I'm solving a min-max problem, which to me seems like it must be some sort of canonical problem. However, I cannot figure out which problem it resembles in the literature.
Description:
- Given people (e.g. A, and B)
- Given items $i=1....I$
- Given costs for each item for person p $c_{p,i}$
- Notice that the costs can be different for each person (e.g. $c_{A,1}$ might not equal $c_{B,1}$ for item $1$)
- Allocate items to people to minimize the maximum cost for any person. All items must be allocated.
Stated more formally:
$$\min_{c_p\, \forall p} \max_{p} \sum_i^I c_{p,i}$$ $$\text{s.t.} \bigcup_{p}^{P} I_p = I$$
To me, this seems similar to multi-way number partitioning, except the costs are different for each person. It also seems to have similarities to the multi-knapsack problem, where all items must be allocated, except in this case we are minimizing the maximum burden on any individual, without capacities.
Does this problem seem similar to any known canonical problem?