A multi-stage stochastic supply network design problem with financial decisions and risk management Stefan Nickel a,b , Francisco Saldanha-da-Gama c , Hans-Peter Ziegler a,n a Institute for Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany b Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany c DEIO-CIO, Faculdade de Ciˆ encias, Universidade de Lisboa, Lisboa, Portugal article info Article history: Received 10 May 2010 Accepted 24 September 2011 Processed by B. Lev Available online 17 October 2011 Keywords: Stochastic programming Location Integer programming abstract In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Structuring a global supply chain is a complex decision making process. The complexity arises from the need to integrate several decisions each of which with a relevant contribution to the performance of the whole system. In such problems, the typical input includes a set of markets, a set of products to be manufac- tured and/or distributed, demand forecasts for the different markets and some information about future conditions (e.g. production and transportation costs). Making use of the above information, companies must decide where facilities (e.g. plants, distribution centers) should be set operating, how to allocate procurement/production activities to the different facilities, and how to plan the transportation of products through the supply chain network in order to satisfy customer demands. Often, the objective considered is the minimization of the costs for building and operating the network. Historically, researchers have focused relatively early on the design of production/distribution systems (see [10]). Typically, discrete facility location models were proposed which possibly included some additional features but that still had a limited scope and were not able to deal with many realistic supply chain requirements. However, in the last decade, much research has been done to progressively develop more comprehensive (but tractable) models that can better capture the essence of many supply chain network design (SCND) problems and become a useful tool in the decision making process. This can be seen in the papers by Melo et al. [27] and Shapiro [39], where it also becomes clear that many aspects of practical relevance in supply chain management (SCM) are still far from being fully integrated in the models existing in the literature. As pointed out by Shapiro [39], in corporate planning, financial decisions may strongly interact with the supply chain planning. In fact, structuring and managing a supply chain is often just part of a whole set of activities associated with a company. Accordingly, the investments in the supply chain must be integrated with other profitable investments. Typically, several points in time can be considered, in which the investments can be made or in which their return can occur (which in turn, may allow further invest- ments in the supply chain). Additionally, due to the large capital often associated with the network design decisions, the possibility of taking advantage of some investment opportunity is often considered, which justifies the use of loans. The evaluation of the investments made in a supply chain is usually based on their return rate. This fact calls for the inclusion of revenues in SCND models, which also gives the possibility of Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/omega Omega 0305-0483/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.omega.2011.09.006 n Corresponding author. Tel.: þ49 721 608 43951. E-mail address: hans-peter.ziegler@kit.edu (H.-P. Ziegler). Omega 40 (2012) 511–524