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Augmented Lagrangian Approach to the Newsvendor Model with Component Commonality

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Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
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Department of Industrial Engineering, Alfaisal University, Riyadh 11533, Saudi Arabia
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Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(2), 55; https://doi.org/10.3390/mca24020055
Received: 17 April 2019 / Revised: 14 May 2019 / Accepted: 23 May 2019 / Published: 24 May 2019
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. View Full-Text
Keywords: stochastic inventory systems; component commonality; augmented Lagrangian stochastic inventory systems; component commonality; augmented Lagrangian
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Hamdi, A.; Tadj, L. Augmented Lagrangian Approach to the Newsvendor Model with Component Commonality. Math. Comput. Appl. 2019, 24, 55.

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