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A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders

TOP 2020年第1期28卷 178-192页

作者： Pitombeira-Neto, Anselmo Ramalho Prata, Bruno de Athayde Univ Fed Ceara Dept Ind Engn Campus Pici Fortaleza Ceara Brazil

Cutting stock and bin packing problems are common in several industrial sectors, such as paper, glass, furniture, steel industry, construction, transportation, among others. The classical cutting stock problem (CSP) ignores the production planning and scheduling of multiple customer orders. Nevertheless, in real industrial settings customer orders have to be planned and scheduled over time so as to meet demand and required due dates. We propose an integer linear programming model for the one-dimensional cutting stock and scheduling problem with heterogeneous orders. As this problem is a generalization of the classical single-period one-dimensional CSP, which is known to be NP-hard, it is difficult to solve real-sized instances to optimality. Thus, we propose a novel matheuristic algorithm based on a fix-and-optimize strategy hybridized with a random local search. The proposed matheuristic was tested on a set of 160 synthetic problem instances based on a real-world problem and compared with CPLEX solver. In larger instances, the proposed matheuristic performed better than CPLEX, with average relative percentage deviation (RPD) regarding objective values as high as 72%. On the other hand, in small instances CPLEX showed a marginal advantage, with best average RPD of 18% with relation to the matheuristic. We also performed a paired t-test with significance level 0.05 and null hypothesis: no difference between the proposed matheuristic and CPLEX. In small test instances, the performance of the proposed matheuristic was statistically indistinguishable from CPLEX, while in larger instances the matheuristic outperformed CPLEX in most cases with pvalue<0.05\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\,\text {value} < 0.05$$\end{document}.

关键词： Cutting and packing problems Order scheduling problems fix-and-optimize Matheuristics

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Developing a Matheuristic for the Integrated Planning of a Cold Rolling Steel Plant 10th

Developing a Matheuristic for the Integrated Planning of a C...

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10th IFAC Triennial Conference on Manufacturing Modelling, Management and Control (MIM)

作者： Wegel, Sebastian Volling, Thomas Sahling, Florian Tech Univ Berlin Berlin Germany Tech Univ Kaiserslautern Kaiserslautern Germany

Steel-producing firms are confronted with the challenge of determining plans that coordinate production processes across a set of processing stages. While several approaches for integrated planning of hot rolling mills have been proposed, the cold rolling process is still poorly investigated. Therefore, we present a model formulation to simultaneously form campaigns of coils in cold rolling steel plants. The model considers multiple processing stages with unrelated parallel machines, sequence-dependent setup operations and order-specific due dates. To solve the model, we propose a matheuristic based on fix-and-Relax and fix-and-optimize that utilizes a production line-based decomposition strategy. The results of a numerical study are presented that replicates the realistic production environment of a real cold rolling plant and a planning horizon of up to 10 days. The proposed matheuristic consistently outperforms a commercial solver in terms of solution quality and time. Copyright (C) 2022 The Authors.

关键词： Campaign Formation Cold Rolling fix-and-optimize fix-and-Relax Integrated Production Planning Matheuristics Steel Production

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Maritime Inventory Routing: a practical assessment and robust optimization approach

Maritime Inventory Routing: a practical assessment and robus...

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作者： Gustavo Souto dos Santos Diz Pontificia Universidade Catolica do Rio de Janeiro

学位级别：博士

Maritime inventory routing (MIR) problem is an academic name for a practical logistic problem that represents the routing or scheduling of vessels to carry product(s) between ports. Meanwhile, the product(s) inventory levels in these ports must remain between operational bounds during the entire planning horizon. This thesis focus on how to support decision on a real-life MIR problem faced by a Brazilian petroleum company. To do so, we structure a set of tests to compare different formulation from literature and identify which is more adherent to real problem. Due to computational complexity of the problem, we present an heuristic approach that provides reasonably good solutions when compared to deterministic mixed integer linear programming (MILP) formulations and reduces considerably the computational time of solving real-life instances. However, uncertainty events have great impact in the ship scheduling planning. Therefore, we propose a robust optimization approach that considers uncertainty in the time spent at ports in each ship visit. Our approach is able to determine the probability of infeasibility and the impact in the objective function for each level of robustness, helping to measure the uncertain aversion of the decision maker. Our experiments identified that, for a certain instance, varying the level of robustness one may reduce the probability of infeasibility from 87% (of deterministic solution) to 2% and it represents an increase in the transportation costs of about 13%.

关键词： maritime inventory routing mixed-integer linear programming valid inequalities relax-and-fix fix-and-optimize robust optimization

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A matheuristic approach for solving the high school timetabling problem

A matheuristic approach for solving the high school timetabl...

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作者： Dornelles, Arton Pereira

The school timetabling is a classic optimization problem that has been extensively studied due to its practical and theoretical importance. It consists in scheduling a set of class-teacher meetings in a prefixed period of time, satisfying requirements of different types. Given the combinatorial nature of this problem, solving medium and large instances of timetabling to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Several techniques have been developed in the scientific literature to tackle the high school timetabling problem, however, robust solvers do not exist yet. Since the use of exact methods, such as mathematical programming techniques, is considered impracticable to solve large real world instances, metaheuristics and hybrid metaheuristics are the most used solution approaches. In this research we develop techniques that combine mathematical programming and heuristics, so-called matheuristics, to solve efficiently and in a robust way some variants of the high school timetabling problem. Although we pay special attention to problems arising in Brazilian institutions, the proposed methods can also be applied to problems from different countries. ...

关键词： Programação matemática High school timetabling Mathematical programming Otimizacao combinatoria Grade de horários Meta-heuristics Ensino médio : Brasil Matheuristics fix-and-optimize Tese

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Mid-term energy cost-oriented flow shop scheduling: Integration of electricity price forecasts, modeling, and solution procedures

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 163卷

作者： Busse, Jan Rieck, Julia Univ Hildesheim Inst Business Econ & Informat Syst Operat Res Grp Samelsonpl 1 D-31141 Hildesheim Germany

The paper deals with a flow shop scheduling problem, where energy costs are to be minimized with respect to time-varying electricity prices coming from the day-ahead market EPEX Spot Germany/Austria. To make efficient use of the corresponding price volatility in the production planning phase, i.e., weeks prior to the start of production, price forecasts have to be incorporated into decision making. Since the suitability of mid-term electricity price forecasts for scheduling applications has not been clarified, we analyze forecasts from the literature for their usability by means of extensive scenarios as well as an appropriate evaluation scheme. Furthermore, solution methods are provided for the considered flow shop scheduling problem. We study a fixand-optimize and a priority rule-based sampling procedure in order to solve large-scale instances within a reasonable time. The performance analysis shows that fix-and-optimize achieves very good results in terms of solution quality. If production planners have to make quick decisions, the sampling procedure provides excellent run times.

关键词： Flow shop scheduling Energy costs Electricity price forecasts Mixed-integer linear programming fix-and-optimize Priority rule-based sampling procedure

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Integrated planning for planting and harvesting sugarcane and energy-cane for the production of sucrose and energy

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2021年 184卷 105956-105956页

作者： Poltroniere, Sonia Cristina Filho, Angelo Aliano Caversan, Amanda Suellen Balbo, Antonio Roberto Florentino, Helenice de Oliveira Univ Estadual Paulista Fac Ciencias Bauru SP Brazil Univ Tecnol Fed Dept Acad Matemat Curitiba Parana Brazil Univ Estadual Paulista Fac Engn Bauru SP Brazil Univ Estadual Paulista Inst Biociencias Botucatu SP Brazil

The main products obtained from sugarcane for the global market are sugar, ethanol and energy. Although the demand for these products is high, in Brazil there is no longer space to expand sugarcane cultivation due to other important food crops and environmental protection areas. Therefore, current research seeks ways to increase sugarcane productivity without expanding the planted area. Consequently, a type of cane with higher concentration of fiber has been developed and cultivated called energy-cane. This cane type has more fiber than sucrose in its composition, which makes it better for producing energy and ethanol and inappropriate for sugar production. To meet the demands for these three products, both energy-cane and sugarcane are needed, making the planning and decision-making more difficult in the energy-sugar sector. In this context, a mixed integer linear optimization model for the integrated planning of the planting and harvesting of sugarcane and energy-cane for a sugar-energy plant is proposed to determine an optimized planting and harvesting schedule, that aims to maximize the sucrose and fiber production in the cane fields. The model takes into account a flexible harvest period to meet the demands of the consumer market and respect the operational constraints of the company, which can cause variations in productivity. To solve real-life instances where exact methods fail, a heuristic based on the relax-and-fix and fix-and-optimize concepts is proposed. Numerical experiences with random instances were generated to test both the model and the heuristic. Feasible solutions with an error close to 1% were obtained, consuming one tenth of the CPU time, on average. Thus, the mathematical model and the heuristic method developed have great potential to support decision-making in sugarcane and energy-cane production planning.

关键词： Sugarcane Energy-cane Mathematical optimization Relax-and-fix fix-and-optimize

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Resilience planning for Physical Internet enabled hyperconnected production-inventory-distribution systems

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 158卷

作者： Peng, Xiaoshuai Ji, Shoufeng Thompson, Russell G. Zhang, Lele Northeastern Univ Sch Business Adm Dept Operat & Logist Management Shenyang 110167 Peoples R China Univ Melbourne Dept Infrastruct Engn Parkville Vic 3010 Australia Univ Melbourne Sch Math & Stat Parkville Vic 3010 Australia

Based on the Internet of Things, standard coordination protocol, smart containers and other key foundations, the Physical Internet (PI) provides an interconnected, shared and adaptable logistics system, which has great potential to significantly increase the reliability and resilience of supply chains. In this paper, we assess the effectiveness of the PI for dealing with various disruptions in an integrated production-inventory-distribution system. To attain this, we constructed a two-stage stochastic programming model which captures the main characteristics of the PI and incorporates pre-event and post-event mitigation strategies in an integrated way. In the first stage (before disruptions), pre-event mitigation strategies are identified, while in addition to post-event mitigation strategies, the production, inventory, ordering and pickup and delivery route plans are determined in the second stage (after disruptions). Then a two-level heuristic algorithm that combines a three-phase heuristic and a fix-and-optimize procedure is developed to solve the model effectively. To evaluate the model, risk mitigation strategies and the two-level heuristic algorithm, extensive numerical experiments were conducted based on several realistic instances. The results demonstrate that the developed algorithm significantly outperforms the state-of-the-art solver in terms of solution quality and computational time. The results also indicate that tremendous cost and service level benefits can be achieved by adopting the proposed risk mitigation strategies. Compared with the traditional and horizontal collaborative systems, the PI-enabled system attains better performance in terms of the total cost and service levels. Finally, sensitivity analysis showed that the PI-enabled system has significant performance advantages when a range of parameter values were varied.

关键词： Production-inventory-distribution Physical Internet Resilience Disruption risk Three-phase heuristic fix-and-optimize

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The capacitated multi-level lot-sizing problem with distributed agents

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2021年 235卷 108090-108090页

作者： Gansterer, Margaretha Foedermayr, Patrick Hartl, Richard F. Univ Klagenfurt Dept Operat Energy & Environm Management Univ Str 65-67 A-9020 Klagenfurt Austria Univ Vienna Dept Business Decis & Analyt Oskar Morgenstern Pl 1 A-1090 Vienna Austria

Cloud manufacturing is an emerging concept that enables the orchestration, matching, and sharing of services or resources among collaboration partners or intra-plant facilities. In this context, we introduce the capacitated multi-level lot sizing problem with transshipments and set up carry-over. We consider components that can only be produced by one specific agent as well as components that can be provided by more than one producer. As capacities are limited, agents might have to share resources and jointly cover required demands. In this case, finished components are transshipped between agents. As an agent can be in charge of producing more than one component, we include the concept of set up carry-over into our modeling. We address a centralized planning approach, where the objective is to find a globally optimized lot sizing plan for all participating agents. Thus, we cover both horizontal and vertical collaboration between agents. The new problem class is formulated mathematically. We propose a matheuristic solution approach based on a fix-and-optimize procedure, where the interrelatedness of decision variables is taken into account. We benchmark the proposed approached against optimal or proven near-optimal solutions. Additionally, a decentralized upstream lot-shifting heuristic is generated, which allows us to compare the results to situations in which no central decision maker is present. Both solution approaches are applied to an extensive set of test instances. We show that the centralized approach is able to reduce the total cost by up to 47%. We assess the different levels of interrelatedness of the decision variables and demonstrate that an increase in interrelatedness can even lead to a decrease in the solution quality. Moreover, we provide valuable managerial insights into the impact of the bill-of-material structure on problem complexity.

关键词： Lot sizing Shared resources fix-and-optimize Matheuristic

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Handling fairness issues in time-relaxed tournaments with availability constraints

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COMPUTERS & OPERATIONS RESEARCH 2020年 115卷 104856-000页

作者： Van Buick, David Goossens, Dries Univ Ghent Fac Econ & Business Adm Ghent Belgium

Sports timetables determine who will play against whom, where, and on which time slot. In contrast to time-constrained sports timetables, time-relaxed timetables utilize (many) more time slots than there are games per team. This offers time-relaxed timetables additional flexibility to take into account venue availability constraints, stating that a team can only play at home when its venue is available, and player availability constraints stating that a team can only play when its players are available. Despite their flexibility, time-relaxed timetables have the drawback that the rest period between teams' consecutive games can vary considerably, and the difference in the number of games played at any point in the season can become large. Besides, it can be important to timetable home and away games alternately. In this paper, we first establish the computational complexity of time-relaxed timetabling with availability constraints. Naturally, when one also incorporates fairness objectives on top of availability, the problem becomes even more challenging. We present two heuristics that can handle these fairness objectives. First, we propose an adaptive large neighborhood method that repeatedly destroys and repairs a timetable. Second, we propose a memetic algorithm that makes use of local search to schedule or reschedule all home games of a team. For numerous artificial and real-life instances, these heuristics generate high-quality timetables using considerably less computational resources compared to integer programming models solved using a state-of-the-art solver. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Time-relaxed sports scheduling fix-and-optimize Evolutionary algorithm Round-robin tournament Bipartite tournament Complexity theory

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A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年第0期173卷

作者： Cunha, Jesus O. Mateus, Geraldo R. Melo, Rafael A. Univ Fed Ceara Dept Estat & Matemat Aplicada BR-60440900 Fortaleza CE Brazil Univ Fed Minas Gerais Dept Ciencia Computacao Ave Antonio Carlos 6627 BR-31270010 Belo Horizonte MG Brazil Univ Fed Bahia Inst Comp BR-40170115 Salvador BA Brazil

In this paper, we consider the capacitated three-level lot-sizing and replenishment problem with a distribution structure (3LSPD-C), recently proposed in the literature. In 3LSPD-C, a single production plant delivers items (of a single product or item type) to the warehouses from where they are distributed to their corresponding retailers. There is a capacity on the total amount the plant can produce in each period, whereas there are no capacity constraints on transportation. The goal of this NP-hard optimization problem consists in determining an integrated three-echelon production and distribution plan minimizing the total cost, which is composed of fixed costs for production and transportation setups as well as variable inventory holding costs. We propose a new hybrid mixed integer programming (MIP) heuristic consisting of a relax-and-fix approach to generate initial feasible solutions and a fix-and-optimize improvement procedure grounded on varying-size neighborhoods to obtain high-quality solutions which, to the best of our knowledge, stands as the first heuristic for the problem. The hybrid heuristic is flexible and can be applied to more general variants of the problem. Additionally, we introduce and consider a generalization of 3LSPD-C that also establishes storage capacity constraints (or inventory bounds) on the warehouses and/or retailers, given the importance of such characteristics in practical industrial and commercial environments. Such extension is denoted generalized capacitated three-level lot-sizing and replenishment problem with a distribution structure (G3LSPD-C). Computational experiments are performed to analyze the potential cost reductions achieved using the new hybrid heuristic when compared with a state-of-the-art MIP formulation given a specific time limit. The results show that the proposed hybrid heuristic can match or improve the solution quality obtained by the MIP formulation for the majority of the 3LSPD-C instances within the speci

关键词： Supply chain management Logistics Three-echelon supply chain MIP heuristic fix-and-optimize Storage capacity

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