Optimization of multi-product economic production quantity model with partial backordering and physical constraints: SQP,SFS, SA,and WCA |
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| Affiliation: | 1. Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran;2. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran;2. Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;3. Shanghai Radio Equipment Research Institution, Shanghai 200090, PR China;4. China Academy of Space Technology, Beijing 100094, PR China;1. Computer Science & Engineering Department, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates;2. Computer Science & Engineering Department, American University of Sharjah, Sharjah, United Arab Emirates;3. University of Science and Technology Houari Boumediene, Algeria;4. Tomsk State University, Russia;1. Young Researchers and Elite Club, Qazvin Branch, Islamic Azad University, Qazvin, Iran;2. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran;3. Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran |
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| Abstract: | A multi-product economic production quantity model with several real-world technical and physical constraints is developed in this paper. The cost function includes ordering, holding, backordering, lost sale, and the cost caused by unused space in the warehouse. The goal is to minimize the total inventory cost, where shortages are allowed and partially backordered with fixed and linear costs. The aim is to determine the length of the inventory cycle, the length of positive inventory period, and the backordering rates of the products during the shortage period in order to minimize the total inventory costs while satisfying all constraints. Due to complexity and non-linearity of the proposed model, sequential quadratic programming (SQP), stochastic fractal search (SFS), simulated annealing (SA), and water cycle algorithm (WCA) are utilized for solution. Ninety numerical examples in small, medium, and large sizes are solved to evaluate the efficiency of the solution methods. The performances of the solution methods are compared statistically. Besides, sensitivity analysis is performed to determine the effect of change in the main parameters of the problem on the objective function value and decision variables. |
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| Keywords: | Economic production quantity Partial backordering Sequential quadratic programming Stochastic fractal search Simulated annealing Water cycle algorithm |
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