A sample average approximation-based heuristic for the stochastic production routing problem

The Production Routing Problem under demand uncertainty is an integrated problem containing production, inventory, and distribution decisions. At the planning level, the aim is to meet retailers demand, when only the demand distribution is known in advance, while minimizing the corresponding costs. In this study, a two-stage formulation is presented in which the routing can be adjusted at short notice. In the first stage, only production decisions are made, while delivery and inventory quantities and retailer visit schedules are determined in the second stage. To handle a large number of scenarios, two solution methods based on Sample Average Approximation are introduced. Furthermore, the impact of the routing quality is explored by applying a simple heuristic and an effective metaheuristic on the routing part. It is shown that, on average, the simple heuristic within an adjustable Sample Average Approximation approach provides better objective function values than the metaheuristic within a non-adjustable approach. Also all solution approaches outperform an expected value based approach in terms of runtime and objective function value.