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

Many optimization applications require the final value of decision variables to be integer. In many cases, the relaxed optimal solution does not satisfy the integrality constraint; therefore, the problem must be solved using integer or mix-integer programming algorithms with significant computational effort and most likely a worsen objective function value. The contribution of this paper is two-fold: (a) identification of a type of problems in which the relaxed optimal objective function value can be kept at the implementation phase by modifying the planning horizon and (b) identification 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-scale 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. (C) 2022 Sharif University of Technology. All rights reserved.