Centralized versus Distributed Manufacturing: a Continuous Location-Allocation Problem
Advances in technology have led to the rethinking of traditional manufacturing. In recent years, the concept of Distributed Manufacturing has been discussed as a way to satisfy the new requirements of the market (e.g. customized products) and take advantage of some logistical aspects (e.g. high cost of transportation in the biomass supply chain). However, conventional large-scale centralized manufacturing can be more cost-effective due to the economies of scale.
In this paper, we address a systematic way of evaluating the profitability of centralized versus distributed manufacturing. The problem is formulated as a continuous facility location-allocation problem with limited capacity, also known as the Capacitated Multisource Weber problem. The objective of this type of problem is to generate sites in continuous space for locating new facilities in relation to a set of existing facilities located at given points in space, taking into account limited capacity and transportation costs .
Our generic model considers sources of raw material and consumer markets with specified locations and corresponding availabilities and demands. The problem has a number of potential facilities that can be built with specified maximum capacities. Some of them can be large-scale plants while the remaining facilities can be small/medium scale plants. The location of these plants is a variable to be determined on a two-dimensional plane. Therefore, the model has the option to choose a centralized, distributed, or hybrid configuration consisting of facilities with locations and assignments closer to the raw material or to consumers.
The problem is formulated as a mixed-integer nonlinear program (MINLP) in which the investment cost of the facilities and the transportation costs are to be minimized. The MINLP is nonconvex due to the concave investment cost functions, the Euclidean distances, and the cost dependence of distances and amounts shipped for the transportation. To deal with the nonconvexities, several reformulations are first applied to improve the computational performance of the local and global solvers. A piecewise-linear approximation is also used to approximate the concave separable terms so as to reformulate the problem as a mixed-integer quadratically-constrained quadratic program (MIQCP).
The applicability of the proposed models is illustrated with case studies for different industries, including biomass and shale gas. The results show the capability of the models to find globally optimal solutions for centralized and distributed manufacturing systems. We also compare the results for the MINLP and the approximated MIQCP models using commercial local and global optimization solvers (e.g. SBB, DICOPT, CPLEX, GUROBI, BARON, SCIP).
 Brimberg, Jack, Pierre Hansen, Nenad Mladenovic, and Said Salhi. "A Survey of Solution Methods for Continuous Location-Allocation Problem." International Journal of Operations Research 5.1 (2008): 1-12.