Desenvolvimento de uma heurística para a determinação de rotas de recolha e distribuição de produtos considerando múltiplos veículos

Trabalho de projecto de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2019Neste projeto, apresenta-se um problema de determinação de rotas de recolha e distribuição com escolha seletiva de mercados. Existe uma frota homogénea de veículos e existem pontos onde se faz a recolha de determinados produtos e, posteriormente, faz-se a distribuição pelos clientes, tendo estes uma dada procura que tem que ser satisfeita. Não é obrigatório visitar todos os pontos de recolha disponíveis. O objetivo é construir rotas para os veículos que partam de um depósito, passem por certos mercados para comprar os produtos, entreguem os produtos aos clientes e regressem ao depósito, de modo a minimizar a soma dos custos de aquisição dos produtos e dos custos de deslocação. Neste trabalho, faz-se uma breve referência a alguns problemas de determinação de rotas para veículos e à sua aplicação a casos reais. Apresenta-se, ainda, um modelo matemático em programação linear inteira mista. Desenvolve-se, para obter soluções admissíveis para este problema, uma heurística que é constituída por duas fases. A primeira fase consiste em criar rotas com um único cliente e com os mercados que o servem, tendo como base uma heurística desenvolvida para resolver o Travelling Purchaser Problem. Nesta primeira fase, constrói-se uma solução inicial, a qual é melhorada através de dois procedimentos: Market drop e Market exchange. A segunda fase consiste na fusão das rotas obtidas, juntando vários clientes na mesma rota, de modo a diminuir os custos de viagem. Os resultados computacionais são obtidos para dados gerados aleatoriamente, considerando duas áreas onde estão os clientes, o depósito e os mercados, dois tipos de probabilidade associados à existência de determinado produto em cada mercado e à probabilidade de a procura de determinado produto por parte de um cliente ser superior a zero e diferentes valores para número de mercados e procura. Fazse uma análise dos resultados obtidos em termos de média das melhorias percentuais quando se faz a fusão de rotas e em termos de tempos computacionais, considerando duas capacidades diferentes para os veículos.In this project, a pickup and delivery problem with selective choice of markets is presented. There is a fleet of homogenous vehicles which travels through pickup points to get certain products and then delivers them to the customers who have a certain demand that must be satisfied. It is not necessary to visit every available pickup point. The goal is to find a good, next to optimal, route for the vehicles that leave the depot, stop at certain markets where products are bought, deliver those products to the customers and then return to the depot, in order to minimize the sum of the purchasing costs and the travelling costs. In this project, a brief reference to some vehicle routing problems and some of its applications to the real world is made. A mixed integer linear programming model is presented. A heuristic is built to find feasible solutions for this problem. The heuristic consists of two phases, the first of which, consists of creating routes with a single customer and the markets which satisfy the customer’s demand. This phase is based on a heuristic for the Travelling Purchaser Problem where an initial feasible solution is found and improved upon through two procedures: Market Drop and Market Exchange. The second phase consists of merging the routes obtained beforehand, joining multiple customers in the same route, in order to decrease travelling costs. Some computational results were obtained for randomly generated data, considering two different areas for the depot, customers and markets, two different probabilities for the existence of a certain product in a certain market, two different probabilities for the existence of demand of a certain product for each customer and, lastly, different numbers of customers and markets. The results were analysed in regards to the average percentage improvements for the route merging, as well as regarding the computational time, considering two different maximum vehicle capacities

What drives the Rebound Effect in transportation? An evaluation based on a Traveling Purchaser Problem

Limiting climate change is one of the most important challenges of the 21st century. Focusing on the transport sector, encouraging the use of more energy-efficient transport modes, and improving the performance of vehicles are the main targets in the fight for GHG reductions. However, due to Rebound Effect (RE), it is proven that improvements in engine fuel efficiency result in lower cost per kilometer driven and can induce individuals to use vehicles more often or to drive longer distances. As a result, the potential energy savings from improved energy efficiency could be partially or totally offset. Therefore, we decided to examine "What drives the Rebound Effect in transportation". To answer this research question, a Traveling Purchaser Problem was evaluated. This simple real-life business application models a situation in which a company owns one or several vehicles and has to buy specific products. The goal is to select and visit a subset of suppliers to satisfy a given demand for each product while minimizing both purchasing and travel costs. In total, 510 instances of this problem with various characteristics and parameters were generated and solved using the optimization software AIMMS. The impact of five main experimentations was deeply investigated. In addition, the trends obtained from these experiments were confirmed by fitting a logistic regression and a decision tree. The results of the various experiments showed that four variables can influence the occurrence of RE in a transportation network. On the one hand, RE tended to increase with the number of potential suppliers from which the firm can choose and the number of vehicles that the company owns to procure the products. On the other hand, the exclusivity of the products to source, as well as the introduction of a distance-traveled tax, reduced the occurrence of RE. To sum up, significant conclusions could be drawn from the experiments and the results can be easily transferred to real-life business applications. Recommendations for possible future studies were also discussed.nhhma

Meta-heurísticas para o problema do traveling purchaser

Tese de mestrado, Estatística e Investigação Operacional (Investigação Operacional), Universidade de Lisboa, Faculdade de Ciências, 2015Dados um conjunto de mercados potenciais, uma lista de itens e um depósito, o problema do traveling purchaser (PTP) consiste em determinar uma rota de custo mínimo começando e acabando no depósito e que contenha um subconjunto de mercados de forma a ser possível adquirir todos os itens da lista. Conhecem-se os itens disponíveis em cada mercado, bem como o respetivo custo de aquisição, e o custo de deslocação entre cada par de mercados e entre cada mercado e o depósito. Note-se que cada item é vendido em pelo menos um mercado, caso contrário o problema seria impossível. A cada rota está associado um custo que é a soma dos custos de deslocação e de aquisição. O PTP tem inúmeras variantes mas nesta dissertação apenas será estudada a variante do PTP sem capacidades. Pretende-se adquirir uma unidade de cada item e cada mercado tem disponível no máximo uma unidade. O PTP pertence à classe de problemas NP-difícil, sendo essa a principal razão pela qual se recorre a métodos heurísticos para o resolver. Nesta dissertação são apresentadas três meta-heurísticas, cada uma composta por um algoritmo genético seguido de um procedimento de pesquisa local. Os três algoritmos genéticos representam as diferentes hierarquias de decisão associadas a ambas as partes do problema: rota e aquisição. A pesquisa local é baseada em técnicas de add e drop. Para comparar os métodos propostos foram utilizadas instâncias de referência. Na generalidade dos casos o valor das soluções obtidas recorrendo às meta-heurísticas têm um desvio inferior a 1% relativamente ao valor da solução ótima tendo estas soluções sido obtidas num tempo computacional razoável. Comparativamente a métodos propostos por outros autores, as meta-heurísticas resolvem as instâncias de teste num tempo computacional inferior e oferecem soluções para casos de estudo que os outros métodos não conseguiam resolver.Given a set of markets, a list of items and a depot, the traveling purchaser problem (TPP) consists in determining one route with a minimal cost that satisfies the following conditions: it begins and ends in the depot and we need to be able to buy all the items in the list in the subset of markets that belong to the route. We know which items are sold in each market and their cost, and the cost of traveling between each pair of markets and between each market and the depot. Every item must be sold in at least one market or otherwise the problem would be impossible. Each route has a cost, which is the sum of the traveling cost with the purchase cost. There are several variants of the TPP but in this thesis we will study the uncapacited version. We only wish to buy a copy of each item which is the maximum quantity available in each market. The TPP belongs to the class of NP-hard problems and this is the main reason why heuristic methods are used to solve the problem under study. In this thesis we present three meta-heuristics, each one composed by a genetic algorithm and a local search procedure. The three genetic algorithms represent the several ways we can decide which part of the problem is more important: route, purchase or route and purchase. The local search procedure is based on add and drop techniques. To compare the meta-heuristics we used benchmark instances. In the majority of cases we obtained solutions with a gap lower than 1% regarding the optimal solution within a reasonable computational time. Comparing with methods proposed by other authors, ours are able to solve the benchmark instances in less time and can find solutions to instances that the other methods could not

Mathematical formulations and optimization algorithms for solving rich vehicle routing problems.

Objectives and methods of study: The main objective of this work is to analyze and solve three different rich selective Vehicle Routing Problems (VRPs). The first problem is a bi-objective variant of the well-known Traveling Purchaser Problem (TPP) in which the purchased products are delivered to customers. This variant aims to find a route for which the total cost (transportation plus purchasing costs) and the sum of the customers’s waiting time are simultaneously minimized. A mixed integer bi-objective programming formulation of the problem is presented and tested with CPLEX 12.6 within an ǫ-constraint framework which fails to find non-dominated solutions for instances containing more than 10 nodes. Therefore, a heuristic based on relinked local search and Variable Neighborhood Search (VNS) is proposed to approximate the Pareto front for large instances. The proposed heuristic was tested over a large set of artificial instances of the problem. Computational results over small-sized instances show that the heuristic is competitive with the ǫ-constraint method. Also, computational tests over large-sized instances were carried out in order to study how the characteristics of the instances impact the algorithm performance. The second problem consists of planning a selective delivery schedule of multiple products. The problem is modeled as a multi-product split delivery capacitated team orienteering problem with incomplete services, and soft time windows. The problem is modeled through a mixed integer linear programming formulation and approximated by means of a multi-start Adaptive Large Neighborhood Search (ALNS) metaheuristic. Computational results show that the multi-start metaheuristic reaches better results than its classical implementation in which a single solution is build and then improved. Finally, an Orienteering Problem (OP) with mandatory visits and conflicts, is formulated through five mixed integer linear programming models. The main difference among them lies in the way they handle the subtour elimination constraints. The models were tested over a large set of instances of the problem. Computational experiments reveal that the model which subtour elimination constraints are based on a single-commodity flow formulation allows CPLEX 12.6 to obtain the optimal solution for more instances than the other formulations within a given computation time limit. Contributions: The main contributions of this thesis are: • The introduction of the bi-objective TPP with deliveries since few bi-objective versions of the TPP have been studied in the literature. Furthermore, to the best of our knowledge, there is only one more work that takes into account deliveries in a TPP. • The design and implementation of a hybrid heuristic based on relinked local search and VNS to solve the bi-objective TPP with deliveries. Additionally, we provide guidelines for the application of the heuristic when different characteristics of the instances are observed. • The design and implementation of a multi-start adaptive large neighborhood search to solve a selective delivery schedule problem. • The experimental comparison among different formulations for an OP with mandatory nodes and conflicts

The Traveling Purchaser Problem Under Uncertainty

4The Traveling Purchaser Problem (TPP) is an interesting procurement and routing NP-hard problem that finds application in several domains. The problem aims at determining a tour starting at and ending to the depot while visiting a subset of markets in such a way that a demand for each product is satisfied and that the cost globally spent for purchasing the products and visiting the markets is minimized. The deterministic TPP ignores the uncertain nature of some parameters involved in the model, thus typically providing recommendations with limited practical application. While the deterministic version of the TPP has been largely studied (e.g. see [1]), very few contributions exist in the literature for the TPP under uncertainty [2]. This work proposes a scenariobased stochastic and capacitated version of the TPP which explicitly takes into account uncertainty in prices and/or products availability. Injecting stochastic elements in the model allows us to manage closely real-life applications. We cast the model within a two-stage stochastic paradigm based on a distinction between the first-stage variables, which have to be decided upon before the outcomes of the stochastic variables are observed, and the second stage variables which have to be decided after the uncertainty is resolved. To efficiently solve the problem, we develop a tailored heuristic approach designed to exploit the specific problem structure. Encouraging preliminary computational results are provided. References: [1] G. Laporte, J. Riera-Ledesma, J.J. Salazar-Gonzalez, A branch-and-cut algorithm for the undirected Traveling Purchaser Problem, Operation Research 51(6), pp. 940-951 (2003). [2] S. Kang, Y. Ouyang, The traveling purchaser problem with stochastic prices: exact and approximate algorithms, European Journal of Operational Research 209(3), pp. 265-272 (2011).nonenoneBruni M. E.; Beraldi P.; Manerba D.; Mansini R.Bruni, M. E.; Beraldi, P.; Manerba, Daniele; Mansini, Renat

The Traveling Purchaser Problem Under Uncertainty

The Traveling Purchaser Problem (TPP) is an interesting procurement and routing NP-hard problem that finds application in several domains. The problem aims at determining a tour starting at and ending to the depot while visiting a subset of markets in such a way that a demand for each product is satisfied and that the cost globally spent for purchasing the products and visiting the markets is minimized. The deterministic TPP ignores the uncertain nature of some parameters involved in the model, thus typically providing recommendations with limited practical application. While the deterministic version of the TPP has been largely studied (e.g. see [1]), very few contributions exist in the literature for the TPP under uncertainty [2]. This work proposes a scenariobased stochastic and capacitated version of the TPP which explicitly takes into account uncertainty in prices and/or products availability. Injecting stochastic elements in the model allows us to manage closely real-life applications. We cast the model within a two-stage stochastic paradigm based on a distinction between the first-stage variables, which have to be decided upon before the outcomes of the stochastic variables are observed, and the second stage variables which have to be decided after the uncertainty is resolved. To efficiently solve the problem, we develop a tailored heuristic approach designed to exploit the specific problem structure. Encouraging preliminary computational results are provided. References: [1] G. Laporte, J. Riera-Ledesma, J.J. Salazar-Gonzalez, A branch-and-cut algorithm for the undirected Traveling Purchaser Problem, Operation Research 51(6), pp. 940-951 (2003). [2] S. Kang, Y. Ouyang, The traveling purchaser problem with stochastic prices: exact and approximate algorithms, European Journal of Operational Research 209(3), pp. 265-272 (2011)

The Traveling Purchaser Problem Under Uncertainty

The Traveling Purchaser Problem (TPP) is an interesting procurement and routing NP-hard problem that finds application in several domains. The problem aims at determining a tour starting at and ending to the depot while visiting a subset of markets in such a way that a demand for each product is satisfied and that the cost globally spent for purchasing the products and visiting the markets is minimized. The deterministic TPP ignores the uncertain nature of some parameters involved in the model, thus typically providing recommendations with limited practical application. While the deterministic version of the TPP has been largely studied (e.g. see [1]), very few contributions exist in the literature for the TPP under uncertainty [2]. This work proposes a scenariobased stochastic and capacitated version of the TPP which explicitly takes into account uncertainty in prices and/or products availability. Injecting stochastic elements in the model allows us to manage closely real-life applications. We cast the model within a two-stage stochastic paradigm based on a distinction between the first-stage variables, which have to be decided upon before the outcomes of the stochastic variables are observed, and the second stage variables which have to be decided after the uncertainty is resolved. To efficiently solve the problem, we develop a tailored heuristic approach designed to exploit the specific problem structure. Encouraging preliminary computational results are provided. References: [1] G. Laporte, J. Riera-Ledesma, J.J. Salazar-Gonzalez, A branch-and-cut algorithm for the undirected Traveling Purchaser Problem, Operation Research 51(6), pp. 940-951 (2003). [2] S. Kang, Y. Ouyang, The traveling purchaser problem with stochastic prices: exact and approximate algorithms, European Journal of Operational Research 209(3), pp. 265-272 (2011)

The Stochastic and Dynamic Traveling Purchaser Problem

The Traveling Purchaser Problem (TPP) looks for a tour starting at and ending to the depot that visits a subset of markets so to satisfy the demand for all products while minimizing purchasing and traveling costs (see Laporte et al. [2]). In this paper we study a more realistic procurement setting where products quantity stochastically decreases due to other purchasers competing on the same products. The global effect of the competitors behavior is assumed to be modeled as an array of m × n stochastic consumption processes independent with respect to the m markets and the n products. The problem is also dynamic since information on quantity availability is revealed over time and the decision maker may react to new information by making new plans. We call this problem the Stochastic Dynamic Traveling Purchaser Problem (SDTPP). The problem finds application in different contexts including procurement and large scale emergencies, as those caused by natural disasters, viral spread diseases and/or terrorist attacks. To the best of our knowledge, this version of the TPP has never been addressed before. In Angelelli et al. [1] a simpler variant is studied where no assumption is made on the consumption processes and the decision maker is assumed to be informed in real-time of all occurring events. We will explore the SDTPP under four different operating scenarios all characterized by the presence of a planner who has computing power and makes decisions and an executor (the purchaser) who runs the service in practice and has a very limited or null computing power. Scenarios differ for the communication tools used between planner and executor, and for the level of information available on the state of the world. As far as communication is concerned, different situations can be figured out ranging from the case where no communication technologies are available (after leaving the depot communication between planner and executor is interrupted) to a complete communication between actors. In terms of information, possible situations range from a minimum, characterized by knowledge of the initial state of the world plus an update collected on the field at visited markets, to a maximum like in internet based systems, where current stock levels of all markets are shared by all commercial partners in real time. The contributions provided are multifold. We introduce two consumption models to estimate products inventory and propose three solution approaches, a stochastic, a deterministic and an hybrid one. The proposed approaches have been compared under the analyzed scenarios in terms of both feasibility and total costs. A comparison with a known approach proposed in the literature is also considered. Extensive computational results show how the hybrid approach provides the best compromise in terms of computational burden and quality of the solution and define interesting guidelines for decision makers involved with similar problems. [1] E. Angelelli, R. Mansini, M. Vindigni, Look-ahead heuristics for the Dynamic Traveling Purchaser Problem, Computers & Operations Research 38 (2011) 1867–1876. [2] G. Laporte, J. Riera-Ledesma, J.J. Salazar-Gonzalez, A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem, Operations Research 6 (2003) 940–951