasted in this resource allocation problem?

I have a demand, $$d$$

I also have supply from 1000 sources. The supplies from those $$N$$ (for example, $$N=1000$$) sources are given by

$$s_1,s_2,s_3,\cdots,s_N$$. So,the total supply is : $$s_1+s_2+\cdots+s_N$$

How can I meet the demand with least amount of resources wasted?

so, the objective is to have minimum $$(d-supply)$$. The supply can come from any number of sources.

A heuristic approach is welcome.

• I think you meant to minimize supply minus demand instead of the other way around. – RobPratt Sep 7 '20 at 13:54

Introduce a binary variable $$x_i$$ for each supply and nonnegative waste variable $$w$$. The problem is to minimize $$w$$ subject to $$\sum_i s_i x_i -w= d$$.
• will $\min\hspace{3mm}\sum_{n=1}^Nx_n$ subject to $d\le \sum_{n=1}^N s_nx_n$ do the job? – dipak narayanan Sep 7 '20 at 14:01
• You need $s_n x_n$ in the summand for the objective. With that correction, this is equivalent to my suggestion but with more coefficients and objective parallel to the constraint. – RobPratt Sep 7 '20 at 14:05