No abstract

We consider scheduling issues at Beyçelik, a Turkish automotive stamping company that uses presses to give shape to metal sheets in order to produce auto parts. The problem concerns the minimization of the total completion time of job orders (i.e., makespan) during a planning horizon. This problem may be classified as a combined generalized flowshop and flexible flowshop problem with special characteristics. We show that the Stamping Scheduling Problem is NP‐Hard. We develop an integer programming‐based method to build realistic and usable schedules. Our results show that the proposed method is able to find higher quality schedules (i.e., shorter makespan values) than both the company's current process and a model from the literature. However, the proposed method has a relatively long run time, which is not practical for the company in situations when a (new) schedule is needed quickly (e.g., when there is a machine breakdown or a rush order). To improve the solution time, we develop a second method that is inspired by decomposition. We show that the second method provides higher‐quality solutions—and in most cases optimal solutions—in a shorter time. We compare the performance of all three methods with the company's schedules. The second method finds a solution in minutes compared to Beyçelik's current process, which takes 28 hours. Further, the makespan values of the second method are about 6.1% shorter than the company's schedules. We estimate that the company can save over €187,000 annually by using the second method. We believe that the models and methods developed in this study can be used in similar companies and industries.

In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classify our problem as multicapacitated/heterogeneous fleet/open vehicle routing problem with split deliveries and multiproduct (MCHF/OVRP/SDMP) which is a novel classification of an OVRP. We have developed a mixed integer programming (MIP) model for the problem and generated test problems in different size (10–90 customers) considering real-world parameters. Although MIP is able to find optimal solutions of small size (10 customers) problems, when the number of customers increases, the problem gets harder to solve, and thus MIP could not find optimal solutions for problems that contain more than 10 customers. Moreover, MIP fails to find any feasible solution of large-scale problems (50–90 customers) within time limits (7200 seconds). Therefore, we have developed a genetic algorithm (GA) based solution approach for large-scale problems. The experimental results show that the GA based approach reaches successful solutions with 9.66% gap in 392.8 s on average instead of 7200 s for the problems that contain 10–50 customers. For large-scale problems (50–90 customers), GA reaches feasible solutions of problems within time limits. In conclusion, for the real-world applications, GA is preferable rather than MIP to reach feasible solutions in short time periods.

No abstract

Deneysel tasarım endüstri ve kimya sanayisini de kapsayan çok çeşitli alanlarda kullanılmaktadır. Bu çalışmada deneysel tasarım ve cevap yüzeyi metodu sulu çözeltilerden kadmiyum iyonlarının ayrıştırılmasını etkileyen faktörlerin incelenmesinde kullanılmıştır. Kadmiyum iyonlarının ayrıştırılmasını etkileyen faktörler pH, başlangıç metal konsantrasyonu ve çözelti sıcaklığı olarak belirlenmiştir. Deneylerde kullanılan aktive edilmiş karbonlar, kimyasal ve fiziksel aktivasyon metotlarıyla Tunçbilek linyitinden elde edilmiştir. Deneysel tasarım ile faktörler analiz edilmiş ve önem seviyeleri belirlenmiştir. Ele alınan faktörlerin etkileri ve birbirleriyle etkileşimleri varyans analizi yöntemiyle ortaya çıkarılmıştır. Regresyon analiziyle birlikte cevap yüzeyi metodundan da yararlanarak deney limitleri içinde en iyi kadmiyum ayrışımını sağlayacak optimum koşullar belirlenmiştir.