(442a) Supply Chains with Modular and Mobile Production Units: Optimization Framework and Solution Methods

Meeting highly variable product demands in a cost-efficient manner is an essential task for the chemical industry. Recently, distributed supply chains, whereby small scale production facilities are built close to locations of supply and demand, have become more prevalent due to their ability to respond to changes in demand in an agile and robust manner. Distributed supply chains can be enhanced by modular production units, which are small units that can be constructed off-site, and then transported to production sites where multiple modules can be assembled into a functional production facility. As demand shifts between different locations over time, it is also possible to add additional modules at a site or relocate individual modules between different production sites, allowing for a more agile response to changes while reducing the economic risk of building new units. The new idea of modular and mobile production infrastructure has been applied to shale gas extraction [1] and also holds promise for sustainable ammonia production [2].

In this work, we present a generic mixed-integer linear program (MILP) framework for determining optimal location and relocation of mobile modular production units given time-varying demands, which we call the dynamic modular and mobile facility location problem (DMMFLP). We also develop a novel metric, the value of module mobility, to quantify the economic benefits of mobile production units. Through the use of a small representative example, we demonstrate how the value of module mobility changes as a function of various supply chain economic parameters. While most of the relationships are intuitive, we note that under certain economic parameters, the value of module mobility reaches a local maxima with respect to module capital cost.

We also present multiple different solution methods which help to solve large instances of the DMMFLP. First, we reformulate the original MILP by adding auxiliary variables which track the number of modules active at a site at any given time. This reformulation can be solved on its own, leading to significant computational improvements compared to the original formulation, but is also more amenable to both priority branching and Dantzig-Wolfe decomposition. When solving using priority branching, priority is given to the auxiliary variables, with additional priority given to earlier time points. The Dantzig-Wolfe decomposition is solved using a parallelized column generation approach, whereby pricing subproblems for each time period are solved separately and in parallel to generate new columns for a restricted master problem. We perform computational tests for all four solution methods on multiple instances of a supply chain with 50 customers, 10 production sites, and up to 120 time periods. Our results show that the solving the reformulated problem with priority branching is fastest when the number of time points is small; however, the parallelized column generation approach becomes superior for a large number of time points.

[1] Allen, R.C., Allaire, D., El-Halwagi, M.M. Capacity planning for modular and transportable infrastructure for shale gas production and processing. Ind. Eng. Chem. Res., 2018, in press.
[2] Palys, M.J., Allman, A., Daoutidis, P. Exploring the benefits of modular renewable-powered ammonia production: A supply chain optimization study. Ind. Eng. Chem. Res., 2018, in press.