Developing and Solving a Two Level Lot Sizing Problem

Document Type : Original Article

Authors

1 M.Sc, Islamic Azad University Qazvin.

2 Professor, Allameh Tabatabaei University.

Abstract

In This Article, a two level lot sizing problem with multi production methods and fuzzy demand is presented.The objective of the model is to minimize the costs.Various approaches like Genetic Algorithm (GA), Simulated Annealing (SA) and Vibration Damping Optimization (VDO) are applied to solve the model. Taguchi method has been utilized to calibrate the parameters of algorithms. Then, in order to prove the appropriate performance of the presented solving methods and choosing the most efficient method in order to solve the presented model, first, trial issues created with different dimensions and next solved by Lingo software and the proposed algorithms.Finally, we analyzed the responses.According to the statistical analysis and the results shown by the graph,Vibration Damping Optimization algorithm responses in large dimension issues is better than Simulated Annealing and Genetic Algorithm. Also Simulated annealing responses in large dimensionissues is better than Genetic Algorithm.

Keywords


1. Alinejad, Alireza., Sabet Sajjad., Ekhtiari Mostafa., (1393). Solving a fuzzy multi-objective dynamic cellular production system by using a hybrid NSGA-II- simulated annealing algorithm, Journal of Industrial Management Perspective, 15: 131-156.
2. Amiri Maghsoud., Barzegar Majid., Niknamfar Amirhosein., (1395). Aggregated production- distribution planning by robust optimization approach in three echelon supply chain, Journal of Industrial Management Perspective, 23: 9 – 28.
3. Adeli Majid., Zandieh Mostafa., (1392). Providing a multi-objective simulation optimization for sourcing and integrated inventory decision making, Journal of Industrial Management Perspective, 11: 89-110.
4. Boonmee A., Sethanan K., (2016). A GLNPSO for multi-level capacitated lot-sizing and scheduling problem in the poultry industry.European Journal of Operational Research, 250: 652–665.
5. Chang H.C., Yao J.S., Ouyang L.Y., (2006). Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand.European Journal of Operational Research, 169: 65–80.
6. Chen H., (2015). Fix-and-optimize and variable neighborhood search approaches for Multi-Level Capacitated Lot Sizing Problems.OMEGA: 1-33.
7. Delgado M, Herrera F, Herrera-Viedma E, Marffnez L. (1998). Combining numerical and linguistic information in group decision making. Journal of Information Sciences, 107: 177-194.
8. Guner Goren H., Tunali S., (2015).Solving the capacitated lot sizing problem with setup carryover using a new sequential hybrid approach.Artificial Intelligence, 42: 805–816.
9. Gutierrez E., Hernández W., Süer G.A., (2001). Genetic Algorithms in Capacitated Lot Sizing Decisions, Computing research confrance. University of Puerto Rico, March 31.
10. Hajipour, V., Zanjirani Farahani, R., Fattahi P., (2016). Bi-objective vibration damping optimization for congested location–pricing problem.Computers & Operations Research, 70: 87–100.
11. Hasani K., Kravchenkob S.A., Wernerc F., (2014).Simulated annealing and genetic algorithms for the two-machine scheduling problem with a single server.International Journal of Production Research,52: 3778–3792.
12. Jans R., Degraeve Z.(2007).Meta-heuristics for dynamic lot sizing: A review
and comparison of solution approaches.European Journal of Operational Research 177: 1855–1875.
13. Ketsarapong S., Punyangarm V., Phusavat K., (2011). The single item lot sizing problem with fuzzy parameters: apossibility approach. TIIM2011 CONFERENCE, 28-30 June, Oulu Finland: 193-210.
14. Kirkpatrick S., Gelatt C.D., Vecchi M.P. (1983). Optimization by Simulated Annealing.Science, 220: 671-680.
15. Li X., Baki F., Tian P., Chaouch B.A. (2014). A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing.Omega 42: 75–87.
16. Mehdizaed, Esmaeel,. Atashi Abkenar, Amir Aidin, (1393). Solving an aggregate production planning of a multi-stage production system and by considering the maintenance and repairing cost by using of meta-heuristic algorithms, Master thesis.
17. Mehdizadeh, E., Tavakkoli-Moghaddam, R. (2009). Vibration damping optimization algorithm for an identical parallel machine scheduling problem.Proc.of the 2ndInt.Conf of Iranian Operations Research Society, Babolsar, Iran.
18. Mehdizadeh, E., Fatehi-Kivi, A. (2013). The Single-item Capacitated lot-Sizing Problem with Backlogging.Safety Stocks and Limited Outsourcing.2ndInternational Conference on Industrial Engineering, 2: 516-520.
19. Moti Ghader Habib., Lotfi Shahriar., Seyed Esfehlan Mir Mahdi., (1389).A review on some intelligent optimization, Islamic Azad University Publication, branch of Shabestar.
20. Rabbani,Arash(1390).Using fuzzy approach in determination of lot sizes in multi echelon, multi products, with limited capacity in systems which are based on MRP, Journal of Industrial Management Faculty of Humanities of Islamic Azad University branch of Sanandaj, year 5th, 15: 51- 53.
21. Ramezanian R., Mehrabad M.S. (2013). Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system.Applied Mathematical Modelling, 37:5134–5147.
22. Sadeghi Avval Shahr, Alireza., Babakhani, Abolfazl,. Mostajaboldave, Hasan & Zeberjad, Seyed Mojtaba. (1391). Optimizing the Parameters ofPowder metallurgy process of producing Shape Memory AlloyNitinol by using Taguchi method. 1st International Conference, 6thInternational Joint Conference of Iranian Metallurgical Engineering & Iranian Foundry men Society.
23. Toledo C.F.M., França P.M., Morabito R., Kimms A., (2009). A multi-population genetic algorithm approach to solve the synchronized and integrated two-level lot sizing and scheduling problem.Int J Product Res, 47: 3097–3119.
24. Toledo C.F.M., Oliveira L.d., Pereira R.D.F., França P.M., Morabito R., (2014). A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem.Computers & Operations Research, 48: 40–52.
25. Verma M., Sharma R.R.K., (2015). Lagrangian based approach to solve a two level capacitated lot sizing problem, Cogent Engineering, 2: 1-13.
26. Wu T., Shi L., Song J., (2012). An MIP-based interval heuristic for the capacitated multi-level lot-sizing problem with setup times.Annals of Operations Research, 196: 635–650.