Optimisation of a distribution system in the retail industry: An Australian retail industry

This paper develops a mathematical model based on inventory routing problem that aims to minimise transportation cost, inventory carrying cost and optimises delivery schedules in a retail Australian industry. A supply chain is considered which comprises of a single distribution centre, having homogenous fleet of vehicles, supplying a single product to multiple retailers having deterministic demand. The mathematical model takes into account varying level of road congestion.N/

A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem

Most research about the vehicle routing problem (VRP) does not collectively address many of the constraints that real-world transportation companies have regarding route assignments. Consequently, our primary objective is to explore solutions for real-world VRPs with a heterogeneous fleet of vehicles, multi-depot subcontractors (drivers), and pickup/delivery time window and location constraints. We use a nested bi-criteria genetic algorithm (GA) to minimize the total time to complete all jobs with the fewest number of route drivers. Our model will explore the issue of weighting the objectives (total time vs. number of drivers) and provide Pareto front solutions that can be used to make decisions on a case-by-case basis. Three different real-world data sets were used to compare the results of our GA vs. transportation field experts’ job assignments. For the three data sets, all 21 Pareto efficient solutions yielded improved overall job completion times. In 57 % (12/21) of the cases, the Pareto efficient solutions also utilized fewer drivers than the field experts’ job allocation strategies

The Effects of the Tractor and Semitrailer Routing Problem on Mitigation of Carbon Dioxide Emissions

The incorporation of CO2 emissions minimization in the vehicle routing problem (VRP) is of critical importance to enterprise practice. Focusing on the tractor and semitrailer routing problem with full truckloads between any two terminals of the network, this paper proposes a mathematical programming model with the objective of minimizing CO2 emissions per ton-kilometer. A simulated annealing (SA) algorithm is given to solve practical-scale problems. To evaluate the performance of the proposed algorithm, a lower bound is developed. Computational experiments on various problems generated randomly and a realistic instance are conducted. The results show that the proposed methods are effective and the algorithm can provide reasonable solutions within an acceptable computational time

Integrated network routing and scheduling problem for salt trucks with replenishment before snowfall

Kar yağışı öncesinde ve sırasında yolların zamanında tuzlanması, trafik güvenliğini iyileştirmek ve trafik sıkışıklığını önlemek için önemli bir önleyici faaliyettir. Bu çalışmada, bir şehir yolu ağındaki tuz kamyonlarının rotalama ve çizelgeleme problemi ele alınmıştır. Ele alınan problem İstanbul Büyükşehir Belediyesinin yoğun kar yağışı durumlarında karşılaştığı bir operasyonel problemdir ve periyodik olarak çözülmelidir. Problemde, araç filosu tuz kapasitesi açısından heterojen araçlardan oluşmaktadır ve birden fazla tuz ikmal noktası bulunmaktadır. Hava şartları gerektirdiğinde, tuzlanması gereken yollar ve bu yollar için öncelik seviyeleri belirlenmektedir. Amaç, ağın farklı noktalarında konumlanmış olan araçların, tuzlanması gereken tüm yolları tuzlayacak şekilde ve yolların ağırlıklı tamamlanma süresini en küçükleyerek rotalanması ve çizelgelenmesidir. Tuza ihtiyacı olan her yol tek bir araç tarafından tuzlanmalıdır. Araçlar tuzlanması gereken bir yolu tuzlama yapmadan sadece geçiş yapmak amacıyla da kullanılabilir. Araçlar, tuzları bittiğinde tuz ikmal noktalarını ziyaret etmelidir. Problemin çözümü için ilk olarak bir karma tam sayılı programlama modeli geliştirilmiştir. Problem büyüklüğü arttıkça modelin performansının hızla düştüğü gözlemlenmiş ve iki aşamalı bir sezgisel yöntem geliştirilmiştir. Sezgiselin ilk aşamasında yapıcı algoritma ile olurlu bir başlangıç çözümü elde edilmektedir, ikinci aşamasında bulunan başlangıç çözümü bir komşuluk arama algoritması ile geliştirilmektedir. Çözüm yaklaşımımızın verimliliği, gerçek hayat yol ağlarını yansıtan rastgele oluşturulmuş örnekler üzerinde analiz edilmiştir.Timely salting of roads before the snowfall is an important preventive activity for improving traffic safety and avoiding traffic congestions. We study the problem of routing and scheduling of salt trucks on a city road network. The problem is motivated by the operational problem that the Istanbul Metropolitan Municipality face in case of a heavy snowfall, and thereby should be solved in a periodic manner.In this problem, the vehicle fleet consists of heterogeneous vehicles that differ in salt capacity and there are multiple salt replenishment points. At the beginning of the current planning horizon, given a set of salt needing roads with different urgency levels, the vehicles start from different points of the network (i.e., their final locations at the end of the former planning horizon) and should cover all salt needing roads with the objective of minimizing the total weighted completion time of salting operation of each service needing arc. Each service needing arc should be serviced by exactly one vehicle, however, can be traversed for deadheading by a vehicle as part of its route.Vehicles visit replenishment points when they run out of salt. We first develop a Mixed-Integer Programming model for the problem. Since the performance of the model degrades rapidly as the problem size increases, we propose a simulated annealing metaheuristic, which obtains an initial solution by a constructive heuristic in the first phase, and then improves the solution in the next phase. The efficiency of our solution approach is evaluated on randomly generated instances reflecting real life road networks

Algorithms for the multi-objective vehicle routing problem with hard time windows and stochastic travel time and service time

This paper introduces a multi-objective vehicle routing problem with hard time windows and stochastic travel and service times. This problem has two practical objectives: minimizing the operational costs, and maximizing the service level. These objectives are usually conflicting. Thus, we follow a multi-objective approach, aiming to compute a set of Pareto-optimal alternatives with different trade-offs for a decision maker to choose from. We propose two algorithms (a Multi-Objective Memetic Algorithm and a Multi-Objective Iterated Local Search) and compare them to an evolutionary multi-objective optimizer from the literature. We also propose a modified statistical method for the service level calculation. Experiments based on an adapted version of the 56 Solomon instances demonstrate the effectiveness of the proposed algorithms

Modelling and solving the bi-objective production–transportation problem with time windows and social sustainability

We model and solve the production routing problem (PRP) with time windows, product deterioration and split delivery. A bi-objective PRP model for a single perishable product, which is subject to deterioration, is presented. The two objectives represent the economic and social aspects of sustainability, whereas the environmental impact is enforced by incorporating ad-hoc constraints. The economic dimension of sustainability consists of minimizing the costs related to the production, setup, holding, transportation and lateness penalty. The social responsibilities are modelled through maximizing the total freshness of the delivered products at all nodes over the planning horizon. The outcomes of our formulation are represented by the lot sizes, and the amounts of product to be delivered, as well as the routing at each planning period. To solve the resulting problem, we develop an interval robust possibilistic approach, and we carry out an experimental study and a sensitivity analysis. Finally, we further validate our optimization model and solution method using a real-life case of a food factory producing a product that is subject to perishability and deterioration

Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs

Penyelesaian Permasalahan Vehicle Routing dengan Objektif Jamak yang Mempertimbangkan Keseimbangan Jarak Rute Kendaraan Menggunakan Metode Hiperheuristik

Vehicle Routing Problem (VRP) adalah salah satu permasalahan kombinatorik yang sulit dipecahkan. VRP bertujuan untuk menghasilkan serangkaian rute terpendek dari beberapa kendaraan berkapasitas sama untuk mengunjungi beberapa pelanggan dengan batas waktu tertentu. Sebagian besar penelitian VRP sebelumnya hanya meminimalkan jarak total sebagai objektif tunggal, tanpa mempertimbangkan keseimbangan jarak antar rute yang dihasilkan. Untuk ini diperlukan solusi terhadap permasalahan VRP yang mempertimbangkan faktor keseimbangan jarak antar rute selain batasan yang hanya melibatkan faktor minimalisasi total jarak rute. Dalam penelitian ini dikembangkan algoritma hiperheuristik untuk menyelesaikan permasalahan VRP dengan objektif jamak, yaitu algoritma yang mengombinasikan objektif untuk meminimalkan total jarak rute dan objektif untuk menyeimbangkan jarak antar rute yang dihasilkan. Parameter keseimbangan antar jarak antar rute diukur menggunakan formulasi simpangan baku terhadap masing-masing rute yang dihasilkan. Metode pareto sorting digunakan untuk menghasilkan solusi yang efektif berdasarkan nilai kedua fungsi objektif, indikator jumlah solusi, serta nilai coverage dan nilai hypervolume dari solusi. Algoritma hiperheuristik yang telah berhasil dikembangkan dalam penelitian ini diimplementasikan dengan menggunakan kerangka kerja HyFlex dan bahasa pemrograman Java. Uji coba hasil implementasi dilakukan menggunakan dua set data dengan kompleksitas yang berbeda, yaitu set data Solomon dan set data Gehring dan Homberger. Metode pemilihan low-level heuristic berbasis algoritma hill climbing hyperheuristic dipilih karena memberikan solusi yang lebih baik dibandingkan dengan algoritma great deluge hyperheuristic. Hasil uji coba perbandingan antara solusi VRP dengan objektif jamak dan solusi VRP dengan objektif tunggal menunjukkan bahwa rerata simpangan baku jarak antar rute untuk VRP dengan objektif jamak (sebesar 678) cukup jauh lebih rendah dibandingkan rerata simpangan baku antar rute VRP dengan objektif tunggal (sebesar 1.053), walaupun rerata total jarak minimum yang dihasilkan oleh VRP dengan objektif jamak (sebesar 99.590) relatif lebih besar dibandingkan dengan yang dihasilkan oleh VRP dengan objektif tunggal (sebesar 94.650). Hal ini menunjukkan bahwa tambahan fungsi objektif untuk menyeimbangkan jarak antar rute kendaraan dari solusi VRP yang dihasilkan sesuai dengan tujuan penelitian. ========================================================================================================================Vehicle Routing Problem (VRP) is one of the combinatoric problems hard to solve. VRP aims to generate a set of the shortest routes of vehicles with similar capacity to visit customers with certain time limit. Most previous VRP studies only minimized total distance as a single objective, regardless of the balance of route distances. Therefore, it required a solution to the VRP that considered the balance factor of distance between routes other than minimizing the total distance of the route. In this study, hyper-heuristic algorithm was developed to solve VRP with multi-objective, an algorithm that combines objective function to minimize the total distance of the routes and objective function to balance of obtained route distances. The balance of route distances parameter was measured by standard deviation formulation of route distances. Pareto sorting method was used to generate effective solutions based on the value of the two objective functions, the number of solutions indicators, the coverage value and hypervolume value of the solutions. The developed hyper-heuristic algorithm was implemented using HyFlex framework and Java programming. The experiments of implemented algorithm utilized two datasets with different complexity, Solomon dataset and Gehring and Homberger dataset. The low-level heuristic selection method based on the hill-climbing hyper-heuristic algorithm was chosen because it provided better solutions than the hyper-heuristic of great deluge algorithm. The comparison of multi-objective VRP solutions and single objective VRP solutions indicated that the average of standard deviation between routes of VRP with multi-objective (678) is considerably lower than the average of standard deviation between routes of VRP with single objective (1,053 ), even though the average of minimum total distance obtained by VRP with multi-objective (99,590) was relatively higher than the average of minimum total distance obtained by VRP with single objective (94,650). It showed that additional objective function for balancing vehicle route distances from obtained VRP solution corresponded to the research objectives

Algoritmos genéticos paralelos para resolver el problema de rutas de vehículos con ventanas de tiempo

El problema de rutas de vehículos (VRP por sus siglas en inglés ), consiste en obtener las rutas de costo mínimo para la entrega de productos, a un conjunto de clientes que se encuentran dispersos geográficamente. Este problema es de gran interés por la comunidad científica por los beneficios que representa, y por los beneficios que brinda en el sector industrial, comercial y de servicio. El VRP tiene variantes que se clasifican de acuerdo a ciertas restricciones, una de ellas es el problema de rutas de vehículos con ventanas de tiempo (VRPTW, por sus siglas en inglé s), que es en el que enfocamos esta investigación. En este trabajo se presenta un modelo paralelo de un algoritmo genético, para resolver casos de prueba del VRPTW. Este algoritmo realiza una exploración en el espacio de búsqueda para encontrar soluciones que minimizan el número de rutas y la distancia recorrida, el cual es el objetivo del pro blema. Para la parte del modelo paralelo se utilizó el paradigma de paso de mensajes mediante la biblioteca MPI (Message Passing Interface). Los resultados obtenidos del algoritmo en paralelo para el VRPTW, se compararon con más de cincuenta casos de prue ba disponibles p ú blicamente (ver anexo tabla de resultados) . Las soluciones obtenidas son comparables en términos de calidad de la solución , y tiempo computacional respecto al desempeño de la versión secuencial

Essays on Shipment Consolidation Scheduling and Decision Making in the Context of Flexible Demand

This dissertation contains three essays related to shipment consolidation scheduling and decision making in the presence of flexible demand. The first essay is presented in Section 1. This essay introduces a new mathematical model for shipment consolidation scheduling for a two-echelon supply chain. The problem addresses shipment coordination and consolidation decisions that are made by a manufacturer who provides inventory replenishments to multiple downstream distribution centers. Unlike previous studies, the consolidation activities in this problem are not restricted to specific policies such as aggregation of shipments at regular times or consolidating when a predetermined quantity has accumulated. Rather, we consider the construction of a detailed shipment consolidation schedule over a planning horizon. We develop a mixed-integer quadratic optimization model to identify the shipment consolidation schedule that minimizes total cost. A genetic algorithm is developed to handle large problem instances. The other two essays explore the concept of flexible demand. In Section 2, we introduce a new variant of the vehicle routing problem (VRP): the vehicle routing problem with flexible repeat visits (VRP-FRV). This problem considers a set of customers at certain locations with certain maximum inter-visit time requirements. However, they are flexible in their visit times. The VRP-FRV has several real-world applications. One scenario is that of caretakers who provide service to elderly people at home. Each caretaker is assigned a number of elderly people to visit one or more times per day. Elderly people differ in their requirements and the minimum frequency at which they need to be visited every day. The VRP-FRV can also be imagined as a police patrol routing problem where the customers are various locations in the city that require frequent observations. Such locations could include known high-crime areas, high-profile residences, and/or safe houses. We develop a math model to minimize the total number of vehicles needed to cover the customer demands and determine the optimal customer visit schedules and vehicle routes. A heuristic method is developed to handle large problem instances. In the third study, presented in Section 3, we consider a single-item cyclic coordinated order fulfillment problem with batch supplies and flexible demands. The system in this study consists of multiple suppliers who each deliver a single item to a central node from which multiple demanders are then replenished. Importantly, demand is flexible and is a control action that the decision maker applies to optimize the system. The objective is to minimize total system cost subject to several operational constraints. The decisions include the timing and sizes of batches delivered by the suppliers to the central node and the timing and amounts by which demanders are replenished. We develop an integer programing model, provide several theoretical insights related to the model, and solve the math model for different problem sizes