A simheuristic algorithm for the capacitated location routing problem with stochastic demands

The capacitated location routing problem (CLRP) integrates a facility location problem with a multi-depot vehicle routing problem. We consider the CLRP with stochastic demands, whose specific values are only revealed upon reaching each customer. The main goal is to minimise the expected costs of: (i) opening facilities, (ii) using a fleet of vehicles, (iii) executing a routing plan, and (iv) applying corrective actions. The latter are required whenever a route failure occurs due to unexpected high demands. We propose a simheuristic algorithm hybridizing simulation with an iterated local search metaheuristic, aimed at: (i) proposing a safety-stock policy to diminish the likelihood of route failure; and, (ii) estimating the expected cost and the reliability of each “elite” solution. We assess our approach on classical CLRP benchmarks, which are later extended to consider demand uncertainty. Finally, we also discuss the effects of the safety-stock policy on costs and reliability.