Optimization of log Inventory and log routing by column generation

VITALE, IGNACIO GABRIEL; COCCOLA MARIANA EVANGELINA; DONDO RODOLFO

Conferencia; CLAIO 2022; 2022

Given the supply of several types of logs from a set of forest areas and given demanded quantities of them by a set of mills, a decomposition procedure aimed at optimizing log transportation routes and inventory levels in forest areas, transshipment yards and mills is presented. While forest areas act as suppliers and mills as sinks of logs, transshipment yard may receive logs from forests and Supply them to mills in order to save logistic costs. The decomposition procedure is based in the column generation paradigm which handles the problem by decomposing it into a master problem which handles inventory constraints on facilities and sub-problems that iteratively add routes to the master problem. While the master problem deals with products flows and implicit storage decisions, the lower-level problems generate routes. The LP master is solved by CPLEX while sub-problems are solved by an ad-hoc labeling procedure. The objective function of the master problem is a weighted sum of transportation and inventory costs on all facilities while the objective function of sup-problems are the reduced cost of generated routes. As the problem involves a set of │T│ time periods, the algorithm must feed the duals associated to the constraints of the master problem to │T│ subproblems which have the same structure but differ just in the values of the duals they receive. This allows feeding routes generated for one period of time into the other periods if they retain a negative reduced cost when duals associated to time periods are changed. Although the idea behind the algorithm is simple, the computational implementation demands a complex work. The algorithm was built in PYOMO. Integer solutions were obtained by running a MIP on the pool of generated columns. Several illustrative examples were solved. Further work should include the embedment of this algorithm into a branch-and-price mechanism in order to get an exact algorithm and optimal solutions