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Here is an elaboration of my comment. From what I can understand, the OPs problem can be cast as the solution of a large implicit linear program. Given the $n$ numbers $d_1,d_2,\ldots,d_n$ let $\mathcal{S}$ denote the set of subsets of $[n]$ such that $S \in \mathcal{S}$ iff $\sum_{i \in S} d_i \le s$. These are the feasible customer sets at any given time. ...


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