Volkswagen (VW) manufactures the vehicles marketed in North America in two
plants, one in Germany, the other one in Mexico. Vehicles are first shipped to
one of the five U.S. ports that act like distribution centers (DCs). They are
then transported to the dealerships at major market areas, mainly by trucks. The
company aims to improve its vehicle distribution network with two major
objectives: 1) to improve customer service, vehicle delivery times, and market
responsiveness, and 2) to reduce the total distribution and inventory holding
costs. Production Modeling Corporation was requested to develop simulation and
optimization based tools so that an improved vehicle flow between plants and
dealerships could be developed.
Our basic strategy to improving the vehicle flow was the establishment of
more DCs closer to metro markets so that the following benefits could be
realized: a) part of the current expensive truck routes could be replaced by
cheaper rail or sea routes, b) the chance of meeting a customer's first choice
vehicle increases with combined dealer and DC inventory, and c) customers' first
choice vehicles are delivered with shorter lead times. Clearly, the number and
locations of DCs are major factors that affect both customer service and
distribution cost measures. Moreover, there is a choice for the type of facility
to be installed at each DC location. Type I facilities are smaller in capacity
and cheaper. Type II facilities are larger, but the increase in operating
expenses is nonlinear and allows us to consider economies of scale in locating
DCs in certain high-demand areas.
Given a location scenario (i.e., number and location of DCs),
realistic computation of the performance measures (cost and customer service)
requires explicit consideration of the dynamic and stochastic elements in the
system. Dynamic elements include the inventory control policies (both quantity
and mix) at dealers, truck load factors, and DCs' demand seasonality over the
year. Stochastic elements include customer demand, customer choice, and
transportation delays. We felt that a simulation model was appropriate for the
consideration of both elements. We developed a simulation model and generated a
few location scenarios "by eye" as input to simulation. It became quickly
apparent, however, that a systematic way of generating location scenarios was
needed because of the tremendous number of alternatives.
In an attempt to reduce the number of alternatives, we formulated a Mixed
Integer Program (MIP) that generates a reasonable number of "good" scenarios.
The MIP minimizes a cost function that approximates the distribution cost of the
actual system by ignoring the stochastic and dynamic aspects. The variables
consist of shipment quantities and whether DCs are to be installed at potential
locations (binary variables). The output of the MIP is a location scenario as
input to simulation.
The MIP objective function consists of two components: 1) total
transportation costs, which depend on mileage between locations as well as the
modes of transportation, and 2) fixed facility installation costs at DCs, which
depend on locations and capacities. Inventory holding costs are ignored.
Constraints are specified to assure that a) market demands are satisfied, b)
incremental capacity limitations for facility types are not violated, c) market
orders can be shipped within a prespecified time window, and d) maximum number
of DCs to install is not exceeded.
Two major input parameters to the MIP are market demands and truck load
factors, which, in fact, are both functions of the location policy. (Truck load
factors are used to calculate the shipment costs.) We resolve this problem with
a heuristic iterative procedure. We start with solving the MIP assuming that 1)
all market demands match the planning sales volumes exactly, and 2) all load
factors are 1.0 (i.e., full-load trucks).The resulting location scenario is
given as input to the simulation model.
Considering the dynamic and stochastic elements, the simulation run produces
better estimates of the sales and load factors as a result of implementing this
particular location scenario. Now, we give these better estimates back to the
MIP, and solve it. If the output location policy is changed, we proceed with
running the simulation using the new location scenario as input. Otherwise, the
most recent estimates are not different enough from the previous ones, and the
MIP and simulation agree on a particular solution. Although there is no
guarantee of convergence, this procedure proved satisfactory in our experiments.
To solve the MIP, we used AMPL Plus with CPLEX as solver. It proved
very convenient in implementing the above iterative procedure thanks to its
flexible input and output capabilities. Communication between AMPL Plus and the
simulation software was handled (semi-automated) by an Excel spreadsheet with
macros that read the output files created by one program and generated
appropriate input files for the other program.
Our quantitative analysis based on the combined optimization and
simulation modeling yielded many interesting results. Since railroad
transportation is cheaper than trucks, a cost-optimal policy includes far more
DCs than the current one. Under certain circumstances, an optimal solution has
the potential of saving over $20 million per year in transportation related
costs. Fixed costs of installing and operating DC facilities are insignificant
as compared to savings in transportation costs. Some DC locations considered by
management were never selected due to high shipping cost penalty.
Dr. Karabakal is a Consulting Engineer with Production Modeling
Corporation of Dearborn, Michigan. Production Modeling specializes in consulting
and system development activities related to manufacturing processes, often for
the automotive industry. Dr. Karabakal has worked on a variety of optimization
applications including maintenance schedules for electricity generating coal
units, replacement strategies for waste collection trucks, and capital budgets.
He received his Ph.D. in Industrial and Operations Engineering from the
University of Michigan.
