W e study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.
a b s t r a c tIn this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities.
Bu çalışmanın amacı ortaokul öğrencilerinin STEM'e yönelik tutumlarını belirlemek amacıyla Friday Eğitimde Yenilikçilik Enstitüsü (2012) tarafından geliştirilen STEM'e yönelik tutum ölçeğinin Türkçeye uyarlanarak geçerlik ve güvenirlik çalışmasını yapmaktır. Çalışmanın örneklemi, 2017-2018 eğitim öğretim yılı güz döneminde Türkiye'nin farklı coğrafi bölgesinde yer alan 3 büyükşehrin merkez ilçesine bağlı ortaokulların 6, 7 ve 8. sınıflarında öğrenim görmekte olan öğrencilerden kolay ulaşılabilir durum örneklemesi ile seçilmiştir (n= 1323). Ölçeğin orijinali 37 maddeden oluşmakta olup 5'li likert tipinde düzenlenmiştir. Uyarlanan ölçekten elde edilen veriler, orijinal ölçeğin dört faktörlü yapısına uygunluğunun incelenmesi için Doğrulayıcı Faktör Analizi'ne (DFA) tabi tutulmuştur. DFA sonucu orijinal faktör yapısının korunduğu gözlemlenmiştir. Ölçeğin güvenirliği, ölçeğin tamamı ve faktörleri için iç tutarlılık katsayısı ile kontrol edilmiştir. Elde edilen Cronbach Alpha katsayısı ölçeğin tamamı için .91; matematik faktörü için .86; fen faktörü için .87; mühendislik ve teknoloji faktörü için .86; 21. yüzyıl becerileri faktörü için .88 olarak hesaplanmıştır. Elde edilen bu sonuçlara göre STEM'e yönelik tutum ölçeği geçerli ve güvenilir olarak Türkçeye uyarlanmıştır.
Objective: The aim of this study was to investigate the effect of synthetic cannabinoids (SC) on P-wave dispersion (PD) in patients who consume SC. Materials and Methods: The study population included 72 patients who consumed SC and 36 age- and sex-matched healthy controls. The severity of addiction was detected using the addiction profile index (BAPI). The PD was measured by 12-lead ECG obtained upon admission to hospital. Statistical analyses were performed using the SPSS v20.0 statistical software package. Results: The mean age of the patients and controls was 26.9 ± 7.0 and 26.3 ± 6.5 years, respectively. Mean duration of SC consumption was 1.7 ± 0.7 years. Mean BAPI score of patients who consumed SC was 12.8 ± 3.4. Patients who consumed SC had a significantly higher PD value than controls (37.7 ± 11.5 vs. 30.6 ± 6.4 ms, p < 0.001). The BAPI score was significantly correlated with PD value (r = 0.675, p < 0.001). In the linear regression model that included PD value, age and heart rate, PD value was significantly and independently correlated with BAPI score (r2 of the model = 0.339; p < 0.001). Conclusions: In this study, patients who consumed SC had significantly higher PD values than controls, and the BAPI score correlated with the PD value. Hence SC consumption could lead to an increased risk of cardiovascular disease through prolonged PD. We recommend the use of the simple and inexpensive ECG to assess cardiovascular risk in patients who consume SC.
In this paper, we consider the multistage stochastic lot sizing problem with controllable processing times under nervousness considerations. We assume that the processing times can be reduced in return for extra cost (compression cost). We generalize the static and static-dynamic uncertainty strategies to eliminate setup oriented nervousness and control quantity oriented nervousness. We restrict the quantity oriented nervousness by introducing a new concept called promised production amounts , and considering new range constraints and a nervousness cost function. We formulate the problem as a second-order cone mixed integer program (SOCMIP), and apply the conic strengthening. We observe the continuous mixing set substructure in our formulation that arises due the controllable processing times. We reformulate the problem by using an extended formulation for the continuous mixing set and solve the problem by a branch-and-cut approach. The computational experiments indicate that the reformulation reduces the root gaps and this helps to solve the problem in less computation times. Moreover, in our computational experiments we investigate the impact of new restrictions, specifically the additional cost of eliminating the setup oriented nervousness, on the total costs and the system nervousness. Our computational results clearly indicate that we could significantly reduce the nervousness costs and generate more stable production schedules with a relatively small increase in the total cost.
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