## Abstract

Well known extensions of the classical transportation problem are obtained by including fixed costs for the production of goods at the supply points (facility location) or by introducing stochastic demand, modelled by convex nonlinear cost, at the demand points (the stochastic transportation problem, (STP)). However, the simultaneous use of these generalizations is not very well treated in the literature. Furthermore, economies of scale often yield other concave cost functions than fixed charges, so in this paper we generalize the problem even further, by introducing general concave costs at the supply points, as well as convex costs at the demand points. The objective function can be represented as the difference of two convex functions, and is therefore called a d.c. function. We propose a solution method which reduces the problem to a d.c. optimization problem in a smaller space, then solves the latter by a branch and ground procedure in which bounding is based on solving subproblems of the form of STP. We prove convergence of the method and report computational tests that indicate that quite large problems can be solved efficiently. Problems up to the size of 100 supply points and 500 demand points are solved. 19 refs, 5 tabs

## Citation Formats

Holmberg, K, and Tuy, Hoang.
A production-transportation problem with stochastic demand and concave production costs.
Sweden: N. p.,
1993.
Web.

Holmberg, K, & Tuy, Hoang.
A production-transportation problem with stochastic demand and concave production costs.
Sweden.

Holmberg, K, and Tuy, Hoang.
1993.
"A production-transportation problem with stochastic demand and concave production costs."
Sweden.

@misc{etde_10117249,

title = {A production-transportation problem with stochastic demand and concave production costs}

author = {Holmberg, K, and Tuy, Hoang}

abstractNote = {Well known extensions of the classical transportation problem are obtained by including fixed costs for the production of goods at the supply points (facility location) or by introducing stochastic demand, modelled by convex nonlinear cost, at the demand points (the stochastic transportation problem, (STP)). However, the simultaneous use of these generalizations is not very well treated in the literature. Furthermore, economies of scale often yield other concave cost functions than fixed charges, so in this paper we generalize the problem even further, by introducing general concave costs at the supply points, as well as convex costs at the demand points. The objective function can be represented as the difference of two convex functions, and is therefore called a d.c. function. We propose a solution method which reduces the problem to a d.c. optimization problem in a smaller space, then solves the latter by a branch and ground procedure in which bounding is based on solving subproblems of the form of STP. We prove convergence of the method and report computational tests that indicate that quite large problems can be solved efficiently. Problems up to the size of 100 supply points and 500 demand points are solved. 19 refs, 5 tabs}

place = {Sweden}

year = {1993}

month = {Sep}

}

title = {A production-transportation problem with stochastic demand and concave production costs}

author = {Holmberg, K, and Tuy, Hoang}

abstractNote = {Well known extensions of the classical transportation problem are obtained by including fixed costs for the production of goods at the supply points (facility location) or by introducing stochastic demand, modelled by convex nonlinear cost, at the demand points (the stochastic transportation problem, (STP)). However, the simultaneous use of these generalizations is not very well treated in the literature. Furthermore, economies of scale often yield other concave cost functions than fixed charges, so in this paper we generalize the problem even further, by introducing general concave costs at the supply points, as well as convex costs at the demand points. The objective function can be represented as the difference of two convex functions, and is therefore called a d.c. function. We propose a solution method which reduces the problem to a d.c. optimization problem in a smaller space, then solves the latter by a branch and ground procedure in which bounding is based on solving subproblems of the form of STP. We prove convergence of the method and report computational tests that indicate that quite large problems can be solved efficiently. Problems up to the size of 100 supply points and 500 demand points are solved. 19 refs, 5 tabs}

place = {Sweden}

year = {1993}

month = {Sep}

}