Stochastic capacity planning and dynamic network design Bruno S. Pimentel n , Geraldo R. Mateus, Franklin A. Almeida Department of Computer Science, Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627, Belo Horizonte 31.270-901, Brazil article info Article history: Received 6 February 2012 Accepted 18 January 2013 Available online 29 January 2013 Keywords: Stochastic programming Strategic decision making Network design Capacity expansion Supply chain abstract The present paper proposes a mathematical model and a solution approach to the Stochastic Capacity Planning and Dynamic Network Design Problem. Here, strategic decisions usually comprise developing the necessary capacity — through either incrementing capacity on existing assets (facilities or logistics channels) or establishing new capacity in the form of new assets — in order to satisfy increasing demand. Hence, throughout the planning horizon, decisions on which new assets to establish and where to increment capacity must be taken at minimal cost and in a timely manner. However, when demand varies nonmonotonically, decisions on which assets to temporarily shut down in times of decreasing demand and which of those to reopen when market conditions improve must also be taken into account. We propose a multi-stage stochastic mixed-integer programming approach to the problem as well as a Lagrangian Heuristic procedure to attain reasonably well bounded feasible solutions. The proposed method is evaluated in a Global Mining Supply Chain context which, due to the inherently large capital expenses, could have the outcome of its strategic decision making process significantly improved. & 2013 Elsevier B.V. All rights reserved. 1. Introduction The recent financial crisis has proven how extremely difficult it is to develop accurate predictions of macroeconomic para- meters, and more specifically, of prices and demand levels of commodities such as metals, energy and oil. The complexity of today’s global economic dynamics, the increasing levels of uncer- tainty and information asymmetry and the intricate relationships between productive and financial markets can be overwhelming (Kimura, 2002). Such conditions motivate a look into stochastic aspects on analytics, specially those involving strategic decisions on large capital expenses. In an unstable economic environment, commodity prices and demand can behave nonmonotonically, consequently exerting significant pressure on a systems’ available production and distribution capacities (Caminada and Spinetto, 2012; Stewart, 2013). When demand increases, the strategic decision maker aims at evaluating major capital investments on the establishment of new (or on the capacity expansion of existing) assets. Conversely, in times of economic stagnation or even recession, decisions might involve shutting down specific facilities on a temporary or permanent basis (Dias et al., 2006). In traditional facility location problems, the selection of the sites where new facilities are established is restricted to a finite set of candidate locations (Melo et al., 2009). In many practical situations, however, the optimal topology of the underlying network must be determined together with the facility location decision, thus con- figuring an integrated facility location/network design problem. One can also view those problems as investments in capacity planning — in the form of new assets or discrete capacity incre- ments — which commonly exhibit substantial economies of scale. This means that any strategic investment policy should also consider the tradeoff between the savings of large expansion figures versus the cost of installing capacity before it is actually needed. Furthermore, the planning process need not be static—since demand may vary nonmonotonically, a strategic decision maker must be able to establish, interrupt or even shut down operational assets throughout the planning horizon, while also balancing incrementing capacity where and when needed. Such an uncertain behavior suggests a stochastic approach that, though providing a stronger framework to dealing with uncertain parameters, further increases the inherent computational complexity. Hence, special care must be taken when developing the mathematical formulation and, more importantly, the associated solution procedure. A number of approaches to those problems have been dis- cussed in the literature. Tsiakis and Papageorgiou (2008) develop a deterministic mixed integer linear programming model for the design of multi-echelon, single period supply chain networks, integrating the establishment of production plants, distribution centers and the assignment of products to plants and distribution Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2013.01.019 n Corresponding author. Tel.: þ55 3192811106. E-mail addresses: bruno.pimentel@gmail.com, brunosp@dcc.ufmg.br (B.S. Pimentel), mateus@dcc.ufmg.br (G.R. Mateus), franklin@dcc.ufmg.br (F.A. Almeida). Int. J. Production Economics 145 (2013) 139–149