Generation and presentation of nearly optimal solutions for mixed-integer linear programming, applied to a case in farming system design

Abstract

In complex decision problems, some objectives are not well quantified or are not introduced explicitly in optimization models. In view of this inherent limitation of models, solutions that are nearly optimal, i.e. deviating less than a predefined percentage from the optimal value of the quantified objective functions, can constitute interesting alternatives for stakeholders. The aim of this paper is to extend the analysis of nearly optimal solutions to mixed-integer linear programming (MILP) models. Two branch-and-bound algorithms are described to generate nearly optimal solutions, and methods are discussed to summarise and to present nearly optimal solutions. A case study is introduced with an MILP model developed to design farming systems in the Netherlands. This case study shows that the presentation of nearly optimal solutions provides relevant information to resolve complex decision problems.