Scheduling unbalanced cellular manufacturing systems with lot splitting

Recently, a large number of studies have addressed lot splitting as a means to reduce flow times as well as improve due date performance. Furthermore, a number of studies have examined scheduling policies in cellular manufacturing systems. These studies have been conducted under a variety of experimental factors, shop structures and operational assumptions. This study examines scheduling cellular manufacturing systems in the presence of lot splitting. In addition, we utilize various scheduling policies to test formally the underlying principles of the synchronous manufacturing philosophy. This is accomplished by utilizing exhaustive and non-exhaustive scheduling heuristics simultaneously at bottleneck and non-bottleneck workcentres. The results indicate that, under certain conditions, performing additional set-ups before the bottleneck can improve due date performance without an adverse effect on average flow time. Furthermore, we show that incurring additional set-ups after the bottleneck does not improve due date performance and may deteriorate flow time performance. These results conflict with some of the tenets of the synchronous manufacturing philosophy.     

Stability of ultra-fine and nano-grains after severe plastic deformation: a critical review

In this critical note, the thermal stability behavior of ultra-fine grained (UFG) and nano-structured (NS) metals and alloys produced through severe plastic deformation (SPD) techniques is reviewed. For this case, the common engineering metals with body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) crystal structures such as aluminum, copper, nickel, magnesium, steel, titanium, and their relating alloys were assessed. Microstructural evolution in these severely deformed materials following post-processing annealing treatment was investigated for various times and temperatures below the recrystallization point. The microstructure development reported in the literature was studied in terms of the stable grain structures correlated with different levels of plastic straining. The stacking fault energy (SFE) is noted to be a key issue which has a critical influence in predicting the coalescence or coarsening behavior of ultra-fine and nanoscale grains after SPD treatment by controlling the cross-slip phenomenon for screw dislocations.

Graphical Abstract

     

Complexity of Finding Graph Roots with?Girth Conditions

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Given H it is easy to compute its square H ², however Motwani and Sudan proved that it is NP-complete to determine if a given graph G is the square of some graph H (of girth 3). In this paper we consider the characterization and recognition problems of graphs that are squares of graphs of small girth, i.e. to determine if G=H ² for some graph H of small girth. The main results are the following.

• There is a graph theoretical characterization for graphs that are squares of some graph of girth at least 7. A corollary is that if a graph G has a square root H of girth at least 7 then H is unique up to isomorphism.
• There is a polynomial time algorithm to recognize if G=H ² for some graph H of girth at least 6.
• It is NP-complete to recognize if G=H ² for some graph H of girth 4.

These results almost provide a dichotomy theorem for the complexity of the recognition problem in terms of girth of the square roots. The algorithmic and graph theoretical results generalize previous results on tree square roots, and provide polynomial time algorithms to compute a graph square root of small girth if it exists. Some open questions and conjectures will also be discussed.