Inventory Routing Problem solved by Heuristic based on Column Generation

We consider an application of the inventory routing problem. A fleet of vehicles is devoted to collecting a single product from geographically dispersed sites. Each site has its own accumulation rate and stock capacity. On each visit, the vehicle empties the stock. At the tactical level, the objective is to minimize the fleet size and an estimate of the distance travelled. Moreover, for practical purposes, routes must be geographically clustered and the planning must be repeated over the time horizon with constrained periodicity. We develop a truncated branch-and-price-and-cut algorithm combined with rounding and local search heuristics that yield both primal solutions and dual bounds. Periodic plannings are generated for vehicles by solving a multiple choice knapsack problem. The issues related to the construction of the customer plannings are dealt with in a master program. The key to the success of the approach is the use of a state-space relaxation technique in formulating the master program to avoid the symmetry in time. Real-life instances of the problem are solved with reasonable optimality gaps.