Stochastic Generalized Transportation Problem with discrete distribution of demand
Selected contents from this journal
Languages of publication
The generalized transportation problem (GTP) allows us to model situations where the amount of goods leaving the supply points is not equal to the amount delivered to the destinations (this is the case, e.g. when fragile or perishable goods are transported or complaints may occur). A model of GTP with random, discretely distributed, demand has been presented. Each problem of this type can be transformed either into the form of a convex programming problem with a piecewise linear objective function, or a mixed integer LP problem. The method of solution presented uses ideas applied in the method of stepwise analysis of variables and in the equalization method.
- AHUJA R.K., MAGNANTI T.L., ORLIN J.B., Network Flows. Theory, Algorithms and Applications, Prentice Hall, New York 1993.
- ANHOLCER M., Convergence of the equalization method for nonlinear allocation problems), [in:] Works of the Chair of Operations Research, K. Piasecki, W. Sikora (Eds.), Scientific Papers of the University of Economics in Poznań, 2005, 64, 183–198 (in Polish).
- ANHOLCER M., A Comparative analysis of selected algorithms for nonlinear problems of allocating uniform goods, Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań 2008 (in Polish).
- ANHOLCER M., A Comparison of the performance of selected algorithms for nonlinear allocation problems, [in:] Methods and Application of Operations Research, R. Kopańska-Bródka (Ed.), Scientific Papers of University of Economics in Katowice, Katowice 2008, 9–25 (in Polish).
- ANHOLCER M., Algorithm for stochastic generalized transportation problem, Operations Research and Decisions, 2012 (4), 9–20.
- ANHOLCER M., On the nonlinear generalized transportation problem, preprint.
- ANHOLCER M., KAWA A., Optimization of supply chain via reduction of complaints ratio, Lecture Notes in Computer Science, 2012, 7327, 622–628.
- BALAS E., The dual method for the generalized transportation problem, Management Science, Series A, Sciences, 1966, 12 (7), 555–568.
- BALAS E., IVANESCU P.L., On the generalized transportation problem, Management Science, Series A, Sciences, 1964, 11 (1), 188–202.
- BAZARAA M.S., JARVIS J.J., SHERALI H.D., Linear Programming and Network Flows, 4th Ed., Wiley, New York 2010.
- BAZARAA M.S., SHERALI H.D., SHETTY C.M., Nonlinear Programing. Theory and Algorithms, 3rd Ed., Wiley, New York 2006.
- GLOVER F., KLINGMAN D., NAPIER A., Basic dual feasible solutions for a class of generalized networks, Operations Research, 1972, 20 (1), 126–136.
- GOLDBERG A.V., PLOTKIN S.A., TARDOS E., Combinatorial algorithms for the generalized circulation problem, SFCS ’88, Proceedings of the 29th Annual Symposium on Foundations of Computer Science, 1988, 432–443.
- HOLMBERG K., Efficient decomposition and linearization methods for the stochastic transportation problem, Computational Optimization and Applications, 1995, 4, 293–316.
- HOLMBERG K., JÖRNSTEN K., Cross decomposition applied to the stochastic transportation problem, European Journal of Operational Research, 1984, 17, 361–368.
- HOLMBERG K., TUY H., A production-transportation problem with stochastic demand and concave production costs, Mathematical Programming, 1999, 85, 157–179.
- LOURIE J.R., Topology and computation of the generalized transportation problem, Management Science, Series A, Sciences, 1964, 11 (1), 177–187.
- NAGURNEY A., YU M., MASOUMI A.H., NAGURNEY L.S., Networks Against Time. Supply Chain Analytics for Perishable Products, Springer Briefs in Optimization, Springer, New York 2013.
- PANDIAN P., ANURADHA D., Floating point method for solving transportation problems with additional constraints, International Mathematical Forum, 2011, 6 (40), 1983–1992.
- QI L., Forest iteration method for stochastic transportation problem, Mathematical Programming Study, 1985, 25, 142–163.
- QI L., The A-forest iteration method for the stochastic generalized transportation problem, Mathematics of Operations Research, 1987, 12 (1), 1–21.
- SIKORA W., Transportation problem with random demand, Przegląd Statystyczny, 1993, 39 (3–4), 351–364 (in Polish).
- SIKORA W., Models and methods for the optimal distribution of goods, Scientific Papers of the University of Economics in Poznań, Ser. II, Theses, Poznań 1993 (in Polish).
- SIKORA W., RUNKA H., PYRZYŃSKI D., Optimization of flows in the area of the distribution of uniform goods, Grant No. H\12\209\90-2, University of Economics in Poznań, Poznań 1991 (in Polish).
- WAYNE K.D., A polynomial combinatorial algorithm for generalized minimum cost flow, Mathematics of Operations Research, 2002, 27 (3), 445–459.
Publication order reference