HOPX Crossover Operator for the Fixed Charge Logistic Model with Priority Based Encoding

In this paper, we are interested to an important Logistic problem modelised us optimization problem. It is the fixed charge transportation problem (FCTP) where the aim is to find the optimal solution which minimizes the objective function containig two costs, variable costs proportional to the amount shipped and fixed cost regardless of the quantity transported. To solve this kind of problem, metaheuristics and evolutionary methods should be applied. Genetic algorithms (GAs) seem to be one of such hopeful approaches which is based both on probability operators (Crossover and mutation) responsible for widen the solution space. The different characteristics of those operators influence on the performance and the quality of the genetic algorithm. In order to improve the performance of the GA to solve the FCTP, we propose a new adapted crossover operator called HOPX with the priority-based encoding by hybridizing the characteristics of the two most performent operators, the Order Crossover (OX) and Position-based crossover (PX). Numerical results are presented and discussed for several instances showing the performance of the developed approach to obtain optimal solution in reduced time in comparison to GAs with other crossover operators

Solving the Fixed Charge Transportation Problem by New Heuristic Approach

The fixed charge transportation problem (FCTP) is a deployment of the classical transportation problem in which a fixed cost is incurred, independent of the amount transported, along with a variable cost that is proportional to the amount shipped. Since the problem is considered as an NP-hard, the computational time grows exponentially as the size of the problem increases. In this paper, we propose a new heuristic along with well-known metaheuristic like Genetic algorithm (GA), simulated annealing (SA) and recently developed one, Keshtel algorithm (KA) to solve the FCTP. Contrary to previous works, we develop a simple and strong heuristic according to the nature of the problem and compare the result with metaheuristics. In addition, since the researchers recently used the priority-based representation to encode the transportation graphs and achieved very good results, we consider this representation in metaheuristics and compare the results with the proposed heuristic. Furthermore, we apply the Taguchi experimental design method to set the proper values of algorithms in order to improve their performances. Finally, computational results of heuristic and metaheuristics with different encoding approaches, both in terms of the solution quality and computation time, are studied in different problem sizes

Bulk wheat transportation and storage problem of public distribution system

This research investigates the multi-period multi-modal bulk wheat transportation and storage problem in a two-stage supply chain network of Public Distribution System (PDS). The bulk transportation and storage can significantly curtail the transit and storage losses of food grains, which leads to substantial cost savings. A mixed integer non-linear programming model (MINLP) is developed after studying the Indian wheat supply chain scenario, where the objective is to minimize the transportation, storage and operational cost of the food grain incurred for efficient transfer of wheat from producing states to consuming states. The cost minimization of Indian food grain supply chain is a very complex and challenging problem because of the involvement of the many entities and their constraints such as seasonal procurement, limited scientific storages, varying demand, mode of transportation and vehicle capacity constraints. To address this complex and challenging problem of food grain supply chain, we have proposed the novel variant of Chemical Reaction Optimization (CRO) algorithm which combines the features of CRO and Tabu search (TS) and named it as a hybrid CROTS algorithm (Chemical reaction optimization combined with Tabu Search). The numerous problems with different sizes are solved using the proposed algorithm and obtained results have been compared with CRO. The comparative study reveals that the proposed CROTS algorithm offers a better solution in less computational time than CRO algorithm and the dominance of CROTS algorithm over the CRO algorithm is demonstrated through statistical analysis

Problemas de transporte y problemas de transporte con carga fija

Entre los problemas más interesantes en el campo de la Investigación Operativa, tanto por sus aplicaciones como por los retos teóricos que presentan, figuran los que aparecen en el diseño de redes de distribución. El problema de transporte y el problema de transporte con carga fija son problemas de programación lineal y programación lineal entera, respectivamente. Una de las razones que justifican el estudio individualizado de estos problemas es que tienen una estructura matemática especial que ha permitido diseñar métodos de resolución más eficientes que los que se aplican a los problemas de programación lineal. El objetivo de este trabajo es estudiar el problema de transporte y el problema de transporte con carga fija, demostrar sus propiedades más relevantes y presentar algunos de los algoritmos que se han propuesto para su resolución, además de mostrar algún caso particular del problema de transporte con carga fija. En el Capítulo 1 se estudia el problema de transporte. Tras formularlo matemáticamente, se demuestran algunos resultados basados en las propiedades de la matriz de coeficientes y se presenta un método de resolución basado en el conocido algoritmo simplex. En el Capítulo 2 se estudia el problema de transporte con carga fija. Se formula como un problema de programación entera con variables binarias y se demuestran algunas propiedades que permiten relacionar su solución con la solución del problema de transporte obtenido cuando se relajan las restricciones de integridad de las variables binarias. A continuación, se presentan algunos algoritmos propuestos en la literatura para resolver el problema basados en distintas reformulaciones del mismo. El Capítulo 2 termina con una revisión bibliográfica actualizada sobre el problema. En el Capítulo 3 se estudia algún caso particular del problema de transporte con carga fija y algunas propiedades adicionales. Por último, en el apéndice se proporcionan los resultados de un breve estudio computacional en el que se han resuelto, usando Lingo, algunos problemas de transporte con carga fija generados aleatoriamente. Among the most interesting problems in Operation Research field include the ones that appear in the distribution network design, both for their applications as for the theoretical challenges which show. These problems can include, among other variants, the transportation problem, the travelling salesman problem, the vehicle routing problem with one or more stores, and so on. The transportation problem and the fixed charge transportation problem are linear programming problems and integer linear programming problems, respectively, i.e. they are optimization problems which attempt to maximize (or minimize) a linear function, subject to some restrictions which are linear equations or inequalities and, in the integer programming case, they include integer variables. One of the reasons for the individual study of these problems is that they have a special mathematical structure which has let built more efficient resolution methods than those applied to linear programming. We have to note that the transportation problems have, in general, many variables and constraints, even in not particularly complex distribution systems. Moreover, both problems have applications in many fields, especially in the design of the distribution process in a supply chain. The aim of this project is to study the transportation problem and the fixed charge transportation problem, proving their most relevant properties and introducing some resolution algorithm. The transportation problem is studied in Chapter 1. After formulating it, some results based on the coefficient matrix properties are proved, and a resolution method based on simplex algorithm is introduced. The fixed charge transportation problem is studied in Chapter 2. It is formulated as an integer programming problem with binary variables, and some properties which let link its solution with the transportation problem solution obtained after relaxing the integer restrictions are proved. After that, some resolution algorithm based on different reformulations of the problem are shown. Chapter 2 is ended up with a current bibliographic review and some particular cases of the fixed charge transportation problem

공컨테이너관리 기법을 활용한 효율적인 컨테이너 공급망

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 문일경.Due to a remarkable surge in global trade volumes led by maritime transportation, shipping companies should make a great effort in managing their container flows especially in case of carrier-owned containers. To do so, they comprehensively implement empty container management strategies and accelerate the flows in a cost- and time-efficient manner to minimize total relevant costs while serving the maximal level of customers demands. However, many critical issues in container flows universally exist due to high uncertainty in reality and hinder the establishment of an efficient container supply chain. In this dissertation, we fully discuss such issues and provide mathematical models along with specific solution procedures. Three types of container supply chain are presented in the following: (i) a two-way four-echelon container supply chain; (ii) a laden and empty container supply chain under decentralized and centralized policies; (iii) a reliable container supply chain under disruption. These models explicitly deal with high risks embedded in a container supply chain and their computational experiments offer underlying managerial insights for the management in shipping companies. For (i), we study empty container management strategy in a two-way four-echelon container supply chain for bilateral trade between two countries. The strategy reduces high maritime transportation costs and long delivery times due to transshipment. The impact of direct shipping is investigated to determine the number of empty containers to be repositioned among selected ports, number of leased containers, and route selection to satisfy the demands for empty and laden containers for exporters and importers in two regions. A hybrid solution procedure based on accelerated particle swarm optimization and heuristic is presented, and corresponding results are compared. For (ii), we introduce the laden and empty container supply chain model based on three scenarios that differ with regard to tardiness in the return of empty containers and the decision process for the imposition of fees with the goal of determining optimal devanning times. The effectiveness of each type of policy - centralized versus decentralized - is determined through computational experiments that produce key performance measures including the on-time return ratio. Useful managerial insights on the implementation of these polices are derived from the results of sensitivity analyses and comparative studies. For (iii), we develop a reliability model based on container network flow while also taking into account expected transportation costs, including street-turn and empty container repositioning costs, in case of arc- and node-failures. Sensitivity analyses were conducted to analyze the impact of disruption on container supply chain networks, and a benchmark model was used to determine disruption costs. More importantly, some managerial insights on how to establish and maintain a reliable container network flow are also provided.해상 수송이 주도함으로써 전 세계 무역량이 급증하기 때문에 회사 소유 컨테이너는 컨테이너 흐름을 관리하는 데 많은 노력을 기울여야 한다. 이를 위해 공 컨테이너 관리 전략을 포괄적으로 구현하고 효율적인 수송 비용 및 시간 절감 방식으로 컨테이너 흐름을 원활히 하여 관련 총비용을 최소화하는 동시에 고객의 수요를 최대한 충족하게 된다. 그러나 현실에서는 높은 불확실성 때문에 컨테이너 흐름에 대한 많은 주요한 이슈가 보편적으로 존재하고 효율적인 컨테이너 공급망 구축을 방해한다. 본 논문에서는 이러한 이슈에 대해 전반적으로 논의하고 적절한 해법과 함께 수리 모형을 제공한다. 이를 위해 세 가지 유형의 컨테이너 공급망을 다룬다. 먼저 (i) 양방향 네 단계 컨테이너 공급망, (ii) 분권화 및 중앙 집중화 정책에 따른 적∙공 컨테이너 공급망; 그리고 (iii) disruption 상황 속에서 신뢰성을 고려하는 컨테이너 공급망이다. 본 논문에서 제시한 세 가지 모형은 컨테이너 공급망에 내재 된 높은 위험을 직접 다루며 계산 실험은 해운 회사의 경영진이나 관계자를 위해 주요한 관리 인사이트를 제공한다. (i)의 경우, 두 지역 간 양자 무역을 위한 양방향 네 단계 컨테이너 공급망에서 공 컨테이너 관리 전략을 연구한다. 이 전략은 환적으로 인한 높은 해상 운송 비용과 긴 배송 시간을 줄일 수 있다. 또한, 직항 수송의 영향을 조사하여 선택된 항구 중 재배치 할 공 컨테이너 수, 임대 컨테이너 수, 두 지역의 수출업자와 수입업자의 적∙공 컨테이너 대한 수요를 만족하기 위한 경로 선택을 결정하게 된다. APSO 및 휴리스틱을 기반으로 하는 하이브리드 해법을 제시하며 비교 실험을 하였다. (ii)의 경우 최적 devanning time 결정을 목표로 공 컨테이너의 반환 지연과 해당 수수료 부과 결정 프로세스와 관련하여 서로 다른 세 가지 시나리오를 기반으로 적∙공 컨테이너 공급망 모형을 제시한다. 각 유형의 정책적(분권화 및 중앙 집중화) 효과는 정시 반환율을 포함한 주요 성능 측정을 고려하는 계산 실험을 통해 결정된다. 이러한 정책 실행에 대한 유용한 관리 인사이트는 민감도 분석 및 비교 연구의 결과에서 도출한다. (iii)의 경우, 본 논문은 컨테이너 네트워크 흐름을 기반으로 하는 신뢰성 모형을 개발하는 동시에 아크 및 노드 failure가 있을 때 street-turn 및 공 컨테이너 재배치 비용을 포함한 기대 총 비용을 구한다. 중단이 컨테이너 공급망 네트워크에 미치는 영향을 분석하기 위해 민감도 분석을 수행했으며 disruption 비용을 결정하기 위해 벤치마크 모형을 활용한다. 더불어 신뢰성을 고려한 컨테이너 네트워크 흐름을 구축하고 신뢰성을 유지하는 방법에 대한 관리적 인사이트도 제공한다.Abstract i Contents ii List of Tables vi List of Figures viii 1. Introduction 1 1.1 Empty Container Repositioning Problem 1 1.2 Reliability Problem 3 1.3 Research Motivation and Contributions 4 1.4 Outline of the Dissertation 7 2. Two-Way Four-Echelon Container Supply Chain 8 2.1 Problem Description and Literature Review 8 2.2 Mathematical Model for the TFESC 15 2.2.1 Overview and Assumptions 15 2.2.2 Notation and Formulation 19 2.3 Solution Procedure for the TFESC 25 2.3.1 Pseudo-Function-based Optimization Problem 25 2.3.2 Objective Function Evaluation 28 2.3.3 Heuristics for Reducing the Number of Leased Containers 32 2.3.4 Accelerated Particle Swarm Optimization 34 2.4 Computational Experiments 37 2.4.1 Heuristic Performances 39 2.4.2 Senstivity Analysis of Varying Periods 42 2.4.3 Senstivity Analysis of Varying Number of Echelons 45 2.5 Summary 48 3. Laden and Empty Container Supply Chain under Decentralized and Centralized Policies 50 3.1 Problem Description and Literature Review 50 3.2 Scenario-based Model for the LESC-DC 57 3.3 Model Development for the LESC-DC 61 3.3.1 Centralized Policy 65 3.3.2 Decentralized Policies (Policies I and II) 67 3.4 Computational Experiments 70 3.4.1 Numerical Exmpale 70 3.4.2 Sensitivity Analysis of Varying Degree of Risk in Container Return 72 3.4.3 Sensitivity Analysis of Increasing L_0 74 3.4.4 Sensitivity Analysis of Increasing t_r 76 3.4.5 Sensitivity Analysis of Decreasing es and Increasing e_f 77 3.4.6 Sensitivity Analysis of Discounting 〖pn〗_{f1} and 〖pn〗_{f2} 78 3.4.7 Sensitivity Analysis of Different Container Fleet Sizes 79 3.5 Managerial Insights 81 3.6 Summary 83 4. Reliable Container Supply Chain under Disruption 84 4.1 Problem Description and Literature Review 84 4.2 Mathematical Model for the RCNF 90 4.3 Reliability Model under Disruption 95 4.3.1 Designing the Patterns of q and s 95 4.3.2 Objective Function for the RCNF Model 98 4.4 Computational Experiments 103 4.4.1 Sensitivity Analysis of Expected Failure Costs 106 4.4.2 Sensitivity Analysis of Different Network Structures 109 4.4.3 Sensitivity Analysis of Demand-Supply Variation 112 4.4.4 Managerial Insights 115 4.5 Summary 116 5. Conclusions and Future Research 117 Appendices 120 A Proof of Proposition 3.1 121 B Proof of Proposition 3.2 124 C Proof of Proposition 3.3 126 D Sensitivity Analyses for Results 129 E Data for Sensitivity Analyses 142 Bibliography 146 국문초록 157 감사의 글 160Docto

Uma abordagem para a resolução do problema de transporte com custo fixo

Orientador : Prof. Dr. Arinei Carlos Lindbeck da SilvaCoorientador : Prof. Dr. Gustavo Valentim LochTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 20/06/2017Inclui referências : f. 69-78Resumo: O Problema de Transporte com Custo Fixo (PTCF) é uma classe da Programação Linear (PL), em que o custo total de envio de um produto, de uma origem para um destino, é composto por um custo unitário de transporte, proporcional à quantidade de itens enviados, e um custo fixo, associado à abertura da rota. O PTCF é NP-hard e além disso possui uma característica que à medida que a diferença entre o valor do custo unitário e o do custo fixo aumenta, o tempo computacional sofre alteração, piorando o desempenho. A base de problemas gerada por Sun, em 1998, foi adotada para realizar os testes computacionais. Após revisar alguns métodos da literatura, as heurísticas HEUR-1, HEUR-2, KOWA e HEUR-3 foram desenvolvidas e implementadas, utilizando estrutura de árvores e com otimização em relação ao cálculo das variáveis duais. Após realizar os testes computacionais, os métodos desenvolvidos foram comparados entre si constatando-se a superioridade de HEUR-3. A seguir, HEUR-3 foi comparado com BT, GIP, CORE2 e CORE3, que são métodos da literatura utilizados para resolver o PTCF além de comparar o desempenho com o solver Gurobi. Para todos os testes foi definido como critério de parada o tempo limite de 120 segundos. Cabe ressaltar que HEUR-3 e BT são heurísticas puras enquanto GIP, CORE2 e CORE3 fazem uso de um solver em determinado momento da rotina. Os valores obtidos para o PTCF em cada método da literatura e solver aqui citados, juntamente com HEUR-3, são analisados e discutidos parte a parte. A conclusão dessa tese mostra que HEUR-3 é superior quando comparado ao solver GUROBI e aos métodos BT, CORE2 e CORE3, o que não ocorre apenas com relação à técnica GIP. Palavras-chave: Heurística, implementação computacional, Gurobi.Abstract: The Fixed Charge Transportation Problem (FCTP) is a Linear Programming (LP) class, whereby the total shipping cost of a product, from a source to a destination, consists of a unit transportation cost, proportional to the amount of sent items and a fixed charge associated with the opening of the route. The FCTP is NP-hard and has a characteristic in which, as far as the difference between the value of the unit cost and the fixed charge increases, the computational time changes, worsening the performance. The base of problems generated by Sun, in 1998, was adopted to perform the computational tests. Following the review of some literature methods, the heuristics HEUR-1, HEUR-2, KOWA and HEUR-3 were developed and implemented, using a tree structure and with optimization in relation to the calculation of dual variables. After executing the computational tests, the developed methods were compared to each other, confirming the superiority of HEUR-3. Next, HEUR-3 was compared to BT, GIP, CORE2 and CORE3, which are literature methods used to solve the FCTP, in addition to compare the performance with the Gurobi solver. For all tests, the timeout of 120 seconds was set as stop criterion. It should be noted that HEUR-3 and BT are pure heuristics while GIP, CORE2 and CORE3 make use of a solver at a given moment of the routine. The values obtained for the FCTP in each of the literature methods and solver listed here, together with HEUR-3, are analyzed and discussed side by side. The conclusion of this thesis shows that HEUR-3 is superior when compared to the GUROBI solver and with BT, CORE2 and CORE3 methods, which does not only occur merely to the GIP technique. Keywords: Heuristic, computational implementation, Gurobi

Uma nova abordagem no processo iterativo de melhoria de solução na resolução do problema de transporte

Orientador : Prof. Dr. Arinei Carlos Lindbeck da SilvaTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 12/09/2014Inclui referênciasResumo: Dentre os problemas de Pesquisa Operacional, o Problema de Transporte (PT) é destacado como um dos mais importantes, devido a sua estrutura especial e, principalmente, pelas aplicações que não se limitam a problemas de distribuição. Para a resolução do Problema de Transporte, é amplamente conhecido na literatura e utilizado o método MODI, no qual são calculadas as variáveis duais e com base nelas recalculados os valores dos custos atualizados e que apresenta economia de tempo para resolução em relação ao método Stepping Stone. Na presente tese, a resolução do PT pelo método MODI foi realizada por uma implementação utilizando estrutura de quadro para armazenamento de informações e outra de árvore, sendo concluído que a resolução em árvore gerou uma economia média de 60,24% de tempo em relação à resolução em quadro. Foi demonstrado, sem a utilização das variáveis duais, que é possível o recálculo dos custos atualizados somente em função dos custos atualizados da iteração anterior e com a implementação deste resultado houve redução de 80,78% no tempo de resolução em relação à implementação do método MODI em árvore. Desta forma, a redução média da implementação em árvore recalculando somente os custos atualizados necessários foi de 92,34% em relação à implementação em quadro. Para reduzir ainda mais o tempo de resolução foi proposta uma nova forma de critério para escolha da variável não básica a entrar na base, utilizando uma lista, denominada ReferenciaCAN, menor de variáveis candidatas a tornarem-se básica na iteração e também um parâmetro, denominado PercentualEconomiaAnterior, para evitar a seleção de variáveis não básicas que não gerassem uma economia unitária menor que a desejada. Com isso foi possível reduzir o tempo médio de resolução em 37,06% em relação a situação anterior. De forma final, o tempo de resolução para o método e implementação final proposto na presente tese obteve uma redução de 95,18% em relação ao tempo médio da implementação clássica do método MODI em quadro. Palavras-chave: Problema de Transporte, método MODI, melhoria de solução, recálculo de custos atualizados, implementação computacional.Abstract: Among the Operational Research problems, the Transportation Problem (TP) is highlighted as one of the most important, due to its special structure, and especially by applications that are not limited to distribution problems. In order to solve the Transportation Problem, it is widely known in the literature and used the MODI method, in which the dual variables are calculated and based on them the reduced costs are recalculated, providing time saving when compared to the Stepping Stone method. In this thesis, the PT solver by MODI method was performed by using an implementation in the tableau structure for storing information and other using tree structure. It was concluded that when the problems were solved using tree structure it was generated an average savings of 60.24% of time in comparison to tableau structure. Therefore, it was demonstrated without the use of the dual variables, that it is possible recalculation of reduced costs only considering reduced costs of the previous iteration and the implementation of this rule resulted in 80.78% reduction in time to solve when compared to the implementation of the method MODI using tree structure. Thus, the average reduction in tree implementation recalculating only the updated costs required was 92.34% in relation to the implementation in tableau structure. In order to reduce again the time a new way has been proposed as criteria for the choice of the non basic variable to enter the basis, using a list, called ReferenciaCAN, with fewer variables candidates to become basic at current iteration and also a parameter, called PercentualEconomiaAnterior, to avoid the selection of non-basic variables that do not generate a smaller unitary economy than desired. It was then possible to reduce the average resolution time by 37.06% compared to the previous situation. After the modifications, the solver time for the final implementation and method proposed in this thesis achieved a reduction of 95.18% compared to the average time the classical implementation of MODI method in tableau structure. Keywords: Transportation Problem, MODI method, solution improvement, reduced costs computing, computational implementation

Інформаційні технології: теорія і практика: Тези доповідей VІ-ї Всеукраїнської науково-практичної інтернет-конференції здобувачів вищої освіти і молодих учених, 2023 р., м. Харків) [Електронний ресурс]

У збірнику представлені тези доповідей V Всеукраїнської Інтернетконференції здобувачів вищої освіти і молодих учених, яка мала відбутися 17-18 березня 2022 р. в Національному університеті «Запорізька політехніка», але через військову агресію російської федерації була проведена 10 червня 2022 р. в онлайн форматі. Конференція присвячується до 100-річчя Харківського національного університету міського господарства ім. О.Бекетова. Розглянуто результати досліджень та перспективи розвитку інформаційних технологій. Збірник призначений для науково-технічних підприємств, викладачів вищих навчальних закладів, докторантів, аспірантів і студентів.Зібрані тези доповідей VІ-ї Всеукраїнської інтернет-конференції здобувачів вищої освіти і молодих учених серед студентів, викладачів, науковців, молодих учених і аспірантів. Наукове видання відображає широкий спектр тематики наукових досліджень авторів