Fixed charge solid transportation problem in uncertain environment and its algorithm

- Three models are proposed for uncertain fixed charge solid transportation problem.
- The crisp equivalences of the models are discussed.
- An algorithm is designed based on uncertainty theory and tabu search algorithm.

In this paper, the fixed charge solid transportation problem under uncertainty is investigated. As a result, three mathematical models are constructed for the problem, i.e., expected value model, chance-constrained programming model and measure-chance programming model, where the supplies, demands, conveyance capacities, direct costs and fixed charges are regarded as uncertain variables. After that, the crisp equivalences of the models are discussed. What is more, a hybrid intelligent algorithm is designed based on the uncertainty theory and tabu search algorithm to solve the models. Compared with the existing work, the innovations of the proposed work are briefly illustrated. Finally, some numerical examples are given to show the applications of the models and the algorithm.