A hierarchical supply chain model for the sugar–alcohol energy sector with robust optimization analysis

Abstract

This paper addresses a hierarchical optimization model for the sugar-alcohol energy sector with robust optimization analysis to provide managerial insights. It has two levels: the upper level is a linear model in which more aggregated decisions are related to allocating production targets to mills belonging to a cooperative society aiming to meet the potential market demand, as well as managing the inventories over months in annual planning; the lower level is a mixed-integer model that represents the less aggregated decisions of each mill, such as the milling rhythm, the industrial process selection to produce sugar-alcohol-molasses and energy, purchasing sugarcane from the suppliers on a weekly basis. Robust optimization analysis is performed for product prices and industrial yields to investigate their impacts on the supply chain that could not be inferred through deterministic approaches. One important result was related to the uncertainty in product prices that had a greater impact on the whole supply chain compared to the industrial yield, which affects only the mill itself, particularly increasing the inventory backlog of the mill for not meeting the demand assigned by the cooperative. Cogeneration of energy, and the sale of surplus energy was an important strategy to mitigate the decrease in industrial yield performed in the robust analysis while the change in the product production pattern was a consequence of product price uncertainty. The models can be applied in practice to provide better strategic and tactical planning of mills in cooperatives.

A review of mathematical optimization models applied to the sugarcane supply chain

“…Paiva et al. (2023) propose a hierarchical approach where, at the first level, a linear model is used to take aggregated decisions for the industrial process aiming to meet the potential demand. At the second level, a mixed‐integer model is proposed to take detailed decisions on industrial process selection, weekly harvest and transporting planning.…”

“…The authors define the problem as a scheduling problem that aim to minimize the makespan taking into account sequencing independent setup time, parallel capacitated machines with a cyclic sequence. Paiva et al (2023) propose a hierarchical approach where, at the first level, a linear model is used to take aggregated decisions for the industrial process aiming to meet the potential demand. At the second level, a mixed-integer model is proposed to take detailed decisions on industrial process selection, weekly harvest and transporting planning.…”

Optimizing the Design and Planning of a Sugar-Bioethanol Supply Chain under Uncertain Market Conditions

“…Among the reference papers, about 82% of them apply optimization models based on mixed-integer linear programming (MILP) and linear programming (LP) approaches. Note that the LP approach is just employed inside the bilevel formulation developed by Paiva et al 16 Other approaches are used less often, such as the cases of mixed-integer nonlinear programming (MINLP) and 1−0 integer linear programming (1-0 ILP) ones, which are formulated respectively by about 12% and 6% of the selected papers. Besides, to measure the supply chain performance in terms of economic, environmental, social, and operational goals, the modeling approaches are framed into single-objective (41%), multiobjective (47%), and bilevel (12%) formulations.…”

Coordinating harvest planning and scheduling in an agricultural supply chain through a stochastic bilevel programming

“…Paiva et al. (2023) proposed robust optimization models for a two‐level hierarchical supply chain of the sugar–alcohol energy sector in Brazil, extending previous contributions by the same authors, now including the price of selling products and yields from the industrial process as uncertain parameters. Finally, Albornoz et al.…”