Sugar beet transportation problem under growers’ equity regulations: Metaheuristic approach

We consider the optimization problem related to the sugar beet transportation when supplying sugar mills in the sugar production. The sugar beet transportation comprises of loading the beet collected at storage piles and then delivering it to sugar mills. An essential prerequisite to guarantee a viability of the considered sugar mill, is to transport the required quantities of sugar beet while maximizing technological quality and minimizing transportation costs. Some growers may be privileged to conduct collection activities in days of a planning period when sugar beet is fresh and contains larger amount of sucrose, while others do not. This unfair collect scheduling plan should be avoided to provide equal treatment of growers. We propose an Integer Linear Programming (ILP) model with the aim of simultaneously maximizing the amount of collected sucrose during the planning period while minimizing the number of vehicles of a homogenous vehicle fleet, including constraints that provide equal opportunities for growers in sugar beet collection. The problem is denoted by the Sugar Beet Transportation Problem under Growers’ Equity Regulations (SBT-GER). By applying the weighted sum method, the two objective functions are combined to transform the bi-objective problem into a single-objective one. Equity regulations are expressed through the requirement that the minimum percentage of the quantity of sugar beet is guaranteed to be collected from each grower on the day of harvest. For real-sized instances, we propose two metaheuristic algorithms, based on Variable Neighborhood Search (VNS) and Greedy Randomized Adaptive Search Procedure (GRASP), respectively. The developed mathematical model and the proposed metaheuristic approaches are evaluated on a set of randomly generated test instances. The obtained results show that VNS outperforms exact solver and GRASP for the majority of examples.