Capacitated facility location problem with freight cost discount

In reality, unit shipment cost is a decreasing function in shipment volume because of economics of scale. In this paper, we extend the capacitated facility location problem (CFLP) considering discounted freight cost. We formulate this problem as a mixed integer linear problem (MILP), and minimize the total cost including setup costs for opening the facilities and transportation costs with freight cost discount. Based on the special structure of the MILP, a Benders decomposition algorithm is proposed to solve it.

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