Abstract
Based on a case study, this paper deals with the production planning and scheduling problem of the glass container industry. This is a facility production system that has a set of furnaces where the glass is produced in order to meet the demand, being afterwards distributed to a set of parallel molding machines. Due to huge setup times involved in a color changeover, manufacturers adopt their own mix of furnaces and machines to meet the needs of their customers as flexibly and efficiently as possible. In this paper we proposed an optimization model that maximizes the fulfillment of the demand considering typical constraints from the planning production formulation as well as real case production constraints such as the limited product changeovers and the minimum run length in a machine. The complexity of the proposed model is assessed by means of an industrial real instance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AL-Tahat, M. D., & Bataineh, K. M. (2012). Statistical analyses and modeling of the implementation of agile manufacturing tactics in industrial firms. Mathematical Problems in Engineering, 2012(731092), 23.
Almada-Lobo, B., Klabjan, D., Carravilla, M. A., & Oliveira, J. F. (2010). Multiple machine continuous setup lotsizing with sequence-dependent setups. Computational Optimization and Applications, 47(3), 529–552.
Ball, M. O. (2011). Heuristics based on mathematical programming. Surveys in Operations Research and Management Science, 16(1), 21–38.
Beraldi, P., Ghiani, G., Grieco, A., & Guerriero, E. (2008). Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs. Computers & Operations Research, 35(11), 3644–3656 (Part Special Issue: Topics in Real-time Supply Chain Management).
Camargo, V. C., Toledo, F. M., & Almada-Lobo, B. (2014). Hops hamming-oriented partition search for production planning in the spinning industry. European Journal of Operational Research, 234(1), 266–277.
Chen, W.-L., Huang, C.-Y., & Lai, Y.-C. (2009). Multi-tier and multi-site collaborative production: Illustrated by a case example of TFT LCD manufacturing. Computers & Industrial Engineering, 57(1), 61–72 (Collaborative e-Work Networks in Industrial Engineering).
Copil, K., Wörbelauer, M., Meyr, H., & Tempelmeier, H. (2017). Simultaneous lotsizing and scheduling problems: A classification and review of models. OR Spectrum, 39(1), 1–64.
Fabiano, M. T. C., Arantes, D. S., Márcio, Oliveira, D., Ribeiro, R. R., & Almada-Lobo, B. (2013). Glass container production scheduling through hybrid multi-population based evolutionary algorithm. Applied Soft Computing, 13(3), 1352–1364.
Fabiano Motta Toledo, C., da Silva Arantes, M., Yukio Bressan Hossomi, M., & Almada-Lobo, B. (2016). Mathematical programming-based approaches for multi-facility glass container production planning. Computers & Operations Research, 74, 92–107.
James, R. J., & Almada-Lobo, B. (2011). Single and parallel machine capacitated lotsizing and scheduling. Computers & Operations Research, 38(12), 1816–1825.
Martineza, K. Y., Tosob, E. A., & Morabitoa, R. (2016). Production planning in the molded pulp packaging industry. Computers & Industrial Engineering, 98, 554–566.
Mukhopadhyay, S., Dwivedy, J., & Kumar, A. (2010). Design and implementation of an integrated production planning system for a pharmaceutical manufacturing concern in india. Production Planning & Control, 9(4), 391–402.
Paul, R. J. (1979). A production scheduling problem in the glass-container industry. Operations Research, 27(2), 290–302.
Sahling, F., Buschkühl, L., Tempelmeier, H., & Helber, S. (2009). Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic. Computers & Operations Research, 36(9), 2546–2553.
Setia, P., Sambamurthy, V., & Closs, D. J. (2008). Realizing business value of agile it applications: antecedents in the supply chain networks. Information Technology and Management, 9(1), 5–19.
Wei, W., Guimaraes, L., Amorim, P., & Almada-Lobo, B. (2017). Tactical production and distribution planning with dependency issues on the production process. OMEGA, 67, 99–114.
Acknowledgements
The authors are grateful to Sintec for financial and technical support during the development of this research. Sintec is the leading business consulting firm for Supply Chain, Customer and Operations Strategies with a consultative model in Developing Organizational Skills that enable their customers to generate unique capabilities based on processes, organization and IT. Also, we appreciate the financial support of CONACYT-SNI program in order to promote quality research.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
As mentioned in Problem description section, during this case study, the minimum run length of product j at machine m allowed is 3 days. This condition is given in Eqs. 4 to 6. Where the binary variable \(x^t_{jm}\) takes value of 1 if the shape j is produced in machine m at day t, and zero otherwise. In this “Appendix” the functionality of the constraints is illustrated using all possible scenarios.
- 4.
\({x_{j,m}^{t-1}} + {x_{j,m}^{t+1}} \ge {x_{j,m}^t} \quad \quad \quad \forall j \in J,m \in M,t = 2,\ldots ,|T| - 1\)
- 5.
\({x_{j,m}^{t-2}} + {x_{j,m}^{t+1}}\ge {x_{j,m}^{t-1}} \quad \quad \quad \forall j \in J,m \in M,t = 3,\ldots ,|T| - 1\)
- 6.
\({x_{j,m}^{t-2}} + {x_{j,m}^t}\ge {x_{j,m}^{t-1}} \quad \quad \quad \forall j \in J,m \in M,t = 3,\ldots ,|T|\)
Table 4 shows all possible scenarios for assigning a product j to a machine m during a period of 5 days denoted as: \(k-2, k-1, k, k+1, k+2\). Then, scenario 1 shows that product j is not assigned to machine m at the given period, while scenario 14 shows that the product j has been assigned to machine m for the whole period.
Equations 4 to 6 are tested for \(t=k\) and \(t=k+1\). In this way, a scenario that fulfill the equation is check-marked as \(\checkmark \) or crossed \(\times \) otherwise. Desired scenarios are those that does not violate the 3 days minimum run length condition.
As Table 4 shows, all desired scenarios fulfill the set of equations, while undesired scenarios do not.
Rights and permissions
About this article
Cite this article
Hervert-Escobar, L., López-Pérez, J.F. Production planning and scheduling optimization model: a case of study for a glass container company. Ann Oper Res 286, 529–543 (2020). https://doi.org/10.1007/s10479-018-3099-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-018-3099-1