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European Journal of Operational Research, 2 , — A modified ant colony system for solving the travelling salesman problem with time windows. Mathematical and Computer Modelling, 46 9—10 , — A Scatter Search for the periodic capacitated arc routing problem. Scheduling of vehicles from a central depot to a number of delivery points.

Operations Research, 12 4 , — Universidad de Oviedo. Ding, Q. An improved ant colony optimization and its application to vehicle routing problem with time windows. Neurocomputing, 98, — A review and classification of computer-based manufacturing scheduling tools. Computers and Industrial Engineering, 99, — The vehicle routing problem: A taxonomic review. Logistics Operations and Management.

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Book, Elsevier. A matheuristic for routing real-world home service transport systems facilitating walking. Journal of Cleaner Production, , — Transportation Science, 40 4 , — International Journal of Industrial Engineering Computations, 9 1 , 33— Anticipatory algorithms for same-day courier dispatching. Operations Research, 22 2 , — Handbook of metaheuristics. Kochenberger, Eds. Book, Springer US. Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning.

European Journal of Operational Research, 1 , — Procedia - Social and Behavioral Sciences, 96, — Procedia Economics and Finance, 26, — Distance-constrained capacitated vehicle routing problems with flexible assignment of start and end depots. Mathematical and Computer Modelling, 47 1—2 , — Artificial intelligence and expert systems for engineers.

An advanced hybrid meta-heuristic algorithm for the vehicle routing problem with backhauls and time windows. Intelligent manufacturing systems.


London: Prentice Hall International. Lin, C. A decision support system for optimizing dynamic courier routing operations.

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Expert Systems with Applications, 41 15 , — A vehicle routing problem with pickup and delivery time windows, and coordination of transportable resources. Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care. Beam-ACO for the travelling salesman problem with time windows. Ferro-Escobar Eds. Springer International Publishing AG. A hybrid column generation and clustering approach to the school bus routing problem with time windows.

Current modeling practices in bank courier scheduling. Applied Mathematical Modelling, 24 4 , — Expert system for scheduling production-research and development of a prototype 1st ed. Nagarajan, V. Approximation algorithms for distance constrained vehicle routing problems.

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It includes demand forecasting, suppliers and their performance, and purchasing planning and its relationship with inventory levels. The output of this level feeds the operational level. The output shows the ISC level to determine whether the organisation is in the negotiation, association, cooperation, coordination, or collaboration stage. The output also provides information about the strategic indicators of the SC and the exceptions found in the established contracts.

Model feedback and indicators are used to fix the tactical and operational level deviations, while the exceptions found are used to provide feedback to the strategic level. The application of this ISC model will allow organisations at a strategic level to:. At a tactical level:. At an operational level:. A measurement instrument in the form of a questionnaire was designed to evaluate the ISC level, which considers each of the variables used in the proposed model. Feedback on this instrument was given by academic experts in Mexico and Cuba with PhDs in logistics, SC, and industrial engineering, as well as by personnel from the logistics and SC departments of some of the surveyed enterprises.

The measurement instrument was divided into three sections. The first section consisted of general information about the surveyed enterprise and those responsible for answering it. This revealed the sector in which the enterprise operated, the profile of the surveyed person, how long they had operated in this market, whether they had an established business plan, and whether they had contracts with customers and suppliers. In the second section, the questionnaire provided input for the ISC model through 18 multiple-choice questions using a five-level ordinal scale that allowed the surveyed person to locate their company quickly on an integration level for each specific variable.

The third section allowed the surveyed person to provide comments that were used to improve the instrument. For the application, we designed a computational tool, programmed in Java, that sent the questionnaire to different enterprises by e-mail.

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The tool checked that the questions were answered and that the answers were automatically returned. In Mexico, there are , economic units of small-, medium-, and large-sized enterprises [45], from which a sample was taken to validate the input questionnaire for the ISC model. The questionnaire was administered between the months of May and August Enterprises were contacted through the local chambers of commerce or through the link departments of different professional and higher education schools that provide logistics services to these organisations.

To determine its validity and reliability, the measurement instrument was evaluated with Cronbach's alpha, followed by an evaluation through factor analysis. With these results, the questionnaire was restructured and modifications were made to the proposed ISC model [46]. Cronbach's alpha coefficient method requires a single use of the measurement instrument, for which a coefficient is calculated.

To create a reliable scale, it is desired that items are correlated with each other, with values greater than 0.

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Values over 0. The results are shown in Table 2. It can be seen that the instrument is reliable both in general and in each of the dimensions that constitute it. The validity of the instrument was determined through a factor analysis that indicates how many dimensions integrate a variable, and which items conform to each dimension. Factor analysis is a data reduction technique that is used to find homogeneous groups of variables from numerous sets of variables.

Test items that do not belong to a dimension which means that they are 'isolated' and that their measure is not the same as the rest must therefore be eliminated [47,48]. To analyse the validity of the instrument factor analysis , calculations were performed with the SPSS ver. Two statistics evaluate the adaptation or adjustment goodness of the analysed data to a factor model: Kaiser-Meyer-Olkin's sample adaptation measure KMO and Bartlett's sphericity test.

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In Table 3 , the results of both tests are shown. Values greater than 0. Having analysed the results, it could be concluded that the factor analysis could be properly applied.

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When applying a factor analysis, the principal components method can be used because the objective is to condense most of the original information into a number of factors for prediction purposes. The factors to extract are those that have auto-values greater than 1 [46]. The 18 variables of the designed instrument were analysed, obtaining the results shown in Table 4 , where it can be observed that two factors obtain values greater than 1. This is the number of factors that will be removed.

In Table 5 , the factor solution obtained is shown. The table contains the correlations between the original variables and each of the factors. It can be seen that, excluding question P03, the rest of the questions saturate factor 1 within the correlations matrix values greater than 0. Question P03 is the only item that presents a significant value 0.

After analysing the results shown in Table 5 , it was decided to work with only one variable, to be named 'global integration level'. To determine whether question P03 could be removed from the questionnaire, its information was excluded and the extraction process was repeated. The results Table 6 showed load levels greater than 0. Considering the load factor of each question in Table 6 and regrouping them, we obtained new values for Cronbach's alpha coefficient for the different dimensions of the ISC model.

Expert systems in business: applications and future directions for the operations researcher

Question P07, originally considered part of the tactical level, was regrouped with the strategic level due to the load factor it represented. Table 7 shows the new distribution of questions that fed the model, and the corresponding Cronbach's alpha coefficients obtained. With the results obtained from the analysis, the validity and reliability of the measurement instrument was confirmed.

The fuzzification stage of the ISC model is shown in the block diagram in Figure 5. It can be seen that the strategic integration is provided by the combination of the strategy, information, plans, and contracts variables that in turn are fed by the results of the questionnaire applied to the enterprises. Likewise, the tactical and operational integration levels and corresponding model feedback are defined.

The global integration level of the supply chain is shown in Figure 6. It is formed by the fuzzy outputs from the strategic, tactical and operational integration and the feedback, resulting in a fuzzy value that is converted into a linguistic value defuzzification , indicating whether the SC is in the negotiation, association, cooperation, coordination, or collaboration stage, according to the specific valuation.