Multistage stochastic programming for the closed-loop supply chain planning with mobile modules under uncertainty

Traditional supply chains usually follow fixed facility designs which coincide with the strategic nature of supply chain management (SCM). However, as the global market turns more volatile, the concept of mobile modularization has been adopted by increasingly more industrial practitioners. In mobile modular networks, modular units can be installed or removed at a particular site to expand or reduce the capacity of a facility, or relocated to other sites to tackle market volatility. In this work, we formulate a mixed-integer linear programming (MILP) model for the closed-loop supply chain network planning with modular distribution and collection facilities. To further deal with uncertain customer demands and recovery rates, we extend our model to a multistage stochastic programming model and efficiently solve it using a tailored stochastic dynamic dual integer programming (SDDiP) with Magnanti-Wong enhanced cuts. Computational experiments show that the added Magnanti-Wong cuts in the proposed algorithm can effectively close the gap between upper and lower bounds, and the benefit of mobile modules is evident when the temporal and spatial variability of customer demand is high.