4. A numerical example
In this section we present a numerical example to illustrate the model. The application of the model is performed
for a hypothetical data set which was inspired from the database of a Turkish logistics firm. The considered
SN includes four suppliers that are located in different countries in Europe, a third party logistics firm
that executes the warehousing and transportation functions and four manufacturers that are located in different
cities in Turkey. The SN that is structured to transport automotive industry products from suppliers to
manufacturers is constituted from multi-product, multi-echelon and capacitated suppliers and warehouse
(Fig. 1).
As mentioned in Section 3, the proposed model includes different sub-problems in an integrated structure.
When the automotive industry is considered, the overall objectives such as low overall cost to market,
on-time delivery to customers, correct and quick information flow, flexibility, etc. become more
important than the individual objectives of the specific stages or functional areas. Especially, for the manufacturers
that produce their products according to the just-in-time production principles, on-time deliveries
have vital importance to be able to sustain the production. Depending on this inherent feature of
the automotive industry, the application of the proposed model that includes minimization of the delaying
cost as the overall objective and transportation/warehousing costs as the sub-objectives will be convenient
to examine the model results.
The application is realized for 10 periodical demands of manufacturers. The demands of manufacturers for
10 periods are known and the objective is to satisfy these demands with minimum total cost, i.e. total of transportation
costs from suppliers to warehouse and warehouse to manufacturers, waiting cost in warehouse and
cost of delaying to manufacturers. Three kinds of products supplied from suppliers to manufacturers are
motor engine blocks, pressed sheet iron and plastic spare parts. The periodical demands of manufacturers
and the unit transportation costs between echelons are shown in Tables 1 and 2.
Since the demands of manufacturers are predetermined and certain, the total transportation cost after the
warehouse echelon should be constant. On the other hand, the transportation cost from suppliers to warehouse
changes according to the supplier and the product type. With all suppliers, product 1 is the cheapest
and product 2 is the most expensive. However, the reason of the different cost values among suppliers is
related with the used transportation mode. As shown in Table 3, transportation time of supplier 2 and supplier
3 is shorter than supplier 1 and supplier 4 because of preferring more expensive but faster modes (road vs. sea