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A fix-and-optimize Matheuristic to Solve the Location-Allocation of Vaccination Facilities: Case of Jalisco, Mexico

NETWORKS 2025年第0期 382-395页

作者： Romero-Mancilla, Marisol S. Mora-Vargas, Jaime Ruiz, Angel Tecnol Monterrey Sch Engn & Sci Monterrey Mexico Laval Univ Fac Business Adm Quebec City PQ Canada

Approximately 755 million cases and 7 million deaths have been reported since the COVID-19 pandemic. Based on the availability of vaccines to contain the spread of COVID-19, various vaccination plans have been implemented globally, some more effective than others, depending on each country's social, territorial, economic, and political circumstances. In Mexico and other Latin American countries with similar situations, COVID-19 vaccinations have almost exclusively relied on ephemeral mass vaccination facilities and existing healthcare infrastructure. However, other countries (e.g., the USA and Canada) have opted into pharmacy-based immunization (PBI), which uses community and/or chain pharmacies as vaccination facilities to provide more accessible immunization services. This research aims to evaluate the feasibility and expected performance if PBI had been used in Mexico. Therefore, we propose a mathematical formulation to address the location-allocation problem underlying the pharmacy selection and the assignment of individuals to them. However, since commercial solvers cannot efficiently address the resulting formulation for real-sized instances, the formulation is embedded into a heuristic fix-and-optimize scheme to explore the solution space more efficiently. The case of Jalisco, Mexico, is used to illustrate the performance of the proposed approach.

关键词： fix-and-optimize healthcare humanitarian logistics humanitarian supply chain management location allocation operations research pharmacy-based immunization vaccination

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fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2015年 56卷 25-36页

作者： Chen, Haoxun Univ Technol Troyes Ind Syst Optimizat Lab Charles Delaunay Inst F-10004 Troyes France Univ Technol Troyes UMR CNRS 6281 F-10004 Troyes France

In this paper, a new fix-and-optimize (FO) approach is proposed for two dynamic multi-level capacitated lot sizing problems (MLCLSP), the MLCLSP without setup carryover and the MLCLSP with setup carryover. Given an MIP model of a lot sizing problem, the approach iteratively solves a series of sub-problems of the model until no better solution. can be found. Each sub-problem re-optimizes a subset of binary decision variables determined based on the interrelatedness of binary variables in the constraints of the model, while fixing the values of the other binary variables. Based on the FO, a variable neighbourhood search (VNS) approach for the MLCLSP without setup carryover is also developed, which can further improve the solution obtained by the FO by diversifying the search space. Numerical experiments on benchmark instances show that both our FO and VNS approaches can obtain a better solution for most instances compared with that found by the fix-and-optimize approach proposed by Helber and Sahling (International Journal of Production Economics 2010;123:247-256). (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Production planning Lot sizing fix-and-optimize Variable neighbourhood search Mixed integer programming

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fix-and-optimize METAHEURISTICS FOR MINMAX REGRET BINARYINTEGER PROGRAMMING PROBLEMS UNDER INTERVAL UNCERTAINTY

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RAIRO-OPERATIONS RESEARCH 2022年第6期56卷 4281-4301页

作者： Carvalho, Iago A. A. Noronha, Thiago F. F. Duhamel, Christophe Univ Fed Alfenas Comp Sci Dept Av Jovino Fernandes Sales 2600 BR-37133840 Alfenas MG Brazil Univ Fed Minas Gerais Comp Sci Dept Av Pres Antonio Carlos 6627 BR-31270901 Belo Horizonte MG Brazil Univ Le Havre Normandie Lab Informat Traitement Informat & Syst 25 Rue Philippe F-76600 Le Havre France

The Binary Integer Programming problem (BIP) is a mathematical optimization problem, with linear objective function and constraints, on which the domain of all variables is {0, 1}. In BIP, every variable is associated with a determined cost coefficient. The Minmax regret Binary Integer Programming problem under interval uncertainty (M-BIP) is a generalization of BIP in which the cost coefficient associated to the variables is not known in advance, but are assumed to be bounded by an interval. The objective of M-BIP is to find a solution that possesses the minimum maximum regret among all possible solutions for the problem. In this paper, we show that the decision version of M-BIP is sigma(p)(2)-complete. Furthermore, we tackle M-BIP by both exact and heuristic algorithms. We extend three exact algorithms from the literature to M-BIP and propose two fix-and-optimize heuristic algorithms. Computational experiments, performed on the Minmax regret Weighted Set Covering problem under Interval Uncertainties (M-WSCP) as a test case, indicates that one of the exact algorithms outperforms the others. Furthermore, it shows that the proposed fix-and-optimize heuristics, that can be easily employed to solve any minmax regret optimization problem under interval uncertainty, are competitive with ad-hoc algorithms for the M-WSCP.

关键词： Minmax regret interval uncertainty binary integer programming fix-and-optimize metaheuristics

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fix-and-optimize approach for a healthcare facility location/network design problem considering equity and accessibility: A case study

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APPLIED MATHEMATICAL MODELLING 2022年 102卷 243-267页

作者： Pourrezaie-Khaligh, Pooya Bozorgi-Amiri, Ali Yousefi-Babadi, Abolghasem Moon, Ilkyeong Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Seoul Natl Univ Dept Ind Engn Seoul 08826 South Korea Seoul Natl Univ Inst Ind Syst Innovat Seoul 08826 South Korea

This study addresses a healthcare facility location/network design problem considering equity and accessibility. Locating the healthcare facilities, planning the capacity of healthcare facilities, and designing the transfer network are the primary goals of the given problem. The presented model aims to minimize system costs, maximize accessibility, and minimize inequality among all demand nodes. A real-world case study is presented to elucidate the performance and applicability of the proposed model. Moreover, a fix-and-optimize (FO) approach is proposed for tackling the problem on a large scale. The obtained results from experiments on several test problems indicate the efficiency of the developed FO. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Healthcare Facility location Network design Equity Accessibility fix-and-optimize

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A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 145卷 106531-106531页

作者： Turhan, Aykut Melih Bilgen, Bilge Dokuz Eylul Univ Grad Sch Nat & Appl Sci Dept Ind Engn Tinaztepe Campus TR-35397 Izmir Turkey Dokuz Eylul Univ Dept Ind Engn Tinaztepe Campus TR-35397 Izmir Turkey

The Nurse Rostering Problem (NRP) is a complex scheduling problem in which nurses must be assigned to shifts according to a set of constraints. The NRP is difficult to solve to optimality due to its combinatorial structure. In this paper, we propose a hybrid solution algorithm that combines Mixed Integer Programming (MIP) based heuristics-namely fix-and-Relax (F&R) and fix-and-optimize (F&O)-and Simulated Annealing (SA) to solve the NRP. In MIP-based heuristics, a problem is decomposed into a set of smaller problems and each problem is iteratively solved to optimality. In the hybrid approach, high-quality initial solutions are obtained via the F&R algorithm and fed to the SA part of the algorithm. When solutions can no longer be improved, the F&O algorithm is inserted into the SA algorithm. This enables the hybrid algorithm to diversify the search space and provide better solutions. To assess the quality and efficiency of the hybrid approach, we use 24 publicly available test instances recently introduced in literature in the field. Computational results show that the hybrid method outperforms other advanced solution techniques in most of the test data and seven new best-known results are reported.

关键词： OR in health services Nurse rostering problem fix-and-relax fix-and-optimize Simulated annealing

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A fix-and-optimize approach for the multi-level capacitated lot sizing problem

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2010年第2期123卷 247-256页

作者： Helber, Stefan Sahling, Florian Leibniz Univ Hannover Inst Prod Wirtschaft D-30167 Hannover Germany

This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times. The key idea is to solve a series of mixed-integer programs in an iterative fix-and-optimize algorithm. Each of these programs is optimized over all real-valued variables, but only a small subset of binary setup variables. The remaining binary setup variables are tentatively fixed to values determined in previous iterations. The resulting algorithm is transparent, flexible, accurate and relatively fast. Its solution quality outperforms those of the approaches by Tempelmeier/Derstroff and by Stadder. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Lot sizing MLCLSP Lead times MIP fix-and-optimize Decomposition

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A fix-and-optimize heuristic for the ITC2021 sports timetabling problem

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JOURNAL OF SCHEDULING 2022年第3期25卷 273-286页

作者： Fonseca, George H. G. Toffolo, Tulio A. M. Univ Fed Ouro Preto Dept Comp & Syst DECSI Ouro Preto Brazil Univ Fed Ouro Preto Dept Comp DECOM Ouro Preto Brazil

This paper addresses the general and challenging Sports Timetabling Problem proposed during the International Timetabling Competition of 2021 (ITC2021). The problem is expressed in a flexible format which enables modeling a number of real-world constraints that often occur in Sports Timetabling. An integer programming (IP) formulation and a fix-and-optimize heuristic are proposed to address the problem. The fix-and-optimize approach uses the IP formulation to heuristically decompose the problem into sub-problems and efficiently search on very large neighborhoods. The diverse ITC2021 benchmark instances were used to evaluate the proposed methods. The formulation resulted in proven optimal solutions for two instances. However, it failed to produce feasible solutions for most instances. The proposed fix-and-optimize, which uses an automatic sub-problem size calibration strategy, resulted in feasible solutions for 37 out of the 45 ITC2021 instances. Among these solutions, four are the best known in the literature. The proposed approach participated in the ITC2021 and was one of the finalists.

关键词： ITC2021 Sports timetabling Round robin tournament fix-and-optimize

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A fix-and-optimize approach for efficient and large scale virtual network function placement and chaining

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COMPUTER COMMUNICATIONS 2017年第Apr.1期102卷 67-77页

作者： Luizelli, Marcelo Caggiani da Costa Cordeiro, Weverton Luis Buriol, Luciana S. Gaspary, Luciano Paschoal Univ Fed Rio Grande do Sul Inst Informat Av Bento Gongalves 9500 BR-91501970 Porto Alegre RS Brazil

Network Function Virtualization (NFV) is a novel concept that is reshaping the middlebox arena, shifting network functions (e.g. firewall, gateways, proxies) from specialized hardware appliances to software images running on commodity hardware. This concept has potential to make network function provision and operation more flexible and cost-effective, paramount in a world where deployed middleboxes may easily reach the order of hundreds. In spite of recent research activity in the field, little has been done towards efficient and scalable placement & chaining of virtual network functions (VNFs) - a key feature for the effective success of NFV. More specifically, existing strategies have either neglected the chaining aspect of NFV, focusing on efficient placement only, or failed to scale to hundreds of network functions. In this paper, we approach VNF placement and chaining as an optimization problem, and propose a fix-and-optimize-based heuristic algorithm for tackling it. Our algorithm incorporates a Variable Neighborhood Search (VNS) meta-heuristic, for efficiently exploring the placement and chaining solution space. The goal is to minimize required resource allocation, while meeting network flow requirements and constraints. We provide evidence that our algorithm is able to find feasible, high quality solutions efficiently, even in scenarios scaling to hundreds of VNFs. (C) 2016 Elsevier B.V. All rights reserved.

关键词： NFV Network function placement Service Function Chaining Optimization fix-and-optimize Variable Neighborhood Search

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A hybrid fix-and-optimize heuristic for integrated inventory-transportation problem in a multi-region multi-facility supply chain

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RAIRO-OPERATIONS RESEARCH 2020年第3期54卷 749-782页

作者： Tanksale, Ajinkya Jha, J. K. Indian Inst Technol Kharagpur Dept Ind & Syst Engn Kharagpur 721302 W Bengal India

In this work, we study an integrated inventory-transportation problem in a supply chain consisting of region-bound warehouses located in different regions. The supply chain deals with multiple items that compete for storage space and transportation capacity with multi-modal transportation considering regional capacity constraint for each mode of transportation. The objective is to determine an optimal storage and transportation plan to satisfy the demand of all regions without shortages for known procurement plan for all items. The problem is formulated as a mixed integer programming (MIP) model for minimizing the total costs over a finite planning horizon. An MIP-based fix-and-optimize (F&O) heuristic with several decomposition schemes is proposed to solve the problem efficiently. The performance of the decomposition schemes is investigated against the structure of the sub-problems obtained. To enhance the performance, F&O is crossbred with two metaheuristics - genetic algorithm (GA) and iterated local search (ILS) separately, which lead to hybrid heuristic approach. Extensive numerical experiments are carried out to analyze the performance of the proposed solution methodology by randomly generating several problem instances built using data collected from the Indian Public Distribution System. The proposed solution approach is found to be computationally efficient and effective, and outperforming state of the art MIP solver Cplex for practical size problem instances. Also, the hybridization of F&O heuristic with GA and ILS boosts its performance although with a justified increase in the computational time.

关键词： inventory-transportation problem fix-and-optimize genetic algorithm iterated local search public distribution system

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A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

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JOURNAL OF HEURISTICS 2015年第5期21卷 687-717页

作者： Motta Toledo, Claudio Fabiano Arantes, Marcio da Silva Bressan Hossomi, Marcelo Yukio Franca, Paulo Morelato Akartunali, Kerem Univ Sao Paulo Inst Math & Comp Sci BR-13566590 Sao Carlos SP Brazil UNESP Dept Math & Comp Sci BR-19060080 Presidente Prudente SP Brazil Univ Strathclyde Dept Management Sci Glasgow G1 1QE Lanark Scotland

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems.

关键词： Lot-sizing Heuristics Relax-and-fix fix-and-optimize Backlogging

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