A multi-objective mathematical model for the industrial hazardous waste location-routing problem

Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multi-objective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers; minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues; and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database.     

A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery

This paper addresses a location-routing problem with simultaneous pickup and delivery (LRPSPD) which is a general case of the location-routing problem. The LRPSPD is defined as finding locations of the depots and designing vehicle routes in such a way that pickup and delivery demands of each customer must be performed with same vehicle and the overall cost is minimized. We propose an effective branch-and-cut algorithm for solving the LRPSPD. The proposed algorithm implements several valid inequalities adapted from the literature for the problem and a local search based on simulated annealing algorithm to obtain upper bounds. Computational results, for a large number of instances derived from the literature, show that some instances with up to 88 customers and 8 potential depots can be solved in a reasonable computation time.     

An integer goal programming model for hazardous waste treatment and disposal

The improper handling and disposal of hazardous wastes cause threats to human health and the environment. One reason for the improper handling and disposal of these wastes is that not much consideration is usually given to the logistical aspects of hazardous waste systems. In this paper an integer goal programming model is developed that takes into consideration the multiple goals and needs of many groups involved in managing and planning hazardous waste systems. The model can easily be implemented and can be used to address many of the issues related to facility location, recycling, treatment, and disposal of hazardous wastes.     

A new formulation and an exact approach for the many-to-many hub location-routing problem

An important problem of the freight industry is the parcel delivery network design, where several facilities are responsible for assembling flows from several origins, re-routing them to other facilities where the flows are disassembled and the packages delivered to their final destinations. In order to provide this service, local tours are established for the vehicles assigned to each of the processing facilities, which are then responsible for the pickup and delivery tasks. This application gives rise to the many-to-many hub location routing problem that is the combination of two well known problems: the vehicle routing problem and the single assignment hub location problem. In this work, a new formulation for this important problem is proposed and solved by a specially tailored Benders decomposition algorithm. The proposed method is robust enough to solve instances up to 100 nodes having 4 million integer variables.     

Combining approaches for evaluating auditing populations: A simulation study

This research explores ways of combining four distinct bounds for the mean error in an auditing population. Two competing objectives for a bound are to be close to the true mean being estimated and to be reliable: not less than the true mean in more than 5% of estimations. The optimal combination should provide the best balance of these competing objectives. Estimating the mean error by a single approach is difficult because typically most accounts have no error and the distribution of the errors among those that do is discontinuous and highly skewed. This study reveals that the weights in the optimal combination are not constant but depend on the characteristic of the population being estimated. The optimally combined bound is only 7% smaller overall than the best of the constituents. However, while the best of the constituents fails in 50% of most challenging populations, the optimal combination never fails.     

Supply chain cooperation in industrial districts: A simulation analysis

In the past few years the literature on supply chain management has widely emphasized that cooperation among supply chain (SC) firms is a key source of competitive advantage. This paper explores the topic in a particular context, i.e. the industrial district (ID), which constitutes a specific production model where complex SC networks can be identified. SC cooperation may take on several forms in IDs and may produce several benefits (e.g. upgrading quality and reducing costs) so this paper also analyzes the benefits of a specific form of SC cooperation in different competitive scenarios and for diverse ID organizational structures. An agent-based model of SC cooperation in IDs has been developed and a simulation analysis carried out.     

A facet generation and relaxation technique applied to an assignment problem with side constraints

We consider a solution method for combinatorial optimization problems based on a combination of Lagrangean relaxation and constraint generation techniques. The procedure is applied to a constrained assignment problem, where subsets of variables are specified, and variables belonging to the same subset must have the same value. The model can be applied to solve constrained job assignment or classroom assignment problems. The procedure we suggest requires only the solution of classical assignment subproblems. An illustrative numerical example is given.     

The school bus routing problem: A review

This paper aims to provide a comprehensive review of the school bus routing problem (SBRP). SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated schools while satisfying various constraints such as the maximum capacity of a bus, the maximum riding time of a student in a bus, and the time window of a school. This class of problem consists of different sub-problems involving data preparation, bus stop selection, bus route generation, school bell time adjustment, and bus scheduling. In this paper, the various assumptions, constraints, and solution methods used in the literature on SBRP are summarized. A list of issues requiring further research is also presented.     

The minimization of open stacks problem: A review of some properties and their use in pre-processing operations

Pre-processing operations that reduce the size of a problem may be decisive for solving or not solving practical instances of a NP-hard problem. In this article we review some properties suggested in the literature for the minimization of open stacks problem that can be used in pre-processing operations to reduce the instances sizes. We also present a new pre-processing technique that may be very effective in reducing the size of an instance. We present computational tests with the suggested pre-processing operations applied on sets of MOSP instances of the literature and we show that the reductions obtained can be significant.     

Fractional multi-commodity flow problem: Duality and optimality conditions

This paper deals with multi-commodity flow problem with fractional objective function. The optimality conditions and the duality concepts of this problem are given. For this aim, the fractional linear programming formulation of this problem is considered and the weak duality, the strong direct duality and the weak complementary slackness theorems are proved applying the traditional duality theory of linear programming problems which is different from same results in Chadha and Chadha (2007) [1]. In addition, a strong (strict) complementary slackness theorem is derived which is firstly presented based on the best of our knowledge. These theorems are transformed in order to find the new reduced costs for fractional multi-commodity flow problem. These parameters can be used to construct some algorithms for considered multi-commodity flow problem in a direct manner. Throughout the paper, the boundedness of the primal feasible set is reduced to a weaker assumption about solvability of primal problem which is another contribution of this paper. Finally, a real world application of the fractional multi-commodity flow problem is presented.     

The flow shop problem with no-idle constraints: A review and approximation

The makespan minimization problem in flow shops with no-idle constraints on machines is considered. The latter means that each machine, once started, must process all its operations without intermediate idle time until all those operations are completed. The problem is known to be strongly NP-hard already for three machines. While being based on a geometrical approach, we propose several polynomial time heuristics (for the general case and for special cases of 3 and 4 machines) which provide asymptotically optimal solutions for the increasing number of jobs. A comprehensive review of relevant results is also presented.     

Optimizing stochastic production-inventory systems: A heuristic based on simulation and regression analysis

We present a heuristic optimization method for stochastic production-inventory systems that defy analytical modelling and optimization. The proposed heuristic takes advantage of simulation while at the same time minimizes the impact of the dimensionality curse by using regression analysis. The heuristic was developed and tested for an oil and gas company, which decided to adopt the heuristic as the optimization method for a supply-chain design project. To explore the performance of the heuristic in general settings, we conducted a simulation experiment on 900 test problems. We found that the average cost error of using the proposed heuristic was reasonably low for practical applications.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm

In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy β-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.     

Regularization tools and robust optimization for ill-conditioned least squares problem: A computational comparison

Least squares problems arise frequently in many disciplines such as image restorations. In these areas, for the given least squares problem, usually the coefficient matrix is ill-conditioned. Thus if the problem data are available with certain error, then after solving least squares problem with classical approaches we might end up with a meaningless solution. Tikhonov regularization, is one of the most widely used approaches to deal with such situations. In this paper, first we briefly describe these approaches, then the robust optimization framework which includes the errors in problem data is presented. Finally, our computational experiments on several ill-conditioned standard test problems using the regularization tools, a Matlab package for least squares problem, and the robust optimization framework, show that the latter approach may be the right choice.     

Range-based Multi-Actor Multi-Criteria Analysis: A combined method of Multi-Actor Multi-Criteria Analysis and Monte Carlo simulation to support participatory decision making under uncertainty

Concerns about environmental and social effects have made Multi-Criteria Decision Making (MCDM) increasingly popular. Decision making in complex contexts often – possibly always – requires addressing an aggregation of multiple issues to meet social, economic, legal, technical, and environmental objectives. These values at stake may affect different stakeholders through distributional effects characterized by a high and heterogeneous uncertainty that no social actors can completely control or understand. On this basis, we present a new process framework that aims to support participatory decision making under uncertainty: the range-based Multi-Actor Multi-Criteria Analysis (range-based MAMCA). On the one hand, the process framework explicitly considers stakeholders’ objectives at an output level of aggregation. On the other hand, by means of a Monte Carlo analysis, the method also provides an exploratory scenario approach that enables the capture of the uncertainty, which stems from the complex context evolution. Range-based MAMCA offers a unique participatory process framework that enables us (1) to identify the alternatives pros and cons for each stakeholder group; (2) to provide probabilities about the risk of supporting mistaken, or at least ill-suited, decisions because of the uncertainty regarding to the decision-making context; (3) to take the decision-makers’ limited control of the actual policy effects over the implementation of one or several options into account. The range-based MAMCA framework is illustrated by means of our first case study that aimed to assess French stakeholders’ support for different biofuel options by 2030.     

A general filter regularization method to solve the three dimensional Cauchy problem for inhomogeneous Helmholtz-type equations: Theory and numerical simulation

In this paper, we solve the Cauchy problem for an inhomogeneous Helmholtz-type equation with homogeneous Dirichlet and Neumann boundary condition. The proposed problem is ill-posed. Up to now, most investigations on this topic focus on very specific cases, and with Dirichlet boundary condition. Recently, we solve this problem in 2D for an inhomogeneous modified Helmholtz equation (2012). This work is a continuous expansion of our previous results. Herein we introduce a general filter regularization (GFR) method, and then from the GFR we deduce two concrete filters, which are a foundation to implement a numerical procedure. In addition, we develop a numerical model for solving this problem in three dimensional region. The proposed filter method has been verified by numerical experiments.