# Solving sequential multi-knapsack problem

Suppose I have $$n$$ items, each with value $$v(j)$$ and weight $$w(j)$$, and $$m$$ knapsacks each with capacity $$c(i)$$. If I make the assumption that $$w(j-1)$$ evenly divides $$w(j)$$, then there's a nice optimal packing algorithm outlined in Detti, A polynomial algorithm for the multiple knapsack problem with divisible item sizes.

I have a slight variant to this problem, where the value depends on the knapsack I put the item in: $$v(j,i)$$. Is there any paper or book detailing an exact optimal solution to this problem? In my case $$v(j,i)$$ takes at most 2 distinct values, but I'm not sure if that matters.