(723e) Optimal Supply Chain Redesign in the Electric Motor Industry

Optimal supply chain
redesign in the electric motor industry

Maria
Analia Rodriguez, Aldo R. Vecchietti, Iiro Harjunkoski and Ignacio E. Grossmann

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, a motor malfunction may block the entire
production of a plant and therefore, obtaining a spare motor as soon as
possible is crucial.

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 required.

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 an 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.

References

Daskin, M., Coullard, C. and Shen,
Z-J. An Inventory-Location Model: Formulation, Solution
Algorithm and Computational Results. Annals of Operations Research, 2002, 110,
83?106.

Eppen, G. D. Effect of
centralization on expected costs in a multi-location newsboy problem.
Management Science, 1979, 25, 498 ? 501.

Grossmann, I.E. Challenges in the New
Millennium: Product Discovery and Design, Enterprise and Supply Chain
Optimization, Global Life Cycle Assessment. Computers and Chemical Engineering,
2005, 29, 29-39.

Parker, L. L. and Little, A. D. Economical reorder quantities
and reorder points with uncertain demand. Naval Research Logistics Quarterly,
2006, 11, 351?358.

You, F. and Grossmann, I. E. Integrated Multi-Echelon Supply
Chain Design with Inventories Under Uncertainty: MINLP
Models, Computational Strategies. AIChE Journal, 2010, 56,
2, 419 ? 440.