Innovative Applications of O.R. Harvest planning in the Brazilian sugar cane industry via mixed integer programming Sanjay Dominik Jena, Marcus Poggi ⇑ Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente, 225 RDC CEP, 22451-900 Gávea, Rio de Janeiro RJ, Brazil article info Article history: Received 26 July 2012 Accepted 8 April 2013 Available online 20 April 2013 Keywords: OR in agriculture Sugar cane harvesting Mixed integer programming Valid inequalities abstract This work addresses harvest planning problems that arise in the production of sugar and alcohol from sugar cane in Brazil. The planning is performed for two planning horizons, tactical and operational plan- ning, such that the total sugar content in the harvested cane is maximized. The tactical planning com- prises the entire harvest season that averages seven months. The operational planning considers a horizon from seven to thirty days. Both problems are solved by mixed integer programming. The tactical planning is well handled. The model for the operational planning extends the one for the tactical planning and is presented in detail. Valid inequalities are introduced and three techniques are proposed to speed up finding quality solutions. These include pre-processing by grouping and filtering the distance matrix between fields, hot starting with construction heuristic solutions, and dividing and sequentially solving the resulting MIP program. Experiments are run over a set of real world and artificial instances. A case study illustrates the benefits of the proposed planning. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Sugar cane is one of the most important commodities in the world (FAO, 2012), commonly being further processed to sugar or agro fuel. With more than 420 million tons of harvested sugar cane in the year 2005, Brazil is by far the largest producer of this crop worldwide, followed by India, China and Thailand. Among all agricultural commodities produced in Brazil, sugar cane is its most produced measured in biomass and its fourth most lucrative. Internationally, sugar cane production is a highly competitive mar- ket. Recent studies such as the ones by Higgins et al. (2007) and Bezuidenhout and Baier (2009) indicated great opportunities to improve the value chain and reduce costs in the operational plan- ning to remain competitive. On the level of sugar cane harvest planning, there are com- monly two major planning objectives. First, the highest possible profit in terms of quantity and quality of the harvested cane, respecting certain industrial, social and environmental constraints. Such constraints include limited cutting capacities as well as con- stant cane supply at the mills. Second, the reduction of all costs in- volved. The profit strongly depends on the sugar content when harvesting the cane. Due to limited resources and constraints, har- vesting at each field at its maturation peak is commonly not feasible. Based on the experience of a large Brazilian sugar producer, this work aims at providing mathematical models for tactical and oper- ational harvest planning, focusing on the objective and constraints pointed out above. In the following, we explain the problem in more detail and outline the structure of this paper. 1.1. Problem description The problem, denoted by the Sugar Cane Cultivation and Harvest Problem (SCHP) throughout this work, is now described. One of its most important decisions is the moment to harvest the plantation fields. Clearly, it is desirable to harvest each field at the peak of its sugar content, as the sugar content indicated by the percentage of sucrose in the sugar cane (Pol) and the reduced sugar, vary as the cane grows. The cane at each field possesses a certain initial age and can only be cut within a given interval of its age. 1.1.1. Cutting crews Sugar cane is harvested by cutting crews, chopping down the stems but leaving the roots to re-grow in time for the following harvest. Even though most cutting crews are mechanical, federal working agreements oblige Brazilian harvesting companies to con- tract a certain minimum of manual harvesting, i.e., a group of hu- man workers. One of the Brazilian sugar cane companies involved in this research currently holds five mechanical and one manual harvesting crews, which is referred to be a representative propor- tion. Each cutting crew may be eligible to cut only a certain subset of the fields. Cutting crews may not work every day and work a 0377-2217/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2013.04.011 ⇑ Corresponding author. Tel.: +55 2193841763. E-mail addresses: sjena@inf.puc-rio.br (S.D. Jena), poggi@inf.puc-rio.br (M. Poggi). European Journal of Operational Research 230 (2013) 374–384 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor