(52a) Multi-Period Design and Planning of Centralized and Distributed Manufacturing Networks

Distributed and modular manufacturing has arisen as a promising option for supply chain networks in which the logistics are the main bottleneck. However, economies of scale will always favor large scale centralized production. Therefore, there is a need for a general framework that can support this decision, taking into account the potential tradeoffs [1]. In this paper, we address the multi-period design and planning of manufacturing networks considering the option of centralized and/or distributed facilities. This problem involves the selection of which facilities to build in each time period, and their location in the continuous 2-dimensional space, in order to meet demand and maximize profits.

The problem is formulated as a version of the continuous facility location and allocation problem with limited capacity, also known as the Capacitated Multi-facility Weber Problem (CMWP) [2]. The objective of this type of problem is to determine locations in continuous 2-dimensional space for opening new facilities based on their maximum capacity and the given coordinates of the suppliers or customers. We propose an extension of the original CMWP that considers fixed cost for opening new facilities, fixed transportation costs, and two sets of fixed-location points: suppliers i and customers j [3], and investment decisions in different time periods. The model is formulated as a multi-period nonlinear Generalized Disjunctive Programming (GDP), and reformulated as a multi-period nonconvex Mixed-Integer Nonlinear Programming (MINLP).

We develop a bilevel decomposition algorithm that consists of decomposing the problem into a master problem and a subproblem. The master problem is based on a relaxation of the nonconvex MINLP, which yields an MILP that predicts the selection of facilities and their links to suppliers and customers, as well as a lower bound on the cost of problem. The subproblem corresponds to a nonconvex NLP of reduced dimensionality that results from fixing the binary variables in the MINLP problem, according to the binary variables predicted in the MILP master problem. Based on the bounding properties of their subproblems, ε-convergence is proved for this algorithm.

The applicability of the proposed multi-period model and solution framework is illustrated with a biomass supply chain case study. The results show that the algorithm is more effective at finding global optimal solutions than general purpose global optimization solvers tested.

[1] Lara, C.L., Grossmann, I.E.: Global Optimization for a Continuous Location-Allocation Model for Centralized and Distributed Manufacturing. Proc. of.26th European Symposium on Computer Aided Process Engineering, June 2016, Portorož, Slovenia.

[2] Brimberg, J., Hansen, P., Mladonovic, N., Salhi, S.: A survey of solution methods for the continuous location allocation problem. International Journal of Operational Research 5(1), 1–12 (2008).

[3] Lara, C.L., Trespalacios, F., & Grossmann, I.E.: Global Optimization Algorithm for Capacitated Multi-facility Continuous Location Allocation Problems, Journal of Global Optimization, 2018. https://doi.org/10.1007/s10898-018-0621-6.