An adaptive tabu-simulated annealing for concave cost transportation problems

The transportation problem (TP) is one of the most popular network problems because of its theoretical and practical importance. If the transportation cost linearly depends on the transported amount of the product then TP is solvable in polynomial time with linear programming methods. However, in the real world, the transportation costs are generally nonlinear, frequently concave where the unit cost for transporting products decreases as the amount of products increases. Since concave cost transportation problems (ccTPs) are NP-hard, solving large-scale problems is time consuming. In this study, we propose a hybrid algorithm based on the concepts borrowed from tabu search and simulated annealing to solve the ccTP.