scholarly journals Augmented Lagrangian Approach to the Newsvendor Model with Component Commonality

2019 ◽  
Vol 24 (2) ◽  
pp. 55
Author(s):  
Abdelouahed Hamdi ◽  
Lotfi Tadj
Keyword(s):  
Independent Random Variables ◽  
Newsvendor Model ◽  
Common Component ◽  
Component Commonality ◽  
Multiple Products ◽  
Shortage Cost ◽  
Optimal Allocations ◽  
Primal Dual ◽  
Product Inventory ◽  
Augmented Lagrangian Approach

Component commonality is a well-known approach in manufacturing, where the same components are used for multiple products. It has been implemented by many established companies such as Airbus, Kodak, Toyota, etc. We consider a standard two-product inventory model with a common component. The demands for the products are independent random variables. Instead of the usual approach to minimize the total shortage quantity, we propose to minimize the total shortage cost. The resulting problem is a non-convex nonlinear mathematical program. We illustrate the use of a primal-dual proximal method to solve this problem by obtaining numerically the optimal allocations of components. In particular, we show that a higher unit shortage cost induces a higher allocation.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals ANALISIS DAMPAK COMPONENT COMMONALITY TERHADAP SCHEDULE INSTABILITY PADA SISTEM RANTAI PASOK SEDERHANA

2018 ◽  
Vol 1 (1) ◽  
pp. 1-6
Author(s):  
Bilal Ahmadi ◽  
Dhany Surya Ratana
Keyword(s):  
Lead Time ◽  
Demand Uncertainty ◽  
Cost Structure ◽  
Supply Chain System ◽  
Common Component ◽  
Component Commonality ◽  
Operational Conditions ◽  
Uncertainty Product ◽  
Simulation Results ◽  
The Impact

This study analyzed the impact of component commonality to schedule instability. Analysis was implemented in the use of component commonality (use of same component in different product structures) in a simple supply chain system which is consist of one manufacturer and two suppliers. Different operational conditions were introduced such as: demand uncertainty, product cost structure, product lead time, product structure and inventory policy that company utilized. The simulation results suggested that common component could reduce schedule instability in both manufacturer and suppliers. Furthermore, the results also indicated that suppliers were the more affected entities due to uncertainty rather than manufacturer

scholarly journals ANALISIS DAMPAK COMPONENT COMMONALITY TERHADAP SCHEDULE INSTABILITY PADA SISTEM RANTAI PASOK SEDERHANA

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Bilal Ahmadi ◽  
Dhanny Surya Ratana
Keyword(s):  
Lead Time ◽  
Cost Structure ◽  
Common Component ◽  
Component Commonality ◽  
Structure Lead

<p>Penelitian ini menganalisis dampak penggunaan common component terhadap <br />ketidakpastian jadwal produksi. Analisis dilakukan pada penggunaan tingkat component <br />commonality (penggunaan komponen yang sama dalam struktur produk yang berbeda) tertentu <br />terhadap tingkat schedule instability pada sistem rantai pasok sederhana yang terdiri dari satu <br />pemanufaktur dan dua pemasok. Beragam kondisi operasional yang berbeda seperti: <br />ketidakpastian permintaan, cost structure, lead time, struktur produk serta kebijakan persediaan <br />yang diterapkan oleh perusahaan menjadi bagian yang diamati dalam studi ini. Hasil dari simulasi <br />menunjukkan penggunaan common component mampu mereduksi tingkat schedule instability, <br />baik pada pemanufaktur maupun pemasok. Selain itu juga tergambar dalam hasil tersebut bahwa <br />entitas pemasok mengalami instability yang lebih besar dibandingkan dengan pemanufaktur</p>

An Approach to Evaluate the Profitability of Component Commonality

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Shun Takai ◽  
Sankar Sengupta
Keyword(s):  
Sensitivity Analysis ◽  
Supply Chain ◽  
High Performance ◽  
Product Cost ◽  
Component Commonality ◽  
Product Demand ◽  
Multiple Products ◽  
Electric Bicycle ◽  
Demand Variability

Commonality or the use of same components (parts, assemblies, or subsystems) among multiple products can reduce component inventory and simplify processes and logistics while accommodating variations in product demand. Excessive commonality, however, causes some products to use high-performance components and increase product cost. This paper presents an approach for evaluating profitability of component commonality by integrating commonality and supply chain decisions. The proposed approach is demonstrated using commonality of electric-bicycle motors as an illustrative example. This paper presents a sensitivity analysis of the optimum commonality with respect to motor cost, demand variability, inventory-tracking cost, and inventory-ordering cost.

Correlation analysis of radiation damage

1978 ◽  
Vol 36 (1) ◽  
pp. 214-215
Author(s):  
R. Hegerl ◽  
A. Feltynowski ◽  
B. Grill
Keyword(s):  
Electron Microscopy ◽  
Independent Random Variables ◽  
Optical Parameters ◽  
Bright Field Image ◽  
Bright Field ◽  
Expectation Value ◽  
All Optical ◽  
Image Element ◽  
Stochastic Series ◽  
The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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