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LIOP1  
Overview  
LIOP1 software system is designed to find optimal (minimal or maximal) solutions of linear and linear integer problems. The objective function (the function to be optimized) and the constraints of such problems are described by linear functions. Depending on the variables type, the linear optimization problems are known under different names and abbreviations. In linear optimization (LP) problems all the variables are continuous. In mixed integer (MILP or MIP) problems only some of the variables must accept integer values, while completely integer (ILP or IP) problems require all the variables to be integer. The binary problems (01IĐ) contain variables that can accept two values only: 0 or 1. These problems are widespread because many types of combinatorial problems and problems with logical constraints can be formulated with the help of binary variables. LIOP1 software system includes two types of simplex methods for linear optimization and a branch and bound algorithm for linear integer optimization. 

Application  
LIOP1 software system is a system of general purpose and unlike some specialized software systems it can be used for solving different problems in the area of planning, design and control of the activity of separate companies, organizations and institutions, which are formulated as linear and linearinteger problems. Particular attention is paid to the problems for expenses reducing; for optimization of schedules, prescriptions and technologies; for improving the materials supply and the power consumed, etc. 

Publications  
1. Vassileva, M., Staikov, B., Vassilev, V. (2005). Linear and Linear Integer Programming Software System. In: Proceedings of International Conference “Automatics and Informatics’05” (V. Sgurev and K. Boyanov, Eds.). Sofia, pp. 3134. 

Developers  
LIOP1 software system is designed in Decision Support Systems department of the Institute of Information Technologies by the team: V. Vassilev – team leader, B. Staykov, K. Genova, M. Vassileva and F. Andonov. 

Gallery  
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