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  Uncertain random goal programming# QIN Zhongfeng* 5 10 15 20 25 30 35 40 (School of Economics and Management, Beihang University) Abstract: Goal programming provides an efficient technique to deal with decision making problems with multiple conflicting objectives. This paper aims to provide a new goal programming called uncertain random goal programming to model the multiobjective programming involving uncertain random variables. Some equivalent deterministic forms are derived on the condition that the set of parameters consist of uncertain variables and random variables. Finally, an example is given to illustrate the applications of these approaches. Key words: Goal programming; Uncertainty theory; Uncertain random variable; Uncertain random programming. 0 Introduction Goal programming was introduced by Charnes and Cooper [1], and subsequently developed by Ijiri [2] to efficiently solve multiobjective programming. It is essentially a compromise method by ordering or weighing the unwanted deviations with a number of priority levels. Since then, goal programming has been widely employed in many and diverse fields since its simplicity and ease of use. Considering that the parameters in the practical problem are always nondeterministic, goal programming with incomplete information is introduced and widely investigated. Contini [3] first studied the goal programming with random parameters. Retzlaff-Roberts [4] applied the goal programming method to solve a stochastic allocative data envelopment analysis. Ballestero [5] proposed a stochastic goal programming model leading to a structure of mean-variance minimization. Liu [6] provided a theoretical framework of the third type of stochastic programming named dependent-chance goal programming. For the case lack of historical data, model parameters are often estimated by experienced experts. These parameters are always regarded as fuzzy variables. Tiwari et al. [7] first introduced fuzzy goal programming. Liu [8] prov