Let (L;⊓,⊔) be a finite lattice and let n be a positive integer. A function f : L → R is said to be submodular if f(a ⊓ b) + f(a ⊔ b) ≤ f(a)+f(b) for all a, b ∈ L. In this paper we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding x ∈ L such that f(x) = miny∈Ln f(y) as efficiently as possible. We establish • a min–max theorem, which states tha...

In this paper we develop a multi-objective model to optimally control the lead time of a multistage assembly system. The multistage assembly system is modeled as an open queueing network, whose service stations represent manufacturing or assembly operations. The arrival processes of the individual parts of the product, which should be assembled to each other in assembly stations, are assumed to...