(61o) Multi-Stage Stochastic Programming for the Planning of a Mobile Modular Closed-Loop Supply Chain

Traditionally, supply chains employ a fixed facility design to take advantage of the long strategic planning horizon and economies of scale. However, the global market has turned much more volatile in recent years, so more agile and dynamic supply chain paradigms are arising. The novel concept of modular and mobile supply chains has thus emerged and is beginning to be adopted by industrial decision makers. Mobile modular supply chains contains modular units with standardized interfaces that can be installed or removed at sites to expand or contract the capacity of a facility, or transported between different sites to adapt to market variations. Despite these advantages, the additional flexibility brought up by the modular design poses new challenges for decision makers as the location of modules involves both strategic and tactical decisions.

The planning of a mobile modular closed-loop supply chain network is modeled as a mixed-integer linear programming (MILP) model in this work with the aim of minimizing total costs. The customer demands, return amounts and recoverable fractions of returned products are assumed to be uncertain, and the two echelons adjacent to the customers, distribution and collection centers, are chosen to be mobile and modular facilities. In each time stage, modules can be purchased and installed at sites to expand the capacity of the facilities, or transported to other sites of the same type.

To make optimal decisions for different uncertainty realizations, we reformulate the model into a multi-stage stochastic model with stage-wise independent uncertainty. We also employ the stochastic dynamic dual integer programming (SDDiP) algorithm to solve the large scale MILP with integer state variables. The idea of independent Magnanti-Wong cuts is adopted to form enhanced cuts of the SDDiP algorithm. Computational experiments have shown that the SDDiP with enhanced cuts can more effectively solve the multistage stochastic model which may otherwise be intractable. The value of the mobile and modular design is examined through case study and is positively correlated with the variance of the customer demand. The value of stochastic solution is also confirmed.