On Capacitated Transportation Problem with Bounds on Rim Conditions

Capacitated transportation problem with bounds on rim conditions (CTPBRC) is an extension of classical transportation problem in which routepsilas transportation capacity, originpsilas supply and destinationpsilas demand have lower bound and upper bound. In this paper, CTPBRC is formulated using an integer linear programming model, and transformed into minimum cost flow (MCF) problem for solution. Based on MCF algorithm, an algorithm, named CTPBRC-A, is proposed to solve CTPBRC. The theory, on which CTPBRC-A is based, is presented. CTPBRC-A not only can judge whether CTPBRC has a feasible solution or not, and can find its optimal solution while feasible solution exists, but also has good performance in the sense of being implemented on computer, computational time and required memory for computation. Numerical experiments demonstrate that CTPBRC-A is an efficient and robust method to solve CTPBRC.