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

Many applications of optimisation require the final value of the decision variables tobe 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 worsenobjective function value. The contribution of this paper is twofold: The identificationof a type of problems in which the relaxed optimal objective function value can bekept 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 providedin order to illustrate the methodology as well as the economic impact involved. Inaddition, a fourth industrial size case is included for the benefit of practitioners.This work shows that business profit can be increased for pseudo-continuous-integerperiodical linear problems by identifying optimal decision-making periods.