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This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs' completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NPhard problem; a method based on decomposing the problem into subproblem and solving each subproblem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.The expected real completion time of job j on the machine i

This paper considers a scheduling problem with uncertain processing times and machine breakdowns in industriall/office workplaces and solves it via a novel robust optimization method. In the traditional robust optimization, the solution robustness is maintained only for a specific set of scenarios, which may worsen the situation for new scenarios. Thus, a two-stage predictive algorithm is proposed to efficiently handle the uncertainties and find robust and stable solutions. The first stage creates robust solutions and ensures their stability in the new scenarios. The second stage proposes a novel stability measure to proactively offset the effects of the machine breakdowns of the former stage. Moreover, a tri-component measure based on efficiency, robustness, and stability is proposed which aims to create a realistic schedule to satisfy the customers, manufacturers, and the staff. To meet the customer's requirements, the robustness measure is defined based on the tardiness and the delivery dates of jobs. Finally, the proposed algorithm is applied to a case study, and the findings are compared with the empirical data. The results emphasize the superiority of the proposed technique in satisfying the customers, staff, and increasing the profitability and accountability of the company.

This paper discussed the scheduling problem of outpatients in a radiology center with an emphasis on priority. For more compatibility to real-world conditions, we assume that the elapsed times in different stages to be uncertain that follow from the specific distribution function. The objective is to minimize outpatients' total spent time in a radiology center. The problem is formulated as a flexible open shop scheduling problem and a stochastic programming model. By considering the specific distribution function for uncertain variables, deterministic mixed integer linear programming (MILP) is developed such that the proposed problem can be solved by a linear programming solver in small size. Besides an effective heuristic method is proposed for the moderate size problem. To indicate the applicability of the proposed model, it has been applied to a real radiology center. The results from the proposed optimization models indicate an increase in outpatients' satisfaction, as well as the improvement of the efficiency and productivity of the radiology center.

Résumé De ‘Alī ibn Muḥammad al-Jurjānī (740-816 /1340-1413) on connaît davantage sa maîtrise des subtilités des débats en matière de théologie argumentative que son approche du soufisme qui fait l’objet du présent article, à l’appui d’une documentation inédite fournie par quelques-uns de ses traités persans et complétée par son fameux livre des définitions Kitāb al-Taʿrīfāt ainsi sa glose sur Tasdīd al-Qawāʿid de Shams al-Dīn al-Iṣfahānī. Le but est d’éclairer l’attachement de l’auteur à la connaissance mystique et sa vénération pour les maîtres soufis, sur fond d’apologie de la théorie de l’unicité de l’Être (waḥdat al-wujūd) d’Ibn ‘Arabī et de son école, à une époque où la mystique spéculative akbarienne s’apprête à entrer en résonance avec la gnose philosophique iranienne, à la suite du déclin du kalām ashʿarite.