A review of Goal Programming and its applications

This paper presents a review of the current literature on the branch of multi-criteria decision modelling known as Goal Programming (GP). The result of our indepth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Some guidelines to the scope of GP as an application tool are given and methods of determining which problem areas are best suited to the different GP approaches are proposed. The correlation between the method of assigning weights and priorities and the standard of the results is also ascertained.     

Serial correlation estimation through the imprecise Goal Programming model

The Goal Programming (GP) model was used as a time-series analysis tool that incorporates a Serial Correlation where the dependent variable is considered as precise. This formulation does not take into consideration the decision-maker’s preferences. However, the dependent variable can be imprecise and its value can be expressed through an interval. The aim of this paper is to develop a new formulation of the GP model for regression with Serial Correlation where the dependent variable is imprecise. The proposed model will also integrate explicitly the decision-maker’s preferences. A numerical example was used to illustrate our model.     

A parallel multiple reference point approach for multi-objective optimization

This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper.     

A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions

Stochastic multicriteria acceptability analysis using achievement functions (SMAA-A) is a preference model for discrete-choice decision making that inverts the traditional goal programming process by asking what combinations of aspirations are necessary to make each alternative the preferred one, rather than what alternative is preferred given a set of aspirations. In this paper, we test the ability of the model to discern good-performing alternatives from poorly-performing ones using a simulation study. Simulation results show that a suitably detailed construction of the acceptability index is particularly important, and that the resulting model can be fruitfully applied in the selection of a shortlist of alternatives from a larger set with only very limited decision maker involvement.     

具有独立子块的大系统目标规划问题的解法

分解之后如何进行协调解决大系统规划问题的关键．本文通过利用子系统目标值所提供的信息进行大系统分解之后的协调，并提出了求解具有独立子块的大系统规划问题的串式调优法，同时研究了有关原问题和各子问题最优解的性质．     

Goal programming sensitivity analysis using interval penalty weights

This paper presents an application of the vector-maximum research [4–8] to the sensitivity analysis of goal programming problems as several of the criterion function penalty weights are simultaneously and independently varied. A generalized goal programming capability is presented and a six-stage analytic procedure is described. The problem is generalized in the sense that the regular goal programming penalty weights can be expanded to intervals if desired. The solution procedure is new in that it depends upon an algorithm for the vector-maximum problem, criterion cone contraction procedures, and filtering techniques. Together they are able to generate and process all extreme points on the portion of the surface of the goal programming augmented feasible region corresponding to the interval penalty weights specified. In effect, the procedure and adapted algorithm of this paper delivers to goal programming an operational power of sensitivity analysis not previously available to users. A numerical example is provided in order to illustrate the computerized application of the total goal programming procedure outlined.     

An exact method for computing the nadir values in multiple objective linear programming

In this paper we propose a new method to determine the exact nadir (minimum) criterion values over the efficient set in multiple objective linear programming (MOLP). The basic idea of the method is to determine, for each criterion, the region of the weight space associated with the efficient solutions that have a value in that criterion below the minimum already known (by default, the minimum in the payoff table). If this region is empty, the nadir value has been found. Otherwise, a new efficient solution is computed using a weight vector picked from the delimited region and a new iteration is performed. The method is able to find the nadir values in MOLP problems with any number of objective functions, although the computational effort increases significantly with the number of objectives. Computational experiments are described and discussed, comparing two slightly different versions of the method.     

A multiple criteria decision making approach to manure management systems in the Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers’ conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems.     

具有分数形式的随机目标规划在金属模型中的应用

本文主要应用了Enrique Ballestero提出的一个新的随机目标规划框架，采用了幂效用函数和双曲绝对风险厌恶，以资产组合选择问题为背景，构造了两个具有分数形式目标函数的随机目标规划模型，给出了解法，并讨论了解的经济意义。本文的随机目标规划产生了一种相对风险极小的有效解，为决策提供了一种新的方案选择途径。     

A practical weight sensitivity algorithm for goal and multiple objective programming

This paper presents a weight sensitivity algorithm that can be used to investigate a portion of weight space of interest to the decision maker in a goal or multiple objective programme. The preferential information required from the decision maker is an initial estimate of their starting solution, with an equal weights solution being used as a default if this is not available, and preference information that will define the portion of weight space on which the sensitivity analysis is to be conducted. The different types of preferential information and how they are incorporated by the algorithm are discussed. The output of the algorithm is a set of distinct solutions that characterise the portion of weight space searched. The possible different output requirements of decision makers are detailed in the context of the algorithm.The methodology is demonstrated on two examples, one hypothetical and the other relating to predicting cinema-going behaviour. Conclusions and avenues for future research are given.     

A primal interior point method for the linear semidefinite programming problem

The linear semidefinite programming problem is examined. A primal interior point method is proposed to solve this problem. It extends the barrier-projection method used for linear programs. The basic properties of the proposed method are discussed, and its local convergence is proved.     

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.     

A new efficient short-step projective interior point method for linear programming

In this paper, we are interested in the performance of Karmarkar’s projective algorithm for linear programming. We propose a new displacement step to accelerate and improve the convergence of this algorithm. This purpose is confirmed by numerical experimentations showing the efficiency and the robustness of the obtained algorithm over Schrijver’s one for small problem dimensions.     

Goal programming model for grocery shelf space allocation

The highly competitive grocery retail industry has annual sales of roughly half a trillion dollars in the US. While gross margins average about 28% of sales, net profits after taxes are only 1% industry-wide, causing retailers to continually search for operational improvements that increase profitability and improve customer service. One important decision that affects both of these goals is how to allocate shelf space to different products.     

Satisfactory solution concepts and their relations for Stochastic Multiobjective Programming problems

This work deals with the concept of satisfactory solution for Stochastic Multiobjective Programming (SMP) problems. Based on previous literature, we will introduce different concepts of satisfactory solutions for SMP problems, define a new concept of solution (where the decision maker (DM) sets his/her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels), and establish some relationship between these concepts. The results will aim at featuring these concepts and determine the differences between them. Moreover, the paper proposes a new step by step procedure to exchange information between the analyst and DM prior to solving the problem. Thus, the DM will be able to choose the transformation criterion for each stochastic objective and the aspiration level.     

ISTMO: An interval reference point-based method for stochastic multiobjective programming problems

In this paper, we present an interactive algorithm (ISTMO) for stochastic multiobjective problems with continuous random variables. This method combines the concept of probability efficiency for stochastic problems with the reference point philosophy for deterministic multiobjective problems. The decision maker expresses her/his references by dividing the variation range of each objective into intervals, and by setting the desired probability for each objective to achieve values belonging to each interval. These intervals may also be redefined during the process. This interactive procedure helps the decision maker to understand the stochastic nature of the problem, to discover the risk level (s)he is willing to assume for each objective, and to learn about the trade-offs among the objectives.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

Goal programming in the context of the assignment problem and a computationally effective solution method

This paper develops the goal programming technique to solve the multiple objective assignment problem. The required model is formulated and an appropriate solution method is presented. The proposed method, which is a decomposition method, exploits the total unimodularity feature of the assignment problem and effectively reduces the computational efforts. Some issues related to the efficiency of a GP solution are stated and some specialized techniques for detecting and restoring efficiency are proposed.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Multiattribute preference models with reference points

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the induced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature, most notably models based on concordance and models based on a discrete Sugeno integral.