Integrated design and planning of the supply chain under uncertain demand

VECCHIETTI, ALDO; RODRIGUEZ, MARIA ANALIA

Conferencia; International conference on applied mathematics and informatics; 2013

Supply Chain (SC) design mainly involves decisions about where to place factories and distribution centers considering a long term horizon planning. However, since operational performance is greatly influenced by the SC design, a responsive SC can only be guaranteed when an effective inventory management, as well as an appropriate distribution and storage structure are planned together. Furthermore, rising transport costs are key factors in a companies? economy and managing inventory has become a major target in order to simultaneously reduce costs and improve customer service. When long term planning is involved, demand uncertainty must be taken into account because it might have a relevant influence on warehouses capacity requirement. In fact, if the plan for storage capacity does not consider demand uncertainty, it might be infeasible to provide the products as required. In order to cope with demand uncertainty, stochastic programming uses a scenario based approach (Sahinidis, 2004). The main disadvantage of this method is that the model size tends to increase rapidly with the number of scenarios considered. The second approach is to use chance constraint in which each uncertain parameter is treated as a random variable with a given probability distribution (Charnes and Cooper, 1963). Even though this approach does not involve scenarios, the model gives rise to non-linearities in the formulation. In this work, we propose an optimization model for the design of a multi-echelon SC of multiple products. Long term decisions involve new installations, expansions and elimination of warehouses. Tactical decisions include deciding inventory levels to satisfy the uncertain demand in distribution centers and customer plants, as well as the connection links between the SC nodes. Capacity constraints are also considered when planning inventory levels. A similar problem has been solved by the authors (Rodriguez et al., 2012) applying a chance constraint approach. In this case, we formulate the problem applying two-stage stochastic programming with the aim at comparing both approaches and analyze advantages and drawbacks of them in this specific problem. Regarding the stochastic programming model, each scenario is associated with certain probability of occurrence and represents one possible realization for the uncertain parameter. One of the main challenges is to define the different stages of this process and how scenarios are generated accordingly. In the first stage, ?here and now? decisions have to be made before the uncertain parameter realization is known. In this problem, investment decisions (new assets, expansions and shut-downs) are defined in the first stage. In the second, ?wait and see? decisions involve a recourse action because they can be made after the random parameter is known. They include inventory levels and lost sales. The results obtained from a case study are presented and analyzed in order to discuss the contribution of the approach proposed.