Use of penalties in a branch and bound procedure for the fixed charge transportation problem

The fixed charge transportation problem (FCTP) is an extension of the classic transportation problem in which a fixed cost is incurred for every supply point that is used in the solution. A branch and bound procedure which requires the use of two subproblems (a classic transportation problem and a knapsack problem) can be used to solve the FCTP. Unlike fixed charge problems, with the FCTP, there is a many-to-one correspondence between the continuous variables of the transportation problem and the fixed charge variables of the knapsack problem. This paper incorporates penalties into the branch and bound procedure in order to improve the solution times. Also, an adjacent extreme point heuristic is presented that finds a near optimal solution quickly.