A Robust Possibilistic Chance-Constrained Programming Model for Optimizing a Multi-Objective Aggregate Production Planning Problem under Uncertainty

Subject Areas : Production Control

Navee Chiadamrong ¹ , Tuan Doan ²

1 - SIIT, Thamamsat University, Pathum Thani, Thailand
2 - SIIT, Thammasat University, Pathum Thani, Thailand

Received: 2021-09-13 Accepted : 2022-03-02 Published : 2021-12-01

Keywords: App, Multiple Objective Optimization, robust solution, credibility measure, epsilon-constraint,

Abstract :

Data uncertainty and multiple conflicting objectives are two crucial issues that the Decision Makers (DMs) must handle in making Aggregate Production Planning (APP) decisions in real practice. In order to address these two-mentioned issues, this study presents a multi-objective multi-product multi-period APP problem in an uncertain environment. The model strives to minimize the total costs of the APP plan, total changing rate in workforce levels, and total holding inventory and backorder quantities simultaneously through the Robust Possibilistic Chance-Constrained Programming (RPCCP) optimization approach. In this integrated approach, the RPCCP is applied for handling uncertain data. The RPCCP can not only handle any fuzzy position in the fuzzy model but also control the robustness of optimality and feasibility of the fuzzy model. Then, an Augmented Epsilon-Constraint (AUGMECON) technique is used to cope with multiple conflicting objectives. The AUGMECON technique can produce exact Pareto optimal solutions, which offer the DMs different selections to assess against conflicting objectives. Next, an industrial case study is provided to validate the applicability and effectiveness of the proposed methodology. The obtained outcomes indicate that the proposed RPCCP model outperforms the Possibilistic Chance-Constrained Programming (PCCP) model in terms of interested performance measurements (i.e., average and standard deviation of the objective function). In addition, a set of strong Pareto optimal solutions can be generated to accommodate alternative selections according to the DM’s preferences. Finally, by applying the Max-Min method, the best compromised (trade-off) solution is determined through a comparison among the attained Pareto solutions.

References:

[1] Techawiboonwong, A., & Yenradee, P. (2003). Aggregate production planning with workforce transferring plan for multiple product types. Production Planning & Control, 14(5), 447-458.

[2] Hafezalkotob, A., Chaharbaghi, S., & Lakeh, T. M. (2019). Cooperative aggregate production planning: a game theory approach. Journal of Industrial Engineering International, 15(1), 19-37.

[3] Chiadamrong, N., & Sutthibutr, N. (2020). Integrating a weighted additive multiple objective linear model with possibilistic linear programming for fuzzy aggregate production planning problems. International Journal of Fuzzy System Applications, 9(2), 1-30.

[4] Tuan, D. H., & Chiadamrong, N. (2021). A fuzzy credibilitybased chance-constrained optimization model for multipleobjective aggregate production planning in a supply chain under
an uncertain environment. Engineering Journal, 25(7), 31-58.

[5] Holt, C. C., Modigliani, F., & Simon, H. A. (1955). A linear decision rule for production and employment scheduling. Management Science, 2(1), 1-30.

[6] Silva, J. P., Lisboa, J., & Huang, P. (2000). A labourconstrained model for aggregate production planning. International Journal of Production Research, 38(9), 2143-2152.
[7] Pradenas, L., Peñailillo, F., & Ferland, J. (2004). Aggregate production planning problem. A new algorithm. Electronic Notes in Discrete Mathematics, 18, 193-199.
[8] Sillekens, T., Koberstein, A., & Suhl, L. (2011). Aggregate production planning in the automotive industry with special consideration of workforce flexibility. International Journal of
Production Research, 49(17), 5055-5078.
[9] Ramezanian, R., Rahmani, D., & Barzinpour, F. (2012). An aggregate production planning model for two phase production systems: Solving with genetic algorithm and tabu search. Expert
Systems with Applications, 39(1), 1256-1263.
[10] Zhang, R., Zhang, L., Xiao, Y., & Kaku, I. (2012). The activitybased aggregate production planning with capacity expansion in manufacturing systems. Computers & Industrial Engineering,
62(2), 491-503.
[11] Wang, S. C., & Yeh, M. F. (2014). A modified particle swarm optimization for aggregate  production planning. Expert Systems with Applications, 41(6), 3069-3077.
[12] Erfanian, M., & Pirayesh, M. (2016, December). Integration aggregate production planning and maintenance using mixed integer linear programming. In 2016 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) (pp. 927-930). IEEE.
[13] Dao, S. D., Abhary, K., & Marian, R. (2017). An improved genetic algorithm for multidimensional optimization of precedence-constrained production planning and scheduling.
Journal of Industrial Engineering International, 13(2), 143-159.
[14] Pradenas, L., Bravo, G., & Linfati, R. (2020). Optimization model for remanufacturing in a real sawmill. Journal of Industrial Engineering, International, 16(2), 32-40.
[15] Cha-Ume, K., & Chiadamrong, N. (2012). Simulation of retail supply chain behaviour and financial impact in an uncertain
environment. International Journal of Logistics Systems and Management, 13(2), 162-186.
[16] Bakir, M. A., & Byrne, M. D. (1998). Stochastic linear optimisation of an MPMP production planning model. International Journal of Production Economics, 55(1), 87-96.
[17] Leung, S. C., Wu, Y., & Lai, K. K. (2006). A stochastic programming approach for multi-site aggregate production planning. Journal of the Operational Research Society, 57(2), 123-132.
[18] Kazemi Zanjani, M., Nourelfath, M., & Aït-Kadi, D. (2011). Production planning with uncertainty in the quality of raw materials: a case in sawmills. Journal of the Operational Research Society, 62(7), 1334-1343.
[19] Lai, Y. J., & Hwang, C. L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems, 49(2), 121-133.
[20] Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2012). Robust possibilistic programming for socially responsible supply chain network design: A new approach. Fuzzy Sets and Systems, 206,1-20.
[21] Ghezavati, V. R., & Beigi, M. (2016). Solving a bi-objective mathematical model for location-routing problem with time windows in multi-echelon reverse logistics using metaheuristic procedure. Journal of Industrial Engineering International, 12(4), 469-483.
[22] Masud, A. S., & Hwang, C. L. (1980). An aggregate production planning model and application of three multiple objective decision methods. International Journal of Production
Research, 18(6), 741-752.
[23] Wang, R. C., & Fang, H. H. (2001). Aggregate production planning with multiple objectives in a fuzzy environment. European Journal of Operational Research, 133(3), 521-536.
[24] Wang, R. C., & Liang, T. F. (2004). Application of fuzzy multiobjective linear programming to aggregate production planning. Computers & Industrial Engineering, 46(1), 17-41.
[25] Wang, R. C., & Liang, T. F. (2005). Aggregate production planning with multiple fuzzy goals. The International Journal of Advanced Manufacturing Technology, 25(5-6), 589-597.
[26] Liang, T. F., & Cheng, H. W. (2011). Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial & Management Optimization, 7(2), 365.
[27] Shirazi, H., Kia, R., Javadian, N., & Tavakkoli-Moghaddam, R. (2014). An archived multi-objective simulated annealing for a dynamic cellular manufacturing system. Journal of Industrial
Engineering International, 10(2), 1-17.
[28] Mosadegh, H., Khakbazan, E., Salmasnia, A., & Mokhtari, H. (2017). A fuzzy multi-objective goal programming model for solving an aggregate production planning problem with uncertainty. International Journal of Information and Decision Sciences, 9(2), 97-115.
[29] Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264-281.
[30] Zahiri, B., Tavakkoli-Moghaddam, R., & Pishvaee, M. S. (2014). A robust possibilistic programming approach to multiperiod location–allocation of organ transplant centers under
uncertainty. Computers & Industrial Engineering, 74, 139-148.
[31] Rabbani, M., Zhalechian, M., & Farshbaf‐Geranmayeh, A. (2018). A robust possibilistic programming approach to multiperiod hospital evacuation planning problem under uncertainty. International Transactions in Operational Research, 25(1), 157-189.
[32] Hamidieh, A., Naderi, B., Mohammadi, M., & Fazli-Khalaf, M. (2017). A robust possibilistic programming model for a responsive closed loop supply chain network design. Cogent Mathematics, 4(1), 1329886.
[33] Doodman, M., Shokr, I., Bozorgi-Amiri, A., & Jolai, F. (2019). Pre-positioning and dynamic operations planning in pre-and post-disaster phases with lateral transhipment under uncertainty
and disruption. Journal of Industrial Engineering International, 15(1), 53-68.
[34] Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6), 613-626.
[35] Heilpern, S. (1992). The expected value of a fuzzy number. Fuzzy Sets and Systems, 47(1), 81-86.
[36] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
[37] Li, X., & Liu, B. (2006). A sufficient and necessary condition for credibility measures. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14(05), 527-535.
[38] Mousazadeh, M., Torabi, S. A., & Pishvaee, M. S. (2014). Green and reverse logistics management under fuzziness. In Supply Chain Management under Fuzziness (pp. 607-637). Springer, Berlin, Heidelberg.
[39] Fazli-Khalaf, M., Fathollahzadeh, K., Mollaei, A., Naderi, B., & Mohammadi, M. (2019). A robust possibilistic programming model for water allocation problem. RAIRO-Operations Research, 53(1), 323-338.
[40] Williams, H. P. (2013). Model Building in Mathematical Programming, 5th edition, John Wiley & Sons. 153–154.
[41] Maiti, S. K., & Roy, S. K. (2016). Multi-choice stochastic bilevel programming problem in cooperative nature via fuzzy programming approach. Journal of Industrial Engineering International, 12(3), 287-298.
[42] Kundu, T., & Islam, S. (2019). An interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem. Journal of Industrial Engineering International, 15(1), 95-104.
[43] Mavrotas, G. (2009). Effective implementation of the εconstraint method in multi-objective mathematical programming problems. App