Main Article Content
Optimization Technique aims to find the best possible option that meet all the imposed constraints. In fact, the goal in this paper is to find the best values for the decision variables for various inventory systems in order to maximize net profit by the field of numerical optimization for linear programming using software. Besides, the optimize procedure was applied on the production planning problem (vegetable oil production Problem) models in many methods which is equations and objective, dense matrices and sparse matrices. The optimization was implemented within the Python by GEKKO package. Finally, the numerical results of the techniques used showed a strong convergence in calculating the amount of profit and production lines, which indicates their efficiency and accuracy in obtaining optimal solutions.
- 1. Diwekar, U. M. (2020). Introduction to applied optimization (Vol. 22). Springer Nature.
- 2. Andersson, J. A., Gillis, J., Horn, G., Rawlings, J. B., & Diehl, M. (2019). CasADi: a software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1), 1-36.
- 3. Wu, T., Huang, L., Liang, Z., Zhang, X., & Zhang, C. (2021). A supervised learning-driven heuristic for solving the facility location and production planning problem. European Journal of Operational Research.
- 4. Chakrabortty, R. K., & Hasin, M. A. A. (2013). Solving an aggregate production planning problem by fuzzy based genetic algorithm (FBGA) approach. International Journal of Fuzzy Logic Systems (IJFLS), 3(1), 1-16.
- 5. Haq, A., Kamal, M., Gupta, S., & Ali, I. (2020). Multi-objective production planning problem: a case study for optimal production. International Journal of Operational Research, 39(4), 459-493.
- 6. Gladkov, L. A., Gladkova, N. V., & Gromov, S. A. (2017, April). Hybrid fuzzy algorithm for solving operational production planning problems. In Computer Science On-line Conference (pp. 444-455). Springer, Cham.
- 7. Torkaman, S., Ghomi, S. F., & Karimi, B. (2018). Hybrid simulated annealing and genetic approach for solving a multi-stage production planning with sequence-dependent setups in a closed-loop supply chain. Applied Soft Computing, 71, 1085-1104.
- 8. Brown, C., Abdelfattah, A., Tomov, S., & Dongarra, J. (2020, September). Design, optimization, and benchmarking of dense linear algebra algorithms on AMD GPUs. In 2020 IEEE High Performance Extreme Computing Conference (HPEC) (pp. 1-7). IEEE.
- 9. Chen, S., Fang, J., Chen, D., Xu, C., & Wang, Z. (2018, June). Adaptive optimization of sparse matrix-vector multiplication on emerging many-core architectures. In 2018 IEEE 20th International Conference on High Performance Computing and Communications; IEEE 16th International Conference on Smart City; IEEE 4th International Conference on Data Science and Systems (HPCC/SmartCity/DSS) (pp. 649-658). IEEE.
- 10. Beal, L. D., Hill, D. C., Martin, R. A., & Hedengren, J. D. (2018). Gekko optimization suite. Processes, 6(8), 106.
- 11. Gates, N. S., Hill, D. C., Billings, B. W., Powell, K. M., & Hedengren, J. D. (2021, December). Benchmarks for Grid Energy Management with Python Gekko. In 2021 60th IEEE Conference on Decision and Control (CDC) (pp. 4868-4874). IEEE.
- 12. Bashier, E. B. (2020). Practical Numerical and Scientific Computing with MATLAB® and Python. CRC Press.