A hybrid approach combining interior-point and branch-and-bound methods applied to the problem of sugar cane waste

Abstract

This paper proposes a hybrid approach for solving the multi-objective model related to the minimisation of sugar cane waste collection costs and/or the maximisation of produced energy by this waste, with the aid of strategies for solving multi-objective problems, which transform the problem into a set of single-objective problems. This approach combines the predictor-corrector primal-dual interior-point and branch-and-bound methods in order to solve these single-objective problems. The model consists in identifying the sugar cane varieties with the lowest waste collection costs, while simultaneously it aims to obtain the greatest amount of produced energy by this waste. The hybrid methods are implemented in C++ programming language, and tests are performed to determine the efficient solutions in Pareto optimal sense of the multi-objective model and compare the performance of the hybrid method using the integrality test and without considering it. The mathematical results confirm that the proposed hybrid method for solving the aforementioned models presents good computational performance and reliable solutions.

A Model of Waste Price in a Symbiotic Supply Chain Based on Stackelberg Algorithm

“…In the urban supply chain, various symbiotic relationships for the purpose of waste resource form a symbiotic network, which can realize efficient recycling and utilization of waste [13,23]. Some researchers use PDIPBB method (primal-dual interior-point and branch-and-bound methods) to solve the problem of multi-objective optimization, so as to obtain a solution to maximize the use of waste and minimize the cost in the supply chain [24,25]. A symbiotic supply chain can help enterprises to gain higher ability to resist interruption risk.…”

“…* and P m * are substituted into Equations (4) and (16) to obtain the total revenue model of suppliers, manufacturers, and symbiotic supply chain under the state of supplier dominance: (24) To sum up, the price, income, and demand models of suppliers and manufacturers are obtained under the two conditions of supplier dominance and manufacturer dominance, as shown in Table 2: Table 2. Price, revenue, and demand model summary under different states.…”

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

“…The main decisions to be made at the time of planting are related to: what is the best time to plant, which sugarcane varieties will be planted, and how to estimate what will be obtained when the plant is ready for harvest. Among the papers selected for this study, seven were found proposing mathematical optimization models to represent decisions associated with the planting time (Florentino and Sartori, 2003;Sartori and Florentino, 2007;Florentino et al, 2008;Colin, 2009;Florentino et al, 2011;Florentino and Pato, 2014;Lima et al, 2017). Florentino et al (2008Florentino et al ( , 2011, Florentino and Pato (2014), Lima et al (2017), and Sartori and Florentino (2007) present binary linear optimization models to select the varieties for planting.…”

“…Among the papers selected for this study, seven were found proposing mathematical optimization models to represent decisions associated with the planting time (Florentino and Sartori, 2003;Sartori and Florentino, 2007;Florentino et al, 2008;Colin, 2009;Florentino et al, 2011;Florentino and Pato, 2014;Lima et al, 2017). Florentino et al (2008Florentino et al ( , 2011, Florentino and Pato (2014), Lima et al (2017), and Sartori and Florentino (2007) present binary linear optimization models to select the varieties for planting. Sartori and Florentino (2007) consider the choice of which varieties to plant in a set of areas, taking into account a minimum demand for sugar present in the sugarcane to be harvested and aiming to maximize the energy that can be achieved through the use of the residual biomass for energy production.…”

“…The binary linear optimization model proposed by Florentino et al (2008) to choose the varieties to be planted, also considers the use of sugarcane straw for energy production and aims to minimize the cost of waste collection and maximize the balance of the energy generated and consumed. Florentino et al (2011), Florentino and Pato (2014), and Lima et al (2017) propose biobjective optimization models which, in addition to the demand for sugar, also consider the demand for fiber where two criteria are considered in the decision making: maximizing energy production and minimizing the costs of biomass transfer from the field to the mill. Florentino et al (2011) and Sartori and Florentino (2007) solve the models only through the use of a general-purpose solver with an instance based on a real situation.…”