Optimal Supply Chain in the Electric Motor Industry

MARÍA ANALÍA RODRIGUEZ; ALDO R. VECCHIETTI; IGNACIO E. GROSSMANN; IIRO HARJUNSKONSKY

Pittsburgh, PA

Conferencia; AICHE Annual Meeting 2012; 2012

AICHE

The integration of supply chain redesign and tactical decisions such as defining inventory levels and how supply chain nodes are connected is a challenging problem that can greatly impact companies’ economy. Rising transport costs are key factors in decisions about both where to place the assets (factories and distribution centers) and how much inventory to store. In addition, managing inventory has become a major target in order to simultaneously reduce costs and improve customer service in today’s increasingly competitive business environment (Daskin, Coullard and Shen, 2002). For that reason, over the last few years, there has been an increasing interest in developing enterprise-wide optimization (EWO) models to solve problems that are broad in scope and integrate several decision levels (Grossmann, 2005). In the case of the electric motors industry, the relevance of this problem is given by some key issues. On the one hand, electric motors are expensive products, so keeping them in inventory means that a significant capital cannot be used for other purposes. On the other hand, manufacturing companies usually sign supply contracts with their customers committing themselves to satisfy motor demand within certain time period after a customer order is placed. Another special characteristic of this industry is given by the type of product. Most works from the literature, assume that the products are only moved forward in the supply chain and only the demand of new products is considered. In this case, the situation is more complex. As usual, demand can be originated by new customers or new investments at customer sites but, in addition, motors that are already in use at customer sites can fail. When that happens, clients require a motor in order to replace the one that failed. An important decision in this context is whether to replace failing motors with new units or with repaired products. An efficient inventory management of new and used motors in the supply chain warehouses is another challenge of this problem. Customer plants typically have tens or more different type of motors in their production processes, and also identical motors can be used for a variety of purposes. According to the type of motor and application, the criticality of a given unit can be very different so the time a customer allows that a motor is out of service until another one replaces it, is case dependent. If the time requirement is very tight, it might be necessary to have some motors in stock at customer sites. Taking into account that motor demand is uncertain and depends on motors failure at customer plants, a responsive supply chain can only be guaranteed when an effective inventory management, as well as an appropriate distribution and storage structure are planned together. Furthermore, demand uncertainty might also have a relevant influence on warehouses capacity requirement. In that sense, if the plan for storage capacity does not consider demand uncertainty, it might be infeasible to provide the motors as established in the contract. You and Grossmann (2010) propose an optimization model to design a multi-echelon supply chain and the associated inventory systems under demand uncertainty in the chemical industry. The original model is MINLP with a non-convex objective function so they develop a spatial decomposition algorithm to obtain near global optimal solutions with reasonable computational expense. The supply chain involves one product, design decisions consider the installation of new distribution centers, but no expansions or elimination of installed warehouses are considered. In addition, the model assumes one planning period so investment costs are annualized and capacity constraints are not analyzed. Our approach extends this previous work introducing new considerations regarding the particular industrial context, complexities from the model point of view and novel concepts that were not considered before. We develop an optimization model to redesign the supply chain of the electric motors industry under demand uncertainty from strategic and tactical perspectives in a planning horizon consisting of multiple periods. Long term decisions involve new installations, expansions and elimination of warehouses handling multiple products. It is also considered which warehouses should be used as repair work-shops in order to store, repair and deliver used motors to customers. Tactical decisions include deciding inventory levels (safety stock and expected inventory) for each type of motor in distribution centers and customer plants, as well as the connection links between the supply chain nodes. Capacity constraints are also considered when planning inventory levels. At the tactical level it is analyzed how demand of failing motors is satisfied, and whether to use new or used motors. The uncertain demand is addressed by defining the optimal amount of safety stock that guarantees certain service level at a customer plant. In addition, the risk-pooling effect described by Eppen (1979) is taken into account when defining inventory levels in distribution centers and customer zones. One novel consideration is given by inclusion of lost sales costs in the objective function, which was extended from the work by Parker and Little (2006). Due to the nonlinear and large size nature of the original formulation, piece wise linearization and lagrangean relaxation algorithms are applied to obtain the optimal solution.