Optimization of multi-product economic production quantity model with partial backordering and physical constraints: SQP, SFS, SA, and WCA

The average RPE of the solutions obtained for large size problems.Display Omitted A multi-product EPQ model with several technical and physical constraints is developed.Shortages are allowed and partially backordered with fixed and linear costs.SQP, SFS, SA, and WCA are utilized for solution.Ninety numerical examples in small, medium, and large sizes are solved to evaluate the performances.The results show the better performance of WCA. 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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