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This paper aims to define the class of fragment constructive heuristics used to compute feasible solutions for the traveling salesman problem (TSP) into edge-greedy and vertex-greedy subclasses. As these subclasses of heuristics can create subtours, two known methodologies for subtour elimination on symmetric instances are reviewed and are expanded to cover asymmetric problem instances. This paper introduces a third novel subtour elimination methodology, the greedy tracker (GT), and compares it to both known methodologies.

Computational results for all three subtour elimination methodologies are generated across 17 symmetric instances ranging in size from 29 vertices to 5,934 vertices, as well as 9 asymmetric instances ranging in size from 17 to 443 vertices.

The results demonstrate the GT is the fastest method for preventing subtours for instances below 400 vertices. Additionally, a distinction between fragment constructive heuristics and the subtour elimination methodology used to ensure the feasibility of resulting solutions enables the introduction of a new vertex-greedy fragment heuristic called ordered greedy.

This research has two main contributions: first, it introduces a novel subtour elimination methodology. Second, the research introduces the concept of ordered lists which remaps the TSP into a new space with promising initial computational results.

The purpose of this chapter is to optimize multi-criteria formulation for green vehicle routing problems by mixed integer programming. This research is about the road freight transportation of a Spanish company of groceries. This company has more power in the north of Spain and hence it was founded there. The data used for the computational experiments are focused in the northern region of Spain. The data have been used to decide the best route in order to obtain a minimization of costs for the company. The problem focused on the distance traveled and the altitude difference; by studying these parameters, the best solution of route transportation has been made. The software used to solve this model is CPLEX solver with AMPL programming language. This has been helpful to obtain the results for the research and some conclusions have been obtained from them.

In this chapter, four bi-objective vehicle routing problems are considered. Weighted-sum approach optimization models are formulated with the use of mixed-integer programming. In presented optimization models, maximization of capacity of truck versus minimization of utilization of fuel, carbon emission, and production of noise are taken into account. The problems deal with real data for green logistics for routes crossing the Western Pyrenees in Navarre, Basque Country, and La Rioja, Spain.

Heterogeneous fleet of trucks is considered. Different types of trucks have not only different capacities, but also require different amounts of fuel for operations. Consequently, the amount of carbon emission and noise vary as well. Modern logistic companies planning delivery routes must consider the trade-off between the financial and environmental aspects of transportation. Efficiency of delivery routes is impacted by truck size and the possibility of dividing long delivery routes into smaller ones. The results of computational experiments modeled after real data from a Spanish food distribution company are reported. Computational results based on formulated optimization models show some balance between fleet size, truck types, and utilization of fuel, carbon emission, and production of noise. As a result, the company could consider a mixture of trucks sizes and divided routes for smaller trucks. Analyses of obtained results could help logistics managers lead the initiative in environmental conservation by saving fuel and consequently minimizing pollution. The computational experiments were performed using the AMPL programming language and the CPLEX solver.

The purpose of this paper is to present an optimised scheduling system for facility mangers and custodians. Experience-driven systems currently in use can result in poor ratings for facility maintenance metrics such as overtime hours, utilisation difference and labour costs.

The cleaning schedule and custodian work assignments defined by the manager are simulated for the entire year. Clustering and routing algorithms assign work to custodians equally and find optimal cleaning routes. The manager may use the resulting feedback to iteratively find a suitable schedule which lowers costs.

Data were collected at a large university building in consultation with facility management and custodians. Results indicate a significant reduction in overtime hours, improvement in utilisation difference and a lowering of labour costs.

The methodology was validated at a single building in the facility. Variable selection and optimisation model design will benefit from a comprehensive case study which spans the entire facility.

The methodology may easily be integrated with existing facility maintenance software, adding to it features such as a manager scheduling interface with feedback on critical cleaning metrics and a custodian user interface which highlights room visitation routes and task times.

This study acts on the need for facility cleaning labour cost management highlighted in literature. It achieves its goals using a novel combination of scheduling, simulation and optimisation. It is designed to empower key decision-makers, i.e. facility managers and custodians, with better information.

This paper studies a supply chain consisting of multiple suppliers and a single buyer. It considers the case where a set of heterogeneous trucks is used for transporting products, and develops a mathematical model that coordinates the supply chain. The purpose of this paper is to minimise the costs of producing and delivering a product as well as carbon emissions resulting from transportation. In addition, the authors analyse how imposing a tax on carbon emissions impacts the delivery of products from the suppliers to the buyer.

It is assumed that heterogeneous vehicles are used for transporting products, which have different performance and cost attributes. A mathematical model that considers both operating costs and carbon emissions from transportation is developed. The impact of vehicle attributes on lot sizing and routing decisions is studied with the help of numerical examples and a sensitivity analysis.

The analysis shows that considering carbon emissions in coordinating a supply chain leads to changes in the routing of vehicles. It is further shown that if carbon emissions lead to costs, routes are changed in such a way that vehicles travel long distances empty or with a low vehicle load to reduce fuel consumption and therewith emissions.

Several areas for future work are highlighted. The study of alternative supply chain structures, for example structures which include logistics service providers, or the investigation of different functional relationships between vehicle load and emission generation offer possibilities for extending the model.

The paper is one of the first to study the use of heterogeneous vehicles in an inventory model of a supply chain, and one of the few supply chain inventory models that consider ecological aspects.

Given the importance of estimating the demand for relief items in earthquake disaster, this research studies the complex nature of demand uncertainty in a vehicle routing problem in order to distribute first aid relief items in the post disaster phase, where routes are subject to disruption.

To cope with such kind of uncertainty, the demand rate of relief items is considered as a random fuzzy variable and a robust scenario-based possibilistic-stochastic programming model is elaborated. The results are presented and reported on a real case study of earthquake, along with sensitivity analysis through some important parameters.

The results show that the demand satisfaction level in the proposed model is significantly higher than the traditional scenario-based stochastic programming model.

In reality, in the occurrence of a disaster, demand rate has a mixture nature of objective and subjective and should be represented through possibility and probability theories simultaneously. But so far, in studies related to this domain, demand parameter is not considered in hybrid uncertainty. The worth of considering hybrid uncertainty in this study is clarified by supplementing the contribution with presenting a robust possibilistic programming approach and disruption assumption on roads.

In regarding to operational efficiency and safety improvements, multiple tower crane service scheduling problem is one of the main problems related to tower crane operation but receives limited attention. The current work presents an optimization model for scheduling multiple tower cranes' service with overlapping areas while achieving collision-free between cranes.

The cooperative coevolutionary genetic algorithm (CCGA) was proposed to solve this model. Considering the possible types of cross-tasks, through effectively allocating overlapping area tasks to each crane and then prioritizing the assigned tasks for each crane, the makespan of tower cranes was minimized and the crane collision avoidance was achieved by only allowing one crane entering the overlapping area at one time. A case study of the mega project Daxing International Airport has been investigated to evaluate the performance of the proposed algorithm.

The computational results showed that the CCGA algorithm outperforms two compared algorithms in terms of the optimal makespan and the CPU time. Also, the convergence of CCGA was discussed and compared, which was better than that of traditional genetic algorithm (TGA) for small-sized set (50 tasks) and was almost the same as TGA for large-sized sets.

This paper can provide new perspectives on multiple tower crane service sequencing problem. The proposed model and algorithm can be applied directly to enhance the operational efficiency of tower cranes on construction site.

The traveling purchaser problem (TPP) has gained attention in academics to deal with different variants in real business world. This study aims to study a green TPP with quantity discounts and soft time windows (TPPQS), in which a firm needs to purchase products from a set of available markets and deliver the products to a set of customers.

Vehicles are available to visit the markets, which offer products at different prices and with different quantity discount schemes. Soft time windows are present for the markets and the customers, and earliness cost and tardiness may incur if a vehicle cannot arrive a market or a customer within the designated time interval. The environmental impact of transportation activities is considered. The objective of this research is to minimize the total cost, including vehicle-assigning cost, vehicle-traveling cost, purchasing cost, emission cost, earliness cost and tardiness cost, while meeting the total demand of the customers and satisfying all the constraints. A mixed integer programming (MIP) model and a genetic algorithm (GA) approach are proposed to solve the TPPQS.

The results show that both the MIP and the GA can obtain optimal solutions for small-scale cases, and the GA can generate near-optimal solutions for large-scale cases within a short computational time.

The proposed models can help firms increase the performance of customer satisfaction and provide valuable supply chain management references in the service industry.

The proposed models for TPPQS are novel and can facilitate firms to design their green traveling purchasing plans more effectively in today’s environmental conscious and competitive market.

This study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned.

Owing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds.

The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure.

This paper covers the modeling of some real-world problems in which demand is uncertain and managers face making some concurrent decisions related to supply chain management, transportation and logistics and inventory control issues. Furthermore, considering the perishability of product in modeling makes the problem more practically significant as these days there are many supply chains handling dairy and other fresh products.

Considering uncertainty, production, transshipment and perishable product in the inventory-routing problem makes a new variant that has not yet been studied. The proposed novel solution is based on the LR approach that is enhanced by some heuristics and some valid inequalities that make it different from the current version of the LR used by other studies.

Drugs are strategic products with essential functions in human health. An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health. The vehicle-routing problem, focused on finding the lowest-cost routes with available vehicles and constraints, such as time constraints and road length, is an important aspect of this. In this paper, the vehicle routing problem (VRP) for a pharmaceutical company in Turkey is discussed.

A mixed-integer programming (MIP) model based on the vehicle routing problem with time windows (VRPTW) is presented, aiming to minimize the total route cost with certain constraints. As the model provides an optimum solution for small problem sizes with the GUROBI® solver, for large problem sizes, metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed. A real dataset was used to analyze the effectiveness of the metaheuristic algorithms. The proposed simulated annealing (SA) and adaptive large neighborhood search (ALNS) were evaluated and compared against GUROBI® and each other through a set of real problem instances.

The model is solved optimally for a small-sized dataset with exact algorithms; for solving a larger dataset, however, metaheuristic algorithms require significantly lesser time. For the problem addressed in this study, while the metaheuristic algorithms obtained the optimum solution in less than one minute, the solution in the GUROBI® solver was limited to one hour and three hours, and no solution could be obtained in this time interval.

The VRPTW problem presented in this paper is a real-life problem. The vehicle fleet owned by the factory cannot be transported between certain suppliers, which complicates the solution of the problem.