The Nonlinear Generalized Transportation Problem with convex costs

Abstract

Abstract. We investigate the Nonlinear Generalized Transportation Problem (NGTP), where the transportation costs and the costs that depend on the amount of good delivered to the destination points are strictly convex functions. The amounts of goods change during the transportation process. This model may correspond, for example, with a congested network where the time costs are involved. First, we present the NGTIP model, then provide a method of solving the problems of this type and then we prove convergence of the method. The numerical experiments prove the effectiveness of the presented algorithm.

Bi-criteria stochastic generalized transportation roblem: expected cost and risk minimization

“…In those papers the Equalization Method was considered and it was proved to be convergent in Anholcer (2005Anholcer ( , 2008a. The convergence of the general versions for the Nonlinear and Stochastic GTP was also proved by Anholcer (2012Anholcer ( , 2015.…”

“…In this approach we remove the demand constraints and use them to introduce a new cost function, including the expected extra cost, increasing with the discrepancy between the actual value of the demand and the size of delivery. This approach has been used in such classic papers as Williams (1963), Cooper and LeBlanc (1977), but also in more recent ones, such as Holmberg and Jörnsten (1984), Holmberg (1995), Qi (1985Qi ( , 1987 and Anholcer (2012Anholcer ( , 2015. It is also worth mentioning that this approach is related to the classical Newsvendor Problem which has been known at least from the moment of the publication of Edgeworth (1888), and then analyzed and generalized by numerous authors, see e.g.…”

Novel approach for solving integer equal flow problem

“…One could use an equalization method as proposed by Marcin et al . [2] But this is still a quadratic Transportation problem with no bounds on convergence that can be given.…”

A novel approach for solving fully intuitionistic fuzzy transportation problem

“…The above formulation is a standard generalized quadratic transportation problem which has some known approaches. One could use an equalization method as proposed by Marcin et al [2]. But this is still a quadratic transportation problem with no bounds on convergence that can be given.…”