A METHOD FOR SOLVING THE CANONICAL PROBLEM OF TRANSPORT LOGISTICS IN CONDITIONS OF UNCERTAINTY
DOI:
https://doi.org/10.30837/ITSSI.2021.16.080Keywords:
transport linear programming problem, random cost of transportation, fractional nonlinear optimizationAbstract
Subject.The canonical task of transport logistics in the distributed system "suppliers - consumers" is considered. Goal. Development of an accurate algorithm for solving this problem according to the probabilistic criterion in the assumption of the random nature of transportation costs has been done. Tasks. 1. Development of an exact method for solving the problem of finding a plan that minimizes the total cost of transportation in conditions when their costs are given by their distribution densities. 2. Development of a method for solving the problem when the distribution density of the cost of transportation is not known. Methods. A computational scheme for solving the problem is proposed, which is implemented by an iterative procedure for sequential improvement of the transportation plan. The convergence of this procedure is proved. In order to accelerate the convergence of the computational procedure to the exact solution, an alternative method is proposed based on the solution of a nontrivial problem of fractional nonlinear programming. The method reduces the original complex problem to solving a sequence of simpler problems. The original problem is supplemented by considering a situation that is important for practice when, in the conditions of a small sample of initial data, there is no possibility of obtaining adequate analytical descriptions for the distribution densities of the random costs of transportation. To solve the problem in this case, a minimax method is proposed for finding the best transportation plan in the most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, the modern mathematical apparatus of continuous linear programming was used. Results. A mathematical model and a method for solving the problem of transport logistics in conditions of uncertainty of the initial data are proposed. The desired plan is achieved using the solution of the fractional nonlinear programming problem. Conclusions: The problem of forming a transportation plan is considered, provided that their costs are random values. Also, a method for solving the problem of optimization of transportation for a situation where the density of distribution of random cost cannot be correctly determined is considered.
References
Birman, I. Ya. (1962), Transport Problem of Linear Programming [Transportnaya zadacha lineynogo programmirovaniya], Moscow : Ed. eq. lit., 262 p.
Nesterov, E. P. (1962), Transport Problem of Linear Programming [Transportnaya zadacha lineynogo programmirovaniya], Moscow : Ed. Ministry of Railways, 189 p.
Yudin, D. B., Golstein, E. G. (1969), Transport-type linear programming problems [Zadachi lineynogo programmirovaniya transportnogo tipa], Moscow : "Sov. radio", 382 p.
Chumakov, V. B. (2006), "Solving the problems of organizing road transport in the context of the uncertainty of the state of regional transport systems" ["Resheniye zadach organizatsii avtomobil'nykh perevozok v usloviyakh neopredelennosti sostoyaniya regional'nykh transportnykh sistem"], Novocherkassk : SKSTU, P. 22–26.
Malakhov, V. P., Kondratenko, G. V. (2002), "Simulation models and algorithms for forming routes and trajectories based on fuzzy logic" ["Imitatsiyni modeli ta alhorytmy formuvannya marshrutiv i trayektoriy na osnovi nechitkoyi lohiky"], Proceedings of the OPU, Issue 1 (17), P. 1–10.
Ryan, G. (2005), "Rosandich. Quantification on Uncertainty in Transportation Infrastructure Projects", Santiago: Economics planning, P. 5–14.
Borisova, E. A., Finaev, V. I. (2006), "Triaxial distribution problem with fuzzy parameters" ["Triaksial'naya raspredelitel'naya zadacha s nechetkimi parametrami"], Izvestia TRTU, Issue "Intelligent CAD", No. 8, P. 17–21.
Borisova, E. A., Finaev, V. I. (2007), Three-index distribution problems with fuzzy parameters [Trekhindeksnyye raspredelitel'nyye zadachi s nechetkimi parametrami], Taganrog : TTI SFU, 190 p.
Ermoliev, Yu. M. (1976), Stochastic programming methods [Metody stokhasticheskogo programmirovaniya], Moscow : Nauka, 239 p.
Kaplinsky, A. I., Poznyak, A. S., Propoy, A. I. (1971), "On some methods for solving stochastic programming problems" ["O nekotorykh metodakh resheniya zadach stokhasticheskogo programmirovaniya"], Automation and Remote Control, No. 10, P. 87–94.
Porotsky, S. M. (1977), "Stochastic problems of transport type" ["Stokhasticheskiye zadachi transportnogo tipa"], Izv. Academy of Sciences of the USSR. Tech. Cybernetics, No. 6, P. 34–39.
Yudin, D. B., Yudin, A. D. (2009), Extreme models in economics [Ekstremal'nyye modeli v ekonomike], Moscow : LIBROKOM, 312 p.
Yudin, D. B. (1979), Problems and methods of stochastic programming [Zadachi i metody stokhasticheskogo programmirovaniya], Moscow : "Sov. radio ", 385 p.
Seraya, O. V. Multidimensional models of logistics in conditions of uncertainty [Mnogomernyye modeli logistiki v usloviyakh neopredelennosti], Kharkiv : VOP Stetsenko, 512 p.
Raskin, L. G., Kirichenko, I. O. (2005), Continuous linear programming [Kontinual'noye lineynoye prgrammirovaniye], Kharkiv : VIVV, 175 p.
Zadeh, L. (1965), "Fuzzy Sets", Information and Control, Vol. 8, P. 338–353.
Dubois, D., Prade, A. (1990), Theory of Opportunities. Application to the representation of knowledge in computer science [Teoriya vozmozhnostey. Prilozheniye k predstavleniyu znaniy v informatike] : Per. from French, Moscow : Radio and communication, 286 p.
Raskin, L. G., Gray, O. V. (2008), Fuzzy mathematics [Nechetkaya matematika], Kharkiv : Parus, 352 p.
Pawlak, Z. (1982), "Rough sets", International Journal of Information and Computer Sciences, Vol. 11, No. 5, P. 341–356.
Pawlak, Z. (1991), Rough Sets: Theoretical Aspects of Reasoning about Data, Dordrecht : Kluwer Academic Publisher, 284 p.
Raskin, L., Sira, O. (2016), "Method of solving fuzzy problems of mathematical programming", Eastern–european journal of enterprise technologies, Vol. 5, No. 4 (83). DOI: http://dx.doi.org/10.15587/1729–4061.2016.81292
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