An exact solution approach based on column generation and a partial-objective constraint to design a cellulosic biofuel supply chain

This study provides an exact solution method to solve a mixed-integer linear programming model that prescribes an optimal design of a cellulosic biofuel supply chain. An embedded structure can be transformed to a generalized minimum cost flow problem, which is used as a sub-problem in a column generation approach, to solve the linear relaxation of the mixed-integer program. This study proposes a dynamic programming algorithm to solve the sub-problem in O(m) time, generating improving path-flows. It proposes an inequality, called the partial objective constraint, which is based on the portion of the objective function associated with binary variables, to underlie a branch-and-cut approach. Computational tests show that the proposed solution approach solves most instances faster than a state-of-the-art commercial solver (CPLEX).