Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: $L₅\left(D\right)=ma{x}_{1\le i\le p}(ma{x}_{e\in S_i\cap D}w\left(e\right)-mi{n}_{e\in S_i\cap D}w\left(e\right))$ For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary...

This paper deals with the parallel-machine scheduling problem with the aim of minimizing the total (weighted) tardiness under the assumption of different release dates. This problem has been proven to be NP-hard. We introduce some new lower and upper bounds based on different approaches. We propose a branch-and-bound algorithm to solve the weighted and unweighted total tardiness. Computational experiments were performed on a large set of instances...

This paper deals with the parallel-machine scheduling problem with the aim of minimizing the total (weighted) tardiness under the assumption of different release dates. This problem has been proven to be NP-hard. We introduce some new lower and upper bounds based on different approaches. We propose a branch-and-bound algorithm to solve the weighted and unweighted total tardiness. Computational experiments were performed on a large set of instances...