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

Abstract

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.