Multiple Objective Linear Programming Research Articles

Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case

This work addresses the correction and improvement of Mavrotas and Diakoulaki's branch and bound algorithm for mixed 0-1 multiple objective linear programs. We first elaborate the issues encountered by the original algorithm and then propose a corrected version for the biobjective case using an exact representation of the nondominated set associated with an appropriate update procedure. Then we introduce several improvements using better bound sets and branching strategies and finally present some experiments to study the effectiveness of our propositions.

Evolving the latent variable model as an environmental DEA technology

This article tests several nonparametric DEA models for their ability to accurately decompose CO2 emissions change using a Malmquist styled decomposition framework. This production oriented activity analysis involves panel data and two data sets from the literature for comparison. A new Latent Variable radial input-oriented technology is introduced that is closely associated with a Koopmans Efficient Slacks Based Model. The Latent Variable technology simultaneously reduces inputs and undesirable outputs in a single Multiple Objective Linear Program. This production theoretic methodology is adapted to preserve both scale efficiency and causality within the envelopment framework. Finally, the application studies demonstrate the internal consistency of the Latent Variable reduction coefficients, which overturns previous results and paves the way for further research into undesirable externalities.

A multi-objective decision-making model to select waste electrical and electronic equipment transportation media

Electrical and electronic equipment (EEE) materials possess considerable economic value, together with potential toxicity. The rapidly increasing sales of EEE worldwide, constitutes the rational management of waste electrical and electronic equipment (WEEE) a matter of critical importance, both in economic and environmental terms. Taking into account that reverse logistics is one of the most important parameters in the management of waste equipment, it is particularly important for the manufacturers to control relevant cost in order to be market competitive. One of the most critical decisions regarding reverse logistics costs is the type of carrier to be used. To this end, this paper presents a multicriteria optimisation model for multi-type carriers of WEEE, based on multiple objective linear programming (MOLP). The main goal of a MOLP model is the weighted optimisation of different objectives. In our case, the proposed MOLP approach minimises total logistics costs, consumption of fossil fuel and production of emissions due to transportation of WEEE with the use of different types of containers. The model embodies existing infrastructure in collection points and recycling facilities and targets towards optimisation of the reverse logistics network for a single planning period by taking into account both economic and environmental aspects of the problem under study.

An Improvement on STEM Method in Multi-Criteria Analysis

Multi-criteria decision making (MCDM) refers to making decision in the presence of multiple and conflicting criteria. Multiob- jective programming method such as multiple objective linear program- ming (MOLP) are techniques used to solve such multiple criteria deci- sion making (MCDM) problems. One of the first interactive procedures to solve MOLP is step method (STEM). In this paper we try to improve STEM method by introducing the weight vector of objectives which emphasize that more important objectives be more closer to ideal one. Therefore the presented method try to increase the rate of satisfactoriness of the obtained solution. Finally, a numerical example for illustration of the new method is given to clarify the main results developed in this paper.

NEW APPROACHES FOR RESOURCE ALLOCATION VIA DEA MODELS

This paper focuses on the problem of resource allocation through data envelopment analysis. We propose three integrated models for allocating resources. The first model aims at minimizing the input consumption, the second one aims at maximizing the total outputs within the current resources, and the last one aims at maximizing the total outputs using the predicted resources in the next production season. Since the number of inputs or outputs is usually more than one, the abovementioned issue is often a multiple objective linear programming (MOLP) problem. Through the proportion of inputs (outputs) of new decision making unit (DMU) to the total inputs (outputs) of all old DMUs, we transform the MOLP problem into a single objective linear programming model. We assume that decision maker must ensure that the expected outputs of each DMU after allocation in the next production season are not less than this production season. All these proposed models have the same advantage that the results gained from the models are Pareto efficient. A numerical example of 25 supermarkets is used to illustrate our proposed approach.

An Interactive Procedure to Solve Multi‐Objective Decision‐Making Problem: An Improvment to STEM Method

Decisions in the real‐world contexts are often made in the presence of multiple, conflicting, and incommensurate criteria. Multiobjective programming methods such as multiple objective linear programming (MOLP) are techniques used to solve such multiple‐criteria decision‐making (MCDM) problems. One of the first interactive procedures to solve MOLP is STEM method. In this paper we try to improve STEM method in a way that we search a point in reduced feasible region whose criterion vector is closest to positive ideal criterion vector and furthest to negative ideal criterion vector. Therefore the presented method tries to increase the rate of satisfactoriness of the obtained solution. Finally, a numerical example for illustration of the new method is given to clarify the main results developed in this paper.

Capital markets, corporate governance and capital budgeting: Implications for firm value

The conventional discounting capital budgeting techniques have been widely criticized for being inappropriate in incorporating multi-criteria interactions and for focusing on one-off single objective of maximizing net present value. This paper modifies a Multiple Objective Linear Programming (MOLP) optimization model of Levary and Seitz (1990). It adds to the objective function the mitigation of agency costs as a proxy of good corporate governance principles and capital market interactions. The goal of the study is to examine the impact of agency costs on the present value of a long term capital project and investment appraisal decision making in the airline industry to support better capital investment decision making in the future. Recent collapses of high profile companies in airline industry and other industries such as Flyglobespan Airline (in the year 2009) in Scotland, Ansett Airline (in the year 2001)in Australia, Enron(in the year 2001)and Lehman Brothers (in 2008)in the U.S whose impact is still being experienced today provide us with evidence of how important the minimization of agency costs is for the survival and success of organisations and the huge amounts involved as a result of poor corporate governance. The results reveal that debt financing which is often provided by capital markets plays an influential role in shaping the investment appraisal decisions through interest rates and debt covenants embedded in the debt contracts. The results show that mitigation of agency costs improves the firm’s cash flow, financial management and corporate governance. It discourages illegal earnings management practices, enhances investment decisions, investors’ confidence and reliability in the firm’s investment decisions and hence enhances the firm value.

Finding common weights based on the DM's preference information

Data Envelopment Analysis (DEA) is basically a linear programming-based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach that we term as ‘preference common weights’, which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce a multiple objective linear programming model in which objective functions are input/output variables subject to the constraints similar to the equations that define production possibility set of standard DEA models. Then by using the Zionts–Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.

Technical and economic analysis of electricity generation from forest, fossil, and wood-waste fuels in a Finnish heating plant

The Finnish energy industry is subject to policy decisions regarding renewable energy production and energy efficiency. Conventional electricity generation has environmental side-effects that may cause global warming. Renewable fuels are superior because they offer near-zero net emissions. In this study, I investigated a heating mill’s ability to generate electricity from forest fuels in southern Finland on a 1-year strategic decision-making horizon. I solved the electricity generation problem using optimization of the energy products and fuel mixtures based on energy efficiency and forest technology. The decision environment was complicated by the sequence-dependent procurement chains for forest fuels. The optimal product and fuel mixtures were selected by minimizing procurement costs, maximizing production revenues, and minimizing energy losses. The combinatorial complexity of the problem required the use of adaptive techniques to solve a multiple-objective linear programming system with industrial relevance. I discuss the properties of the decision-support system and methodology and illustrate pricing of electricity generation based on real industrial data. The electricity-generation, -purchase, and -sales decisions are made based on a comprehensive technical and economic analysis that accounts for procurement of local forest fuels in a holistic supply chain model.

A Note on Solvability Conditions for Multiple Objectives Linear Programming (MOLP) Problems

This paper investigates the advantages of using a simple linear programming problem with one unknown to show that whether the given multiple objectives linear programming (MOLP) problems is solvable or not. This kind of investigation is based mainly on both of feasibility and efficiency characterization of the (MOLP) problem. Our goal of this investigation is to help the analyst of better understanding of the nature and the theory of the given problem under consideration. Some illustrative examples is given to clarify this investigation study.

SENSITIVITY ANALYSIS OF WEAK EFFICIENCY IN MULTIPLE OBJECTIVE LINEAR PROGRAMMING

This paper, studies the sensitivity analysis of weakly efficient extreme solutions in multiple objective linear programming (MOLP). The aim of the paper is to compute the set of the parameters (corresponding to one coefficient) for which a given extreme point is a weakly efficient solution. We also focus on the properties of the parameters set by proving convexity and closeness of this set. Moreover, we compare the results of the sensitivity analysis of efficiency and of weak efficiency in MOLP.

A New Link Between Output-oriented BCC Model with Fuzzy Data in the Present of Undesirable Outputs and MOLP

In recent years, the relation between data envelopment analysis and multiple objective linear programming has received a great deal of attention from researchers. However, there are two difficulties in doing an objective evaluation of the performance of decision making units. The first one is how to treat undesirable factors jointly produced with the desirable factors and the second one is how to treat with imprecise data. In this paper, we establish an equivalence relation between multiple objective linear programming and the output-oriented Banker, Charnes, Cooper(BCC) model in the present of undesirable factors and fuzzy data such that the decision maker's preference can be taken into account in an interactive fashion for finding target unit.

A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming

Outcome space methods construct the set of nondominated points in the objective (outcome) space of a multiple objective linear programme. In this paper, we employ results from geometric duality the...

On duality in multiple objective linear programming

In this paper we present two approaches to duality in multiple objective linear programming. The first approach is based on a duality relation between maximal elements of a set and minimal elements of its complement. It offers a general duality scheme which unifies a number of known dual constructions and improves several existing duality relations. The second approach utilizes polarity between a convex polyhedral set and the epigraph of its support function. It leads to a parametric dual problem and yields strong duality relations, including those of geometric duality.

Global supplier selection and order allocation using FQFD and MOLP

This paper proposes an integrated model of Fuzzy Quality Function Deployment (FQFD) and Multiple Objective Linear Programming (MOLP) for supplier selection and order allocation in global context. Various criteria for global supplier selection are explored through literature review and divided into two categories: buyer attributes and supplier attributes. Some of the criteria for supplier selection incorporated in this paper are very important in global context, which is generally ignored in local supplier selection such as geographical location, money exchange rate and terrorism. The fuzzy-extended Quality Function Deployment (QFD) helps to incorporate the uncertainty in thinking state of decision-makers in establishing the correlation between buyer attributes and supplier attributes and also in supplier rating against various supplier attributes. This paper may help the supply chain managers/purchasing managers in supplier selection in global market and allocate the order among them considering all the constraints under fuzzy environment.

Sensitivity analysis on the priority of the objective functions in lexicographic multiple objective linear programs

This paper deals with a class of multiple objective linear programs (MOLP) called lexicographic multiple objective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems.

Equivalence relationship between the general combined-oriented CCR model and the weighted minimax MOLP formulation

In many applications, finding target unit is required, particularly when decision maker (DM) wants to search along the efficient frontier to locate the most preferred solution. Wong et al. [Wong, Y.H., Luque, M., Yang, J.B., 2009. Using interactive multiple objective methods to solve DEA problem with value judgments. Computers and Operations Research 36, 623–636] established an equivalence model between output-oriented dual DEA models and multiple objective linear programming (MOLP). In a similar vein, the aim of this paper is to establish an equivalence model between the general combined-oriented CCR model and multiple objective linear programming and also using Zionts–Wallenius’s method to integrate combined-oriented CCR performance assessment and target setting such that the DM’s preference can be taken into account in an interactive fashion. Our proposed model gives the most preferred solution for DM with trade off analysis on both input and output values of DMUs. The applicability of the proposed equivalence model is illustrated, using a real data set as a case study, which consists of 20 bank branches.

Finding DEA-efficient hyperplanes using MOLP efficient faces

This paper suggests a method for finding efficient hyperplanes with variable returns to scale the technology in data envelopment analysis (DEA) by using the multiple objective linear programming (MOLP) structure. By presenting an MOLP problem for finding the gradient of efficient hyperplanes, We characterize the efficient faces. Thus, without finding the extreme efficient points of the MOLP problem and only by identifying the efficient faces of the MOLP problem, we characterize the efficient hyperplanes which make up the DEA efficient frontier. Finally, we provide an algorithm for finding the efficient supporting hyperplanes and efficient defining hyperplanes, which uses only one linear programming problem.

Target setting in data envelopment analysis using MOLP

Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods.

Independent, convergent, and divergent decision behaviour for interactive multiple objectives linear programming

An interactive paired comparison approach for multiple objective linear programming (MOLP) problems is developed where the Decision Maker's preferential behaviour is presented by a utility function. The preferential behaviour can be independent, convergent, or divergent; which are mathematically presented by additive, quasi-concave, or quasi-convex utility functions respectively. The approach to find the best alternative consists of four phases: I. An additive utility function. II. A quasi-concave utility function. III. A quasi-convex utility function. IV. A feasible goal utility function. In the first three phases a paired comparison of alternatives are used and in Phase IV a feasible goal method is developed that finds the closest feasible efficient point for a given goal by the decision maker. This method also identifies resources required to make a given goal feasible. The approach can be extended to solve multiple objective integer/nonlinear optimization problems. Some experiments and examples are provided.