Hazardous waste management problem: The case for incineration

We define the hazardous waste management problem as the combined decisions of selecting the disposal method, siting the disposal plants and deciding on the waste flow structure. The hazardous waste management problem has additional requirements depending on the selected disposal method. In this paper we focus on incineration, for which the main additional requirement is to satisfy the air pollution standards imposed by the governmental restrictions. We propose a cost-based mathematical model in which the satisfaction of air pollution standards is also incorporated. We used the Gaussian Plume equation in measuring the air pollution concentrations at population centers. A large-scale implementation of the proposed model within Turkey is provided.     

A robust fuzzy multi-objective location-routing problem for hazardous waste under uncertain conditions

Industrialization and population growth have been accompanied by many problems such as waste management worldwide. Waste management and reduction have a vital role in national management. The presents study represents a multi-objective location-routing problem for hazardous wastes. The model was solved using Non dominated Sorting Genetic Algorithm-II, Multi-Objective Particle Swarm Optimization, Multi-Objective Invasive Weed Optimization, Pareto Envelope-based Selection Algorithm, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer algorithms. The findings revealed that the Multi-Objective Invasive Weed Optimization algorithm was the best and the most efficient among the algorithms used in this study. Obtaining income from the incineration of the wastes and reducing the risk of COVID-19 infection are the first innovation of the present study, which considered in the presented model. The second innovation is that uncertainty was considered for some of the crucial parameters of the model while the robust fuzzy optimization model was applied. Besides, the model was solved using several meta-heuristic algorithms such as Multi-Objective Invasive Weed Optimization, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer, which were rarely used in literature. Eventually, the most efficient algorithm was identified by comparing the considered algorithms.

     

A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem

The two-echelon location-routing problem (LRP-2E) is raised by the design of transportation networks with two types of trips: first-level trips serving from one main depot a set of satellite depots, to be located, and second-level trips supplying customers from these satellites. In the proposed multi-start iterated local search (MS-ILS), three greedy randomized heuristics are used cyclically to get initial solutions. Each ILS run alternates between two search spaces: LRP-2E solutions, and travelling salesman (TSP) tours covering the main depot and the customers. The number of iterations allotted to a run is reduced whenever a known solution (stored in a tabu list) is revisited. MS-ILS can be reinforced by a path-relinking procedure (PR), used internally for intensification, as post-optimization, or both. On two sets with 24 and 30 LRP-2E instances, MS-ILS outperforms on average two GRASP algorithms and adding PR brings a further improvement. Our metaheuristic also surpasses a tabu search on 30 instances for a more general problem with several main depots. It is still effective on a particular case, the capacitated location-routing problem (CLRP): In a comparison with four published metaheuristics, only one (LRGTS, Prins et al., 2007) does better.     

考虑公众风险的多目标医疗废物选址路径问题及樽海鞘算法求解

针对医疗废物处理中心的选址路径问题,在考虑公众风险的情况下,构建多目标优化模型。首先,分别从政府、公众和处理中心承包商角度出发,构建了以运营成本、风险成本以及运输成本最小化的多目标选址路径模型;其次,针对所构建模型的特点,设计了一种改进的多目标樽海鞘算法对模型进行求解;最后,以四川省成都市的医疗废物处理中心的规划项目为例,对构建的模型和算法进行验证,通过优化结果的对比分析,验证了模型的可行性和算法的有效性。     

A Lagrangian relaxation approach for a large scale new variant of capacitated clustering problem

This paper studies a new variant of capacitated clustering problem (VCCP). In the VCCP, p facilities which procure a raw material from a set of suppliers are to be located among n potential sites (n > p) such that the total cost of assigning suppliers to the facilities and opening such facilities is minimized. Each supplier has a limited supply volume and each facility has a minimum supply requirement that must be satisfied by assigning enough suppliers to the facility. Each supplier can be assigned to at most one facility. When a supplier is assigned to a facility, the former will supply its all available volume to the latter. In order to solve the VCCP, a Lagrangian relaxation approach (LR) with two phases of dual optimization, the subgradient deflection in the first phase and the standard subgradient method in the second phase, is proposed. In the approach, the assignment constraints are relaxed. The resulting Lagrangian relaxed problem can be decomposed into a set of independent knapsack problems, which can be solved to optimality efficiently. At each Lagrangian iteration, a feasible solution is constructed from that of the Lagrangian relaxed problem by applying a greedy algorithm. Finally, the best feasible solution found so far is improved by a simple tabu search algorithm. Numerical tests on random instances show that the proposed LR can produce a tight lower bound and a high quality feasible solution for all instances with up to 4000 suppliers, 200 potential sites, and 100 plants to locate.     

Genetic algorithm with iterated local search for solving a location-routing problem

This paper deals with a location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. We seek for new methods to make location and routing decisions simultaneously and efficiently. For that purpose, we describe a genetic algorithm (GA) combined with an iterative local search (ILS). The main idea behind our hybridization is to improve the solutions generated by the GA using a ILS to intensify the search space. Numerical experiments show that our hybrid algorithm improves, for all instances, the best known solutions previously obtained by the tabu search heuristic.     

考虑负效应的垃圾回收两级选址-路径模型与算法

针对生活垃圾中转站和焚烧站的选址-路径问题（LRP）,考虑经济目标和垃圾设施的负面影响,设计了与风向和距离有关的负效应分段函数,构建了两级多目标选址-路径（2E-MOLRP）模型,并提出了鲸鱼优化算法（WOA）和模拟退火（SA）算法结合的非支配算法WOA-SA。首先,结合随机方法与Clarke和Wright(CW)节约算法优化初始种群;其次,采用非线性动态惯性权重系数调整收敛速度;然后,设计WOA-SA的并行结构来增强全局搜索能力;最后,使用非支配排序法得到帕累托解集。对Prins和Barreto等35个基准案例以及天津市模拟案例进行分析。结果表明,WOA-SA可以找到20个基准案例的已知最优解（BKS）,且对Prins和Barreto案例的求解结果与BSK差距的平均值分别为0.37%和0.08%,具有很好的收敛性和稳定性。将所提模型和算法应用于实例,给决策者提供了三种不同方案的负效应值及经济成本的方案,以支持不同偏好决策者选择,从而减少垃圾回收物流成本和设施对环境的负面影响。     

A branch-and-cut algorithm for the hub location and routing problem

We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes.     

Lower and upper bounds for the two-echelon capacitated location-routing problem

In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times.     

A Stackelberg game model for construction waste transportation

The transportation of construction and demolition waste (CDW) is an essential problem in waste management. The CDW generated in large construction projects is typically transported by designated trucks. However, the disposal of scattered CDW produced by individuals or small projects is typically not planned, leading to its illegal dumping. Hong Kong aims to recycle scattered CDW by an appointment-recycling mechanism that involves a three-layered transportation network consisting of construction sites, recycling locations, and disposal facilities. In this study, we develop a two-stage Stackelberg game model to minimize the social costs of this three-layered transportation network. In the first stage, we consider the optimal decisions regarding the recycling locations, assigned trucks, and transport routes from the perspective of the government. In the second stage, the delivery routes for small projects are identified based on the government decisions. We transform the proposed model into a single-level integer program (IP) and conduct numerical experiments to demonstrate its efficiency and effectiveness. To the best of our knowledge, this is the first study to focus on the collection of scattered CDW. Thus, our study contributes to the literature on CDW transportation. Moreover, this study helps address a practical problem, i.e., the illegal dumping of scattered CDW, which is a common concern in many cities. In particular, even small amounts of CDW must be appropriately treated because it may contain hazardous materials.     

Local search heuristics for the mobile facility location problem

In the mobile facility location problem (MFLP), one seeks to relocate (or move) a set of existing facilities and assign clients to these facilities so that the sum of facility movement costs and the client travel costs (each to its assigned facility) is minimized. This paper studies formulations and develops local search heuristics for the MFLP. First, we develop an integer programming (IP) formulation for the MFLP by observing that for a given set of facility destinations the problem may be decomposed into two polynomially solvable subproblems. This IP formulation is quite compact in terms of the number of nonzero coefficients in the constraint matrix and the number of integer variables; and allows for the solution of large-scale MFLP instances. Using the decomposition observation, we propose two local search neighborhoods for the MFLP. We report on extensive computational tests of the new IP formulation and local search heuristics on a large range of instances. These tests demonstrate that the proposed formulation and local search heuristics significantly outperform the existing formulation and a previously developed local search heuristic for the problem.     

Solving a new bi-objective location-routing-inventory problem in a distribution network by meta-heuristics

This paper presents a novel bi-objective location-routing-inventory (LRI) model that considers a multi-period and multi-product system. The model considers the probabilistic travelling time among customers. This model also considers stochastic demands representing the customers’ requirement. Location and inventory-routing decisions are made in strategic and tactical levels, respectively. The customers’ uncertain demand follows a normal distribution. Each vehicle can carry all kind of products to meet the customer’s demand, and each distribution center holds a certain amount of safety stock. In addition, shortage is not allowed. The considered two objectives aim to minimize the total cost and the maximum mean time for delivering commodities to customers. Because of NP-hardness of the given problem, we apply four multi-objective meta-heuristic algorithms, namely multi-objective imperialist competitive algorithm (MOICA), multi-objective parallel simulated annealing (MOPSA), non-dominated sorting genetic algorithm II (NSGA-II) and Pareto archived evolution strategy (PAES). A comparative study of the forgoing algorithms demonstrates the effectiveness of the proposed MOICA with respect to four existing performance measures for numerous test problems.     

A compact model and tight bounds for a combined location-routing problem

This paper considers a combined location-routing problem. We define an auxiliary network and give a compact formulation of the problem in terms of finding a set of paths in the auxiliary network that fulfill additional constraints. The LP solution to the considered model provides an initial lower bound and is also used in a rounding procedure that provides the initial solution for a Tabu search heuristic. Additionally, we propose a different lower bound based on the structure of the problem. The results of computational testing on a set of randomly generated instances are promising.     

Determining the timing of project control points using a facility location model and simulation

Projects are usually performed in relatively unstable environments. As such, changes to the baseline schedules of projects are inevitable. Therefore, project progress needs to be monitored and controlled. The control process can be assumed as a continuum in which one side is continuous control and the other side is no-control. Continuous control and no-control strategies are cost-wise prohibited. Hence, project progress should be controlled at some discrete points in time during the project׳s duration. The optimal number and timing of control points are the main issues that should be addressed. In this paper, taking a dynamic view to the project control, for the first time we use an adapted version of the facility location model (FLM) to find the optimal timing of project control points. Initially, the adapted FLM determines the optimum timing of the control points in the project׳s duration. A simulation model is then used to predict the possible disruptions in the time period between the beginning of the project and the first control point (monitoring phase). If no disruptions are observed, the project׳s progress is monitored in the second control point, otherwise possible corrective actions are taken using an activity compression model. Whenever due to disruptions, the baseline schedule is to be updated, the FLM is run again to determine the new timing of the control points for the rest of the project׳s duration. In an iterative manner, this process continues until the timing of the last control point is determined.     

A branch-and-cut algorithm for the partitioning-hub location-routing problem

We introduce the Partitioning-Hub-Location-Routing Problem (PHLRP), a hub location problem involving graph partitioning and routing features. The PHLRP consists of partitioning a given network into sub-networks, locating at least one hub in each sub-network and routing the traffic within the network at minimum cost. This problem finds applications in deployment of an Internet Routing Protocol called Intermediate System–Intermediate System (ISIS), and strategic planning of LTL ground freight distribution systems. We present an Integer Programming (IP) model for solving exactly the PHLRP and explore possible valid inequalities to strengthen it. Computational experiments prove the effectiveness of our model which is able to tackle instances of PHLRP containing up to 20 vertices.     

A continuous network location problem for a single refueling station on a tree

This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refueling station to maximize the traffic flow covered in round trips/day. Two reduction properties regarding the problem size and some optimality conditions are derived. Based on these conditions, an exact polynomial algorithm is developed to determine the set of optimal locations for the refueling station. A small tree network example is solved to illustrate the algorithm.     

A simulated annealing heuristic for the open location-routing problem

This paper introduces the open location-routing problem (OLRP) that is a variant of the capacitated location-routing problem (CLRP). OLRP is motivated from the rise in contracting with third-party logistic (TPL) companies and is different from CLRP in that vehicles do not return to the distribution center after servicing all customers. The goal of OLRP is to minimize the total cost, consisting of facility operation costs, vehicle fixed costs, and traveling costs. We propose a simulated annealing (SA)-based heuristic for solving OLRP, which is tested on OLRP instances that have been adopted from three sets of well-known CLRP benchmark instances with up to 318 customers and 4 potential depots. The computational results indicate that the proposed heuristic efficiently solves OLRP.     

A facility location allocation model for reusing carpet materials

Re-using the huge quantities of carpet waste that are yearly generated has become a must. A facility location–allocation model for the collection, preprocessing and redistribution of carpet waste is presented. This model differs from other mathematical models for supporting the design of the logistic structure of reuse networks among others in a completely free choice of the locations for preprocessing and in explicitly taking into account depreciation costs. Two applications of the model, one in Europe and one in the United States of America, are described.     

Fuzzy multi-objective chance-constrained programming model for hazardous materials transportation

Hazardous materials transportation is an important and hot issue of public safety. Based on the shortest path model, this paper presents a fuzzy multi-objective programming model that minimizes the transportation risk to life, travel time and fuel consumption. First, we present the risk model, travel time model and fuel consumption model. Furthermore, we formulate a chance-constrained programming model within the framework of credibility theory, in which the lengths of arcs in the transportation network are assumed to be fuzzy variables. A hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed for finding a satisfactory solution. Finally, some numerical examples are given to demonstrate the efficiency of the proposed model and algorithm.     

A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm

The location of manufacturing facilities is one of the most important strategic decisions considered in the design of logistic systems. Another important strategic decision is the structure and management of the fleets. Most often, even if two types of problem (i.e., location of facilities and vehicle routing) have occurred in a given scenario, they have been studied and solved separately. This paper presents a new integrated mathematical model for a bi-objective multi-depot location-routing problem where the total demand served is to be maximized and the total cost, consisting of start-up of the facility, fixed and variable depots and variable delivery cost, is to be minimized. Since this type of the problem is NP-hard, a new multi-objective scatter search (MOSS) algorithm is proposed to obtain the Pareto frontier for the given problem. To validate the performance of the proposed MOSS algorithm in terms of the solution quality and diversity level, various test problems are carried out and the efficiency of this algorithm based on some comparison metrics is compared with the elite tabu search (ETS). The computational results show that the proposed MOSS outperforms the ETS, especially in large-sized problems.