The business advantage of identifying and solving pseudo-continuous-integer periodical linear problems

Document Type : Article


1 Tecnologico de Monterrey, EGADE Business School, Ave. Eugenio Garza Lagueray Rufino Tamayo, San Pedro Garza Garcia, N.L., Mexico, 66269

2 Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., Mexico, 64849


Many applications of optimisation require the final value of the decision variables to
be integer. In many cases the relaxed optimal solution does not satisfy the integral-
ity constraint therefore, the problem must be solved by integer or mix-integer pro-
gramming algorithms at a significant computational effort and most likely a worsen
objective function value. The contribution of this paper is twofold: The identification
of a type of problems in which the relaxed optimal objective function value can be
kept in the implementation by a change in the planning horizon; and the identifica-
tion of a multi-period based solution procedure. Three small instances are provided
in order to illustrate the methodology as well as the economic impact involved. In
addition, a fourth industrial size case is included for the benefit of practitioners.
This work shows that business profit can be increased for pseudo-continuous-integer
periodical linear problems by identifying optimal decision-making periods.


1. Oluleye, G., Vasquez, L., Smith, R., et al. "A multiperiod mixed integer linear program for design of residential distributed energy centres with thermal demand data discretisatio", Sustainable Production and Consumption, 5, pp. 16-28 (2016).
2. Tan, R.R. "A multi-period source-sink mixed integer linear programming model for biochar-based carbon sequestration systems", Sustainable Production and Consumption, 8, pp. 57-63 (2016).
3. Ciavotta, M., Ardagna, D., and Gibilisco, G.P. "A mixed integer linear programming optimization approach for multi-cloud capacity allocation", Journal of Systems and Software, 123, pp. 64-78 (2017).
4. Oluleye, G., Allison, J., Kelly, N., et al. "A multiperiod mixed integer linear program for assessing the benefits of power to heat storage in a dwelling energy system", In Computer Aided Chemical Engineering, 43, pp. 1451-1456 (2018).
5. Zeng, Y., Xiao, X., Li, J., et al. "A novel multi-period mixed-integer linear optimization model for optimal distribution of byproduct gases, steam and power in an iron and steel plant", Energy, 143, pp. 881-899 (2018).
6. Bastos, L.S., Marchesi, J.F., Hamacher, S., et al. "A mixed integer programming approach to the patient admission scheduling problem", European Journal of Operational Research, 273(3), pp. 831-840 (2019).
7. Dorneanu, B., Sidnell, T., Clarke, F., et al. "A Mixedinteger linear programming model for the optimal operation and design of residential neighbourhoods", IFAC-PapersOnLine, 52(1), pp. 934-939 (2019).
8. Abbaszadeh, N., Asadi-Gangraj, E., and Emami, S. "Flexible flow shop scheduling problem to minimize makespan with renewable resources", Scientia Iranica, 28(3), pp. 1853-1870 (2021).
9. Abrishami, S.J., Vahdani, H., and Rezaee, B. "An integrated lot-sizing model with supplier and carrier selection and quantity discounts considering multiple products", Scientia Iranica, 27(4), pp. 2140-2156 (2020).
10. Zeballos, L.J., Mendez, C.A., and Povoa, A.P.B. "Mixed-integer linear programming approach for product design for life-cycle profit", Computers & Industrial Engineering, 137, p. 106079 (2019).
11. Dantzig, G., Linear Programming and Extensions, Princeton University Press (1963).
12. Khachiyan, L.G. "Polynomial algorithms in linear programming", USSR Computational Mathematics and Mathematical Physics, 20(1), pp. 53-72 (1980).
13. Karmarkar, N. "A new polynomial-time algorithm for linear programming", In Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, pp. 302-311 (1984).
14. Lawler, E.L. and Wood, D.E. "Branch-and-bound methods: A survey", Operations Research, 14(4), pp. 699-719 (1966).
15. Balas, E. "Intersection cuts-A new type of cutting planes for integer programming", Operations Research, 19(1), pp. 19-39 (1971).
16. Chen, D.-S., Batson, R.G., and Dang, Y. "Branch-andcut approach", Applied Integer Programming: Modeling and Solution, John Wiley & Sons, pp. 305-333 (2009).
17. Chvatal, V., Linear Programming, Macmillan (1983).
18. Trigos, F. and Lopez, E.M. "Maximising profit for multiple-product, Single-period, single-machine manufacturing under sequential set-up constraints that depend on lot size", International Journal of Production Research, 54(4), pp. 1134-1151 (2016).
19. Applegate, D.L., Cook, W., Dash, S., et al. "Exact solutions to linear programming problems", Operations Research Letters, 35(6), pp. 693-699 (2007).
20. Arreola, J. and Arreola, A., Programacion Lineal, una Introduccion a la Toma de Decisiones Cuantitativa Thomson, (2003).
21. Slotnick, S.A. "Order acceptance and scheduling: A taxonomy and review", European Journal of Operational Research, 212(1), pp. 1-11 (2011).