A Column-Generation Based Tactical Planning Method for Inventory Routing

Inventory routing problems combine the optimization of product deliveries (or pickups) with inventory control at customer sites. The application that motivates this paper concerns the planning of single-product pickups over time; each site accumulates stock at a deterministic rate; the stock is emptied on each visit. At the tactical planning stage considered here, the objective is to minimize a surrogate measure of routing cost while achieving some form of regional clustering by partitioning the sites between the vehicles. The fleet size is given but can potentially be reduced. Planning consists of assigning customers to vehicles in each time period, but the routing, i.e., the actual sequence in which vehicles visit customers, is considered an "operational" decision. The planning is due to 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. On a large-scale industrial test problem (with close to 6,000 customer visits to schedule), we obtain a solution within 6.25% deviation from the optimal to our model. A rough comparison between an operational routing resulting from our tactical solution and the industrial practice shows a 10% decrease in the number of vehicles as well as in the travel distance. 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.