Assembly lines (conveyors) are traditional means of large-scale and mass-scale productions. An assembly line balancing problem is needed for optimizing the assembly process by configuring and designing an assembly line for the same or similar types of final products. This problem consists of designing the assembly line and distributing the total workload for manufacturing each unit of the fixed product to be assembled among the ordered workstations along the constructed assembly line. The assembly line balancing research is focused mainly on simple assembly line balancing problems, which are restricted by a set of conditions making a considered assembly line ideal for research. A lot of published research has been carried out in order to describe and solve (usually heuristically) more realistic generalized assembly line balancing problems. Assembly line designing, balancing and scheduling problems with not deterministic (stochastic, fuzzy or uncertain) parameters have been investigated in many published research works. This paper is about the design and optimization methods for assembly and disassembly lines. We survey the recent developments for designing, balancing and scheduling assembly (disassembly) lines. New formulations of simple assembly line balancing problems are presented in order to take into account modifications and uncertainties characterized by real assembly productions.

This paper presents a historical review and recent developments in mixed graph colorings in the light of scheduling problems with the makespan criterion. A mixed graph contains both a set of arcs and a set of edges. Two types of colorings of the vertices of the mixed graph and one coloring of the arcs and edges of the mixed graph have been considered in the literature. The unit-time scheduling problem with the makespan criterion may be interpreted as an optimal coloring of the vertices of a mixed graph, where the number of used colors is minimum. Complexity results for optimal colorings of the mixed graph are systematized. The published algorithms for finding optimal mixed graph colorings are briefly surveyed. Two new colorings of a mixed graph are introduced.