Metaheuristics for the mixed shop scheduling problem

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence’s benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

Complexity of mixed shop scheduling problems: A survey

We survey recent results on the computational complexity of mixed shop scheduling problems. In a mixed shop, some jobs have fixed machine orders (as in the job shop), while the operations of the other jobs may be processed in arbitrary order (as in the open shop). The main attention is devoted to establishing the boundary between polynomially solvable and NP-hard problems. When the number of operations per job is unlimited, we focus on problems with a fixed number of jobs.

Metaheuristics for minimizing the makespan of the dynamic shop scheduling problem

For the shop scheduling problems such as flow-shop, job-shop, open-shop, mixed-shop, and group-shop, most research focuses on optimizing the makespan under static conditions and does not take into consideration dynamic disturbances such as machine breakdown and new job arrivals. We regard the shop scheduling problem under static conditions as the static shop scheduling problem, while the shop scheduling problem with dynamic disturbances as the dynamic shop scheduling problem. In this paper, we analyze the characteristics of the dynamic shop scheduling problem when machine breakdown and new job arrivals occur, and present a framework to model the dynamic shop scheduling problem as a static group-shop-type scheduling problem. Using the proposed framework, we apply a metaheuristic proposed for solving the static shop scheduling problem to a number of dynamic shop scheduling benchmark problems. The results show that the metaheuristic methodology which has been successfully applied to the static shop scheduling problems can also be applied to solve the dynamic shop scheduling problem efficiently.

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.

Shop-scheduling problems with fixed and non-fixed machine orders of the jobs

The paper deals with the determination of an optimal schedule for the so-called mixed shop problem when the makespan has to be minimized. In such a problem, some jobs have fixed machine orders (as in the job-shop), while the operations of the other jobs may be processed in arbitrary order (as in the open-shop). We prove binary NP-hardness of the preemptive problem with three machines and three jobs (two jobs have fixed machine orders and one may have an arbitrary machine order). We answer all other remaining open questions on the complexity status of mixed-shop problems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms.

Evidence for insertional codemixing: mixed compounds and French nominal groups in Brussels Dutch

In this paper we analyse mixed compounds, such as legume+winkel ‘vegetable shop, greengrocery’ and winter+paletot ‘winter coat’ which contain a French and a Dutch element, and French nominal groups, such as carte d’identité ‘identity card’, and journal parlé ‘radio news’, which bilingual speakers from Brussels frequently insert into Brussels Dutch utterances. Using Muysken’s (2000) typology of bilingual speech, we claim that the mixed compounds and the nominal groups display the characteristics of insertional code-mixing. In addition, some evidence for the existence of a continuum between borrowing and code-switching can be obtained from these examples. As the multimorphemic units that are inserted into Dutch are neither single words, nor full constituents, their status in the lexicon raises interesting issues for researchers interested in the interface between syntax and the lexicon (see also Backus 2003). We try to argue that nominal groups such as carte d’identité and journal parlé are probably best seen as lexical templates or constructional idioms (Booij, 2002b). The insertion of French constructional idioms in Brussels Dutch represents an innovation in the lexical patterns that are available to speakers of this language, which is highly relevant for theories of language change.

New dimeric supramolecular structure of mixed (phthalocyaninato)(porphyrinato)-europium(III) sandwiches : preparation and spectroscopic characteristics

The mixed double-decker Eu\[Pc(15C5)4](TPP) (1) was obtained by base-catalysed tetramerisation of 4,5-dicyanobenzo-15-crown-5 using the half-sandwich complex Eu(TPP)(acac) (acac = acetylacetonate), generated in situ, as the template. For comparative studies, the mixed triple-decker complexes Eu2\[Pc(15C5)4](TPP)2 (2) and Eu2\[Pc(15C5)4]2(TPP) (3) were also synthesised by the raise-by-one-story method. These mixed ring sandwich complexes were characterised by various spectroscopic methods. Up to four one-electron oxidations and two one-electron reductions were revealed by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). As shown by electronic absorption and infrared spectroscopy, supramolecular dimers (SM1 and SM3) were formed from the corresponding double-decker 1 and triple-decker 3 in the presence of potassium ions in MeOH/CHCl3.

Raman spectroscopic characteristics of phthalocyanine and naphthalocyanine in sandwich-type phthalocyaninato and porphyrinato rare earth complexes Part 5. – Raman spectroscopic characteristics of naphthalocyanine in mixed [tetrakis(4-tert-butylphenyl)porphyrinato]-(naphthalocyaninato) rare earth double-deckers

Raman spectra were recorded in the range 400–1800 cm−1 for a series of 15 mixed \[tetrakis(4-tert-butylphenyl)porphyrinato](2,3-naphthalocyaninato) rare earth double-deckers M(TBPP)(Nc) (M = Y; La–Lu except Pm) using laser excitation at 632.8 and 785 nm. Comparisons with bis(naphthalocyaninato) rare earth counterparts reveal that the vibrations of the metallonaphthalocyanine M(Nc) fragment dominate the Raman features of M(TBPP)(Nc). When excited with radiation of 632.8 nm, the most intense vibration appears at about 1595 cm−1, due to the naphthalene stretching. These complexes exhibit the marker Raman band for Nc•− as a medium-intense band in the range 1496–1507 cm−1, attributed to the coupling of pyrrole and aza stretching, while the marker Raman band of Nc2− in intermediate-valence Ce(TBPP)(Nc) appears as a strong band at 1493 cm−1 and is due to the isoindole stretchings. By contrast, when excited with radiation of 785 nm that is in close resonance with the main Q absorption band of the naphthalocyanine ligand, the ring radial vibrations at ca 680 and 735 cm−1 for MIII(TBPP)(Nc) are selectively intensified and are the most intense bands. For the cerium double-decker, the most intense vibration also acting as the marker Raman band of Nc2− appears at 1497 cm−1 with contributions from both pyrrole CC and aza CN stretches. The same vibrational modes show weak to medium intensity scattering at 1506–1509 cm−1 for MIII(TBPP)(Nc) and this is the marker Raman band of Nc•− when thus excited. The scatterings due to the Nc breathings, ring radial vibration, aza group stretchings, naphthalene stretchings, benzoisoindole stretchings and the coupling of pyrrole CC and aza CN stretchings in MIII(TBPP)(Nc) are all slightly blue shifted along with the decrease in rare earth ionic radius, confirming the effects of increased ring–ring interactions on the Raman characteristics of naphthalocyanine in the mixed ring double-deckers.

Raman spectroscopic study of the mixed anion mineral Yecoraite Bi5Fe3O9(Te4+O3)(Te6+O4)2•9H2O

Tellurates are rare minerals as the tellurate anion is readily reduced to the tellurite ion. Often minerals with both tellurate and tellurite anions in the mineral are found. An example of such a mineral containing tellurate and tellurite is yecoraite. Raman spectroscopy has been used to study this mineral, the exact structure of which is unknown. Two Raman bands at 796 and 808 cm-1 are assigned to the ν1 (TeO4)2- symmetric and ν3 (TeO3)2- antisymmetric stretching modes and Raman bands at 699 cm-1 are attributed to the the ν3 (TeO4)2- antisymmetric stretching mode and the band at 690 cm-1 to the ν1 (TeO3)2- symmetric stretching mode. The intense band at 465 cm-1 with a shoulder at 470 cm-1 is assigned the (TeO4)2- and (TeO3)2- bending modes. Prominent Raman bands are observed at 2878, 2936, 3180 and 3400 cm-1. The band at 3936 cm-1 appears quite distinct and the observation of multiple bands indicates the water molecules in the yecoraite structure are not equivalent. The values for the OH stretching vibrations listed provide hydrogen bond distances of 2.625 Å (2878 cm-1), 2.636 Å (2936 cm-1), 2.697 Å (3180 cm-1) and 2.798 Å (3400 cm-1). This range of hydrogen bonding contributes to the stability of the mineral. A comparison of the Raman spectra of yecoraite with that of tellurate containing minerals kuranakhite, tlapallite and xocomecatlite is made.