Les α et β-Cetophosphonates,des Precurseurs de Pyrrolidines et de Quinoleines Phosphonatees

The condensation of primary amines on α- or β-ketophosphonates affords the corresponding iminophosphonates. The reaction was found to be highly stereoselective, affording the E isomer exclusively. These phosphonylimines were then treated in basic media to give pyrrolidines and quinolines through intramolecular cyclization. The structures of all obtained products were confirmed by NMR spectroscopy (¹H, ³¹P, ¹³C), and in some cases by mass spectrometry.     

An Algorithm for the Single-item Capacitated Lot-Sizing Problem with Concave Production and Holding Costs

We consider a multi-period single-item production scheduling problem with a deterministic, time-varying demand pattern and concave cost functions. Optimal production lot sizes, so as to minimize the total costs of production, set-up, and inventory, are determined subject to dynamic production capacity and no backlogs. The proposed algorithm was tested extensively by solving several randomly generated problems with varying degrees of complexity. The proposed algorithm appears to perform quite reasonably for practical applications.     

A Final-Exam-Scheduling Package

This paper presents the implementation of a multi-phase final-exam-scheduling package at a large university. The problem as it had evolved over time is discussed and a solution is presented. The implementation was undertaken over a three-year period and involved a multi-phase approach. The multi-phase final-exam-scheduling process consists of first grouping the final exams into sets called `blocks' in such a way as to minimize the number of students with simultaneous exams. Second, the blocks are assigned to exam days while minimizing the number of students with two or more exams per day. Third, the exam days and exam blocks within days are arranged so as to minimize the number of students with consecutive exams. Fourth, exams are assigned to classrooms so as to maximize the space utilization. New formulations and solution methods for the stated four phases are presented. The approach is well suited for a practical application and has been implemented at a large university.     

Data envelopment scenario analysis with imprecise data

In the existing DEA models, we have a centralized decision maker (DM) who supervises all the operating units. In this paper, we solve a problem in which the centralized DM encounters limited or constant resources for total inputs or total outputs. We establish a DEA target model that solves and deals with such a situation. In our model, we consider the decrease of total input consumption and the increase of total output production; however, in the existing DEA models, total output production is guaranteed not to decrease. Considering the importance of imprecise data in organizations, we define our model so as to deal with interval and ordinal data. A numerical illustration is provided to show the application of our model and the advantages of our approach over the previous one.     

Ranking DMUs by ideal points with interval data in DEA

An original DEA model is to evaluate each DMU optimistically, but the interval DEA model proposed in this paper has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and the pessimistic viewpoints.     

Sensitivity and stability analysis on the first and second levels of efficiency score relative to data error

In data envelopment analysis (DEA), efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for a category DMUs and finds the stability radius for all efficient DMUs. By means of combining some classic DEA models and with the condition that the efficiency scores of efficient DMUs remain unchanged, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalizes the conventional sensitivity analysis approach in which the inputs of efficient DMUs increase and their outputs decrease, while the inputs of inefficient DMUs decrease and their outputs increase. We find the maximum quantity of perturbations of data so that all first level efficient DMUs remain at the same level.     

A posteriori analysis: error estimation for the eighth order boundary value problems in reproducing Kernel space

In the previous work (Akram and Rehman Numer. Algor. 62 527–540 2013), Akram and Rehman presented the reproducing kernel method (RKM) for solving various eighth order boundary value problems. However, an effective error estimation for this method has not yet been discussed. This work is devoted to deal with this problem. Some other aspects of the RKM will be considered such as convergence analysis and numerical implementations.