A fractional model for locating semi-desirable facilities on networks

In this paper, we address the problem of locating a series of facilities on a network maximizing the average distance to population centers (assumed to be distributed in the plane) per unit transportation cost (a function of the network distances to users). A finite dominating set is constructed, allowing the resolution of the problem by standard integer programming techniques. We also discuss some extensions of the model (including, in particular, the Weber problem with attraction and repulsion in networks), for which (ε-) dominating sets are derived.     

A multiobjective programming model for locating treatment sites and routing hazardous wastes

In this paper, a multiobjective model for locating disposal or treatment facilities and transporting hazardous waste along the links of a transportation network are presented. Some of the nodes of this network may be population centres generating hazardous waste which must be transported to the treatment facilities. Four objectives are considered: (1) minimisation of total operating cost, (2) minimisation of total perceived risk, (3) equitable distribution of risk among population centres and (4) equitable distribution of the disutility caused by the operation of the treatment facilities. A goal programming model to solve the problem is developed and a small hypothetical example is presented to illustrate how penalty functions can be used to obtain more satisfactory solutions in real life applications.     

A multiobjective planning model for university resource allocation

Application of systematic approaches and dynamic planning for efficient resources allocation in institutions of higher education has been quite prevalent the past fifteen years. However, most models developed for university management have focused upon the analysis of input (budget/resource) requirements. They have generally neglected the existing environment, unique institutional values, and bureaucratic decision structures. In this study, a large scale goal programming model is developed for an efficient allocation of resources for an entire university for a five year planning period. The results of the model have been implemented in the form of administrative actions to achieve a set of multiple objectives.     

A multiobjective optimization model for water resources planning

A technique is developed for solving multiple objective optimization programs. The approach decomposes the system into groups of objectives according to their priority in the model. A lexicographic ordering (goal programming) approach is used to analyse this system of groups, while the solution structure of each individual group is developed using the method of constraints. The technique is applied to a planning model for river basins.     

A general model for the undesirable single facility location problem

In this paper, a finite set in which an optimal solution for a general Euclidean problem of locating an undesirable facility in a polygonal region, is determined and can be found in polynomial time. The general problem we propose leads us, among others, to several well-known problems such as the maxisum, maximin, anticentdian or r-anticentrum problem.     

A multiobjective fuzzy bandwidth partitioning model for self-sizing networks

The ability to cope with dynamic bandwidth demands is a special feature for Quality of Service provisioning in networks carrying bandwidth hungry applications. This paper introduces a novel approach based on multiobjective fuzzy optimization for dynamic bandwidth allocation. This new approach deals with uncertain bandwidth demands more efficiently than approaches based on Classical Optimization Theory and yet supports Quality of Service commitments.     

A mathematical immunochemoradiotherapy model: A multiobjective approach

This study developed a near optimization immunochemoradiotherapy model, which has three objectives; maximizing total weighted damage of cancer cells, minimizing total weighted side effect and minimizing total dose related therapy costs, originated from the Weapon–Target Assignment problem (WTA) of military operations research. The multi-objective structure is transformed into a single-objective format via goal programming. The presented model is a mixed-integer nonlinear goal programming model. A non-clinical hypothetical illustrative example is solved using MS Excel's Solver tool as a powerful spreadsheet tool. The theoretical result is extremely impressive especially compared with result of the single-objective program. The model facilitates cancer therapists to act in a multi-objective frame. However, the model is extremely needed to have clinical experiments to validate its theoretical power. This theoretical model is a virtuous synthesis of military and medical operations research.     

一种多目标条件风险值数学模型

研究了一种多目标条件风险值(CVaR)数学模型理论.先定义了一种多目标损失函数下的α-VaR和α-CVaR值,给出了多目标CVaR最优化模型.然后证明了多目标意义下的α-VaR和α-CVaR值的等价定理,并且给出了对于多目标损失函数的条件风险值的一致性度量性质.最后,给出了多目标CVaR模型的近似求解模型.     

A new approach in modelling undesirable output in DEA model

With an increasing attention on the environment, one of the major research thrusts in Data Envelopment Analysis (DEA) based performance evaluation is the undesirable output in the conventional DEA model. There is considerable research published on the undesirable aspects of production outputs. However, the economic implications and the suitability of the DEA models for incorporating the undesirable outputs are less carefully investigated and discussed. In this paper, a comparative study is conducted of typical eco-DEA models to illustrate this issue. We propose a ratio model to evaluate the undesirable as well as the desirable outputs simultaneously. We apply the specially developed model to investigate the impact of production pollutants while conducting the efficiency evaluation in the textile industry of China. The results reveal that the production output-oriented efficiency evaluation can be significantly altered once the environmental aspects are factored into the model.     

On the complexity of locating linear facilities in the plane

We consider the computational complexity of linear facility location problems in the plane, i.e., given n demand points, one wishes to find r lines so as to minimize a certain objective-function reflecting the need of the points to be close to the lines. It is shown that it is NP-hard to find r lines so as to minimize any isotone function of the distances between given points and their respective nearest lines. The proofs establish NP-hardness in the strong sense. The results also apply to the situation where the demand is represented by r lines and the facilities by n single points.     

A multiobjective optimization model for processing and distributing biosolids to reuse fields

Advanced wastewater treatment plants remove deleterious nutrients, chemicals, and microorganisms from wastewater and produce biosolids products to be reused at farms and other sites. These biosolids are carefully regulated by environmental restrictions but still may be malodorous to the local populations. In this paper, we develop a multiobjective optimization model to simultaneously minimize the biosolids odours as well as processing and distribution costs. The model employs a linear odour function and bilinear costs; the latter being approximated via Schur's decomposition and special ordered set (SOS) type 2 variables resulting in a mixed integer linear multiobjective optimization problem. Such a model can be used proactively by these plants to produce the least malodorous product at minimal costs. We demonstrate use of the model with a case study for the Blue Plains advanced wastewater treatment plant run by the DC Water and Sewer Authority in Washington, DC.     

A multiobjective optimization model for the waste management of the petrochemical industry

A multiobjective optimization model based on the goal programming approach is proposed in this paper to assist in the proper management of hazardous waste generated by the petrochemical industry. The analytic hierarchy process (AHP), a decision-making approach, incorporating qualitative and quantitative aspects of a problem, is incorporated in the model to prioritize the conflicting goals usually encountered when addressing the waste management problems of the petrochemical industry. The application of the model has been illustrated through a numerical example, using hypothetical but representative data.     

A multiobjective model of wholesaler-retailers' problem via genetic algorithm

In the existing literature, most of the purchasing models were developed only for retailers problem ignoring the constraint of storage capacity of retailers shop/showroom. In this paper, we have developed a deterministic model of wholesaler-retailers' problem of single product. The storage capacity of wholesaler's warehouse/showroom and retailers' showroom/shop are assumed to be finite. The items are transported from wholesaler's warehouse to retailers' Own Warehouse (OW) in a lot. The customer's demand is assumed to be displayed inventory level dependent. Demands are met from OW and that spaces of OW will immediately be filled by shifting the same amount from the Rented Warehouse (RW) till the RW is empty. The time duration between selling from OW and filling up its space by new ones from RW is negligible. According to relative size of the retailers' existing (own) warehouse capacity and the demand factors, different scenarios are identified. Our objectives are to optimize the cost functions of wholesaler and two retailers separately. To solve this problem, a real coded Genetic Algorithm (GA) with roulette wheel selection/reproduction, whole arithmetic crossover and non-uniform mutation is developed. Finally a numerical example is presented to illustrate the results for different scenarios. To compare the results of GA, Generalised Reduced Gradient Method has been used for the problem. Also, a sensitivity analysis has been performed to study the variations of the optimal average cost with respect to the different parameters.     

A multiobjective immune algorithm based on a multiple-affinity model

This paper presents a new multiobjective immune algorithm based on a multiple-affinity model inspired by immune system (MAM-MOIA). The multiple-affinity model builds the relationship model among main entities and concepts in multiobjective problems (MOPs) and multiobjective evolutionary algorithms (MOEAs), including feasible solution, variable space, objective space, Pareto-optimal set, ranking and crowding distance. In the model, immune operators including clonal proliferation, hypermutation and immune suppression are designed to proliferate superior antibodies and suppress the inferiors. MAM-MOIA is compared with NSGA-II, SPEA2 and NNIA in solving the ZDT and DTLZ standard test problems. The experimental study based on three performance metrics including coverage of two sets, convergence and spacing proves that MAM-MOIA is effective for solving MOPs.     

A short note on locating facilities on a path to minimize load range equity measure

This work considers the problem of locating \(p\) facilities on the nodes of a path such that the range of the weights assigned to facilities will be as small as possible. We present a polynomial progressive search algorithm to solve the problem.     

A subgradient method for multiobjective optimization

A method for solving quasiconvex nondifferentiable unconstrained multiobjective optimization problems is proposed in this paper. This method extends to the multiobjective case of the classical subgradient method for real-valued minimization. Assuming the basically componentwise quasiconvexity of the objective components, full convergence (to Pareto optimal points) of all the sequences produced by the method is established.     

A resolution method for multiobjective problems

A resolution method for multiobjective problems, based on a maximin criterion, is developed. Given the multiobjective problem Max_{Ax=b,x?0}{c_ix; i = 1,2,…,k}, we suppose that the decisor can construct, for each i, a function h_i:$\text{R}$ → $\text{R}$ (or h_i:$\text{R}$ⁿ→-$\text{R}$), such that h_i(c_i,x) is his satisfaction degree produced by the value c_ix, and we substitute the original problem by Max_{Ax=b,x?0～min_i{h_i(c_ix)}. We analize its resolution and basic properties.     

A weighting subgradient algorithm for multiobjective optimization

We propose a weighting subgradient algorithm for solving multiobjective minimization problems on a nonempty closed convex subset of an Euclidean space. This method combines weighting technique and the classical projected subgradient method, using a divergent series steplength rule. Under the assumption of convexity, we show that the sequence generated by this method converges to a Pareto optimal point of the problem. Some numerical results are presented.     

A class of multiobjective linear programming model with fuzzy random coefficients

The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.