Whey reverse logistics network design: a stochastic hierarchical facility location model

Whey reverse logistics has received a considerable attention due to the recent environmental legislation and competitive advantages. In this paper, we study a whey reverse logistics network design problem with stochastic demand, where demand is the amount of raw whey produced by a cheese maker that should be converted into a commercial product. We formulate this problem as a hierarchical facility location problem with two levels of facilities, namely collection centers and plants. Collection centers receive raw whey from cheese makers and convert it to concentrated whey. Then the concentrated whey is sent to plants for further processing. A plant can be established in a potential location if a collection center has already been established in that point. The objective is to determine which facilities to open and to allocate each demand point to the open facilities such that the total expected cost is minimized. The total cost is comprised of transportation cost and fixed cost of opening facilities. The problem with deterministic demand is formulated as a mixed integer linear program. We use this formulation to model the stochastic version of the problem as a two-stage stochastic program, where decisions are made at two sequential stages. At the first stage, we decide which facilities to open and at the second stage, after observing a realization of demands, we decide how to allocate each cheese maker to the open facilities. We use the sample average approximation method to estimate the expected value function. The resulting formulation can be solved using a standard linear solver. Results of a computational study on a set of randomly generated instances will be reported.