Transportation cost minimization of a manufacturing firm using genetic algorithm approach

This study utilizes a Genetic Algorithm in solving the transportation problem of a beverage producing company in Nigeria with a view to minimizing the total transportation cost and obtaining an optimal schedule or schedules using transportation cost data from the peak periods (January to April and August to December) in the 2014/2015 production year which witnessed a fifty per cent (50%) rise in the cost of diesel (a major contributor to the transportation cost) and a corresponding increase in its transportation cost as a result of government’s removal of subsidy on petroleum products. The obtained data were analyzed and formulated into a transportation matrix with three routes and ten depots which were coded into strings after which the GA was applied to generate optimal schedules for six to nine depots that optimize the total transportation cost, revealing marked savings when compared with the company’s current evaluation method. The cost savings reduced as the number of depots in the generated schedules increased with the six-depot schedule having the highest cost saving of N347, 552 daily.  http://dx.doi.org/10.4314/njt.v35i4.2

An Improved Mathematical Formulation For the Carbon Capture and Storage (CCS) Problem

abstract: Carbon Capture and Storage (CCS) is a climate stabilization strategy that prevents CO2 emissions from entering the atmosphere. Despite its benefits, impactful CCS projects require large investments in infrastructure, which could deter governments from implementing this strategy. In this sense, the development of innovative tools to support large-scale cost-efficient CCS deployment decisions is critical for climate change mitigation. This thesis proposes an improved mathematical formulation for the scalable infrastructure model for CCS (SimCCS), whose main objective is to design a minimum-cost pipe network to capture, transport, and store a target amount of CO2. Model decisions include source, reservoir, and pipe selection, as well as CO2 amounts to capture, store, and transport. By studying the SimCCS optimal solution and the subjacent network topology, new valid inequalities (VI) are proposed to strengthen the existing mathematical formulation. These constraints seek to improve the quality of the linear relaxation solutions in the branch and bound algorithm used to solve SimCCS. Each VI is explained with its intuitive description, mathematical structure and examples of resulting improvements. Further, all VIs are validated by assessing the impact of their elimination from the new formulation. The validated new formulation solves the 72-nodes Alberta problem up to 7 times faster than the original model. The upgraded model reduces the computation time required to solve SimCCS in 72% of randomly generated test instances, solving SimCCS up to 200 times faster. These formulations can be tested and then applied to enhance variants of the SimCCS and general fixed-charge network flow problems. Finally, an experience from testing a Benders decomposition approach for SimCCS is discussed and future scope of probable efficient solution-methods is outlined.Dissertation/ThesisMasters Thesis Industrial Engineering 201

An Enhanced Dynamic Slope Scaling Procedure with Tahu Scheme for Fixed Charge Network Flow Problems

In this thesis, a heuristic algorithm for solving large scale fixed charge network problems (FCNFP) based on the dynamic slope scaling procedure (DSSP) and tabu search strategies is presented. The proposed heuristic (the enhanced DSSP) integrates the DSSP with the classical short-term memory intensification and long-term memory diversification mechanism in the tabu search to improve the performance of the pure DSSP. With the feature of dynamically evolving memory, the enhanced DSSP evaluates the solutions in the search history and it iteratively adjusts the linear factors of the LP approximations of the FCNFP to produce promising search neighborhoods for good quality solutions. Comprehensive numerical experiments are included in this thesis, ranging from sparse to dense network problems generated randomly. The computational results of the pure DSSP, the enhanced DSSP and branch and bound (B&B) are compared in terms of solution quality and CPU time. The enhanced DSSP approach has higher solution quality than the pure DSSP and much less computation time than B&B

Decomposition Algorithm in Fixed Charge Time-Space Network Flow Problems

A wide range of network flow problems primarily used in transportation is categorized as time-space fixed charge network flow (FCNF) problems. In this family of networks, each node is associated with a specific time and is replicated across all time-periods. The cost structure in these problems consists of variable and fixed costs where continuous and binary variables are required to formulate the problem as a mixed integer linear programming. FCNF problems are classified as NP-hard problems, therefore, adding another component (i.e., time) to this type of problem results in a complex problem which is time-consuming and CPU and memory intensive. Various exact and heuristic methods have been proposed and implemented to solve FCNF problems. In this work, a decomposition heuristic is proposed that subdivides the problem into various time epochs to create smaller and more manageable subproblems. These subproblems are solved sequentially to find an overall solution for the original problem. To evaluate the capability and efficiency of the decomposition method vs. exact method, a total of 1600 problems is generated and solved using Gurobi MIP solver, which runs parallel branch & bound algorithm. Statistical analysis indicates that depending on the problem specification, the average solution time in decomposition methods is improved by up to four orders of magnitude. While statistically, there is a significant difference between the mean objective value of exact method and each TPV configuration in both decomposition methods, however, the average difference (0-2.16% in decomposition and 1.55-7.85% in decomposition method with relaxation) may not be a serious concern for many practical large-scale problems. This shows great promise for decomposition method to significantly reduce the solution time which has been an outstanding issue in complicated large-scale problems

Optimization-based algorithms for a single level constrained resource problem.

So Wai Kuen.Year shown on spine: 1997.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 87-92).INTRODUCTION --- p.1Chapter 1.1 --- Introduction to SLCR Problem --- p.1Chapter 1.2 --- Our Contributions --- p.1Chapter 1.3 --- Organization of the thesis --- p.3LITERATURE REVIEW --- p.4Chapter 2.1 --- Research in the Capacitated Resource Constraint Problem --- p.4Chapter 2.2 --- The Single Level Constrained Resource Problem --- p.5Chapter 2.3 --- The Multiple Level Constrained Resource Problem --- p.8Chapter 2.4 --- Research in the Fixed Charge Problem --- p.9Chapter 2.4.1 --- Approximate Methods --- p.9Chapter 2.4.2 --- Exact Methods --- p.10Chapter 2.5 --- Conclusion --- p.11THE SLCR PROBLEM WITH BACKORDERING --- p.12Chapter 3.1 --- Problem Description and Formulation --- p.13Chapter 3.2 --- Description of the heuristic --- p.19Chapter 3.2.1 --- Phase I --- p.19Chapter 3.2.2 --- Phase II --- p.26Chapter 3.3 --- Design of Computational Experiments --- p.30Chapter 3.3.1 --- Specifications of test problems ( 3 products and 12 period case ) --- p.31Chapter 3.3.2 --- Computation of the Lower Bound --- p.38Chapter 3.4 --- Computational Results --- p.39Chapter 3.5 --- Comparison to Millar and Yang's Algorithm --- p.48Chapter 3.5.1 --- Comparison Results --- p.49Chapter 3.6 --- Conclusion --- p.50THE OPTIMIZATION BASED ALGORITHM --- p.51Chapter 4.1 --- The Formulation --- p.52Chapter 4.2 --- The Algorithm --- p.60Chapter 4.2.1 --- Phase I --- p.60Chapter 4.2.2 --- Phase II --- p.63Chapter 4.2.3 --- Phase III --- p.70Chapter 4.3 --- An Illustrative Example --- p.72Chapter 4.4 --- Computational Results --- p.79Chapter 4.5 --- Conclusion --- p.84CONCLUSION --- p.85BIBLIOGRAPHY --- p.8

Nova metodologia para resolução de problemas de transporte em casos esparsos

Resumo: Entre áreas de estudo da Programação Linear o Problema de Transporte é uma das aplicações de destaque. Os Problemas de Transporte podem ser classificados em densos ou esparsos. O modelo é denominado denso quando existem todas as ligações entre origens e destinos e esparsos quando algumas ou várias destas ligações não existem. O presente trabalho propõe uma alteração no algoritmo de resolução do Problema de Transporte para o caso esparso, que consiste basicamente da inclusão de uma nova origem e um novo destino com elevado custo de transporte para as origens e destinos originais e custo nulo entre a origem e destino acrescentados. O método é demonstrado e testado para instâncias geradas aleatoriamente. Depois de feita a explanação sobre o funcionamento do método e de demonstrar a validade das modificações, os conceitos são implementados computacionalmente. Os testes realizados mostram ganhos significativos no tempo de processamento. Para problemas com densidade 0,05, este tempo chega a ser de somente 25% do necessário para resolver o mesmo problema através do algoritmo tradicional, onde as ligações não existentes são admitidas com custo extremamente elevado. Em problemas com densidade 0,3 este tempo é de aproximadamente 50% daquele necessário pelo tradicional. O método desenvolvido tem desempenho equivalente quando utilizado sobre Problemas Densos. Também é feita uma explanação sobre a utilização de grafos, que são facilitadores na determinação de locais para colocação de variáveis degeneradas e sua aplicação na determinação dos ciclos. Discute-se a importância de utilizar características peculiares de um problema para métodos específicos de resolução. A economia no processamento pode viabilizar a utilização de modelagens deste tipo em processos meta-heurísticos que utilizem iterativamente o problema de transporte

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