The state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory are surveyed.Expand

A classification of scheduling problems on single, different and identical machines is given and NP-completeness is established for a large number of other machine scheduling problems.Expand

A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification.Expand

A class of production planning problems is considered in which known demands have to be satisfied over a finite horizon at minimum total costs. For each period, production and storage cost functions… Expand

The complexity of a class of vehicle routing and scheduling problems is investigated and known NP-hardness results are reviewed and compiled to compile the worst-case performance of approximation algorithms.Expand

Asymptotically optimal bounds and heuristics are developed for a capacitated routing problem that will find a solution with relative error at most (epsilon) in time polynomial in the number of customers.Expand

This study tested human performance on a real and virtual floor, as well as in a threedimensional (3D) virtual space, and modeled these results by a graph pyramid algorithm, which suggests that deterioration of performance in the 3D space can be attributed to geometrical relations between hierarchical clustering in a3D space and coarse-to-fine production of a tour.Expand

The use of precedence constraints between jobs that have to be respected in every feasible schedule is illustrated by extending some typical NP-completeness results and simplifying their correctness proofs for scheduling problems involving precedence constraints.Expand

It is shown that it is possible to apply ideas of Paull and Unger and of Tsukiyama et al. to obtain polynomial-time algorithms for a number of special cases, e.g. the efficient generation of all maximal feasible solutions to a knapsack problem.Expand