Sequencing mixed-model assembly lines: Survey,classification and model critique

Manufacturers in a wide range of industries nowadays face the challenge of providing a rich product variety at a very low cost. This typically requires the implementation of cost efficient, flexible production systems. Often, so called mixed-model assembly lines are employed, where setup operations are reduced to such an extent that various models of a common base product can be manufactured in intermixed sequences. However, the observed diversity of mixed-model lines makes a thorough sequence planning essential for exploiting the benefits of assembly line production. This paper reviews and discusses the three major planning approaches presented in the literature, mixed-model sequencing, car sequencing and level scheduling, and provides a hierarchical classification scheme to systematically record the academic efforts in each field and to deduce future research issues.     

Solving the car sequencing problem via Branch & Bound

In a mixed-model assembly line, varying models of the same basic product are to be produced in a facultative sequence. This results to a short-term planning problem where a sequence of models is sought which minimizes station overloads. In practice – e.g. the final assembly of cars – special sequencing rules are enforced which restrict the number of models possessing a certain optional feature k to r_k within a subsequence of s_k successive models. This problem is known as car sequencing. So far, employed solution techniques stem mainly from the field of Logic and Constraint Logic Programming. In this work, a special Branch & Bound algorithm is developed, which exploits the problem structure in order to reduce combinatorial complexity.     

1,4‐Di(isopropyl)‐1,4‐diazabutadien als Abfangreagenz für monomere Bruchstücke des Tetragalliumclusters Ga4[C(SiMe3)3]4 – Bildung eines ungesättigten GaN2C2‐Heterocyclus und eines Oxidationsprodukts mit Ga‐O‐O‐Ga‐Gruppe

1,4‐Di(isopropyl)‐1,4‐diazabutadiene as a Reagent for the Trapping of Monomeric Fragments of the Tetragalliumcluster Ga₄[C(SiMe₃)₃]₄ – Formation of an Unsaturated GaN₂C₂ Heterocycle and an Oxidation Product Containing a Ga‐O‐O‐Ga Group The tetrahedral tetragallium cluster Ga₄[C(SiMe₃)₃]₄ ( 1 ) dissociates upon dissolution to yield the monomeric fragments Ga‐R [R = C(SiMe₃)₃]. These monomers could be trapped now by the treatment of their solutions with 1,4‐di(isopropyl)‐1,4‐diazabutadiene. The product of the cycloaddition reaction ( 2 ) possesses a five‐membered GaN₂C₂ heterocycle with a coordinatively unsaturated gallium atom and an endocyclic C=C double bond. 2 is rather sensitive towards oxidation by traces of air. The contact with oxygen yielded a digallium peroxide [(C₂N₂iPr₂)RGa‐O‐O‐GaR(C₂N₂iPr₂)] ( 3 ) which was isolated in a very low yield only and which has a gallium atom attached to each oxygen atom of the inner peroxo group. Both chelating ligands of 3 possess an unpaired electron.     

Selective propargylic C(sp3)–H activation of methyl-substituted alkynes versus [2 + 2] cycloaddition at a titanium imido template

The reaction of the titanium imido complex 1b with 2-butyne leads to the formation of the titanium azadiene complex 2a at ambient temperature instead of yielding the archetypical [2 + 2] cycloaddition product (titanaazacyclobutene) which is usually obtained by combining titanium imido complexes and internal alkynes. The formation of 2a is presumably caused by an initial propargylic C(sp³)–H activation step and quantum chemical calculations suggest that the outcome of this unexpected reactivity is thermodynamically favored. The previously reported titanaazacyclobutene I (which is obtained by reacting 1b with 1-phenyl-1-propyne) undergoes a rearrangement reaction at elevated temperature to give the corresponding five-membered titanium azadiene complex 2b.

An unexpected reactivity between a titanium imido complex and internal alkynes was unveiled yielding titanaazacyclobutenes instead of the expected [2 + 2] cycloaddition products.     

Zum Cauchyschen und Dirichletschen Problem

Ohne Zusammenfassung