A unified framework for rich routing problems with stochastic demands

Abstract

We introduce a unified framework for rich vehicle and inventory routing problems with complex physical and temporal constraints. Demands are stochastic, can be non-stationary, and are forecast using any model that provides the expected demands and their error term distribution, which can be any theoretical or empirical distribution. We offer a detailed discussion on the modeling of demand stochasticity, focusing on the probabilities and cost effects of undesirable events, such as stock-outs, breakdowns and route failures, and their associated recourse actions. Tractability is achieved through the ability to pre-compute or at least partially pre-process the stochastic information, which is possible under mild assumptions for a general inventory policy. We integrate the stochastic aspect into a mixed integer non-linear program, illustrate applications to various problem classes, and show how to model specific problems through the lens of inventory routing. The case study is based on two sets of realistic instances, representing a waste collection inventory routing problem and a facility maintenance problem, respectively. We analyze the effects of our assumptions on modeling realism and tractability, and demonstrate that our framework significantly outperforms deterministic policies in its ability to limit the number of undesirable events for the same routing cost.

Heuristics for Vehicle Routing Problem: A Survey and Recent Advances

“…Some of them, for example, HGS and ALNS, can handle VRPs with more than ten different attributes. Note that there are other successful unified vehicle routing solvers, which are not included here, such as the exact methods [17,18,183].…”

A Mathematical programming approach for a vessel scheduling-transportation problem with multiple sources and destinations, and normal daily demand distributions

“…Rafie-Majd et al (2018) used a Lagrangian relaxation algorithm to solve an integrated inventory-location-routing problem with normally distributed demands. Markov et al (2018) introduced a unified framework for rich vehicle and inventory routing problems with complex physical and temporal constraints.…”