Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm

• Published in: European journal of operational research Vol. 16; no. 3; pp. 345 - 357
• Main Authors: Seppälä, Yrjö, Orpana, Tuomo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.1984; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Linear programming; Mathematical models; Problem solving; Random variables; Simplex method
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/0377-2217(84)90289-3

The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method. According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10 −5 –10 −6). The algorithm converges linearly and its asymptotic error constant is 1 4 .