GESJ: Computer Science and Telecommunications 2014|No.3(43) ISSN 1512-1232 42 On Multicriteria Algorithm for Specific Problem of Scheduling Theory Liana Lortkipanidze 1 , Nana Odishelidze 1 , Ketevan Kuthashvili 2 , Liana Karalashvili 2 1 Computer Science Department, Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, 0143, Georgia 2 School of Information Technologies, Engineering and Mathematics, The University of Georgia, 0171, Georgia Abstract One of the areas of discrete optimization problem - the scheduling theory is considered. As it is known, the problems of scheduling theory are of NP difficulty and only in the certain cases it has been managed to construct the algorithm of polynomial difficulty. In the paper it is considered the problem for which the set of additional resources and partially ordered set are empty. Under such conditions the effective algorithm is constructed to order the sequence of tasks. The schedule length and maximal price of tasks’ implementation are considered as the measure of the algorithm effectiveness. The constructed algorithm takes into account the construction of tasks implementation schedule. It is possible to construct such schedule, which gives Pareto- optimal solution for both criteria. Keywords: scheduling theory, multicriteria optimization, Pareto-optimal solution. 1. Introduction Many practical problems, for instance, transport or management and running of industry process, under conditions of fixed resources require scheduling of tasks at a time. The given system of tasks must be implemented by certain set of resources or by means /devices of services. In terms of tasks system and the given properties of resources with certain restrictions to them we have to construct an efficient algorithm of the task implementation sequence, which gives possibility to attain efficiency by certain measure of optimum. Under measure of optimum there may be considered scheduling length in terms of time, average time of being in the tasks system or maximum cost of the system. As it is known, schedule such problems is of NP difficulty [5,37] and requires great deal of applications of the modern applied mathematics. Basically difficulty is caused by great volume of tasks. In such situations, to receive best decisions, new methods are creating and practical recommendations of planning and control are producing. [13,30,39], [5]. Because of above-mentioned, for the certain problem it is actual to construct comparatively accurate mathematical model and create such algorithms, which totally will use the specific character of the problem and give possibility of the optimal decision in polynomial time. In this paper, on the basis of schedule theory common methods, the mathematical model and algorithm are constructed, for which task implementation is possible by single-step multiprocessor system, where processors are mutually half-interchangeable, but set of additional resources and partially ordered set are empty.