In 1985 Dow Consumer Products, Inc. acquired a division of Morton Thikol, Inc.
giving rise to DowBrands, which produces and markets more than 80 convenience goods all over North America. On that occasion, the management of the new-born company decided to redesign the distribution network. After a preliminary analysis, it was decided that the new distribution system should be made up of CDCs and RDCs.
LINKING THEORY TO PRACTICE 315
LTL transportation TL transportation
Production plants
CDCs
RDCs
Demand points
...
Figure 8.10 Distribution system of DowBrands.
In the proposed system, CDCs receive TL shipments from the production plants and supply the RDCs as well as a restricted number of major supermarkets. RDCs are suburban warehouses from which customers are replenished (see Figure 8.10).
Shipments originating from a CDC are TL, while shipments from an RDC may be TL or LTL. In all cases freight transportation is performed by common carriers. Each RDC can be served by a single CDC and each customer can be assigned to a single CDC or RDC. Thirteen potential CDCs and 23 potential RDCs were selected. The demand points were aggregated into 93 sales districts while the products were combined in two macro-products (home products, HP, and food products, FP).
Because customers issue their orders within short notice (a single day or even a few hours) the management of DowBrands decided to impose an upper bound L on the maximum distance of an LTL shipment, but no limit was imposed for TL transportation which is much faster and reliable (see Section 1.2.3).
The distribution system redesign was designed in two stages: first, the curve of the total logistics cost as a function of the service level (represented byL) was defined;
then, an efficient configuration was selected on the basis of a qualitative analysis (see Section 1.3). The cost versus level of service curve was drawn as follows. For a pre-established set of values ofL, the least-cost configuration was determined by solving an IP model. The outcome was the number and the locations of the CDCs and of the RDCs, the allocation of the RDCs to the CDCs, the assignment of the demand points to the RDCs and to the CDCs, as well as freight routes through the distribution network.
In order to simplify the formulation, for each sales district and for each macro- product, a dummy macro-customer TL and a dummy macro-customer LTL were defined. Therefore, each demand point was represented by four macro-customers:
TL-HP, LTL-HP, TL-FP, LTL-FP. Finally, a virtual RDC for each CDC was introduced so that, in the next modelling representation, all macro-customers would be served by an RDC.
316 LINKING THEORY TO PRACTICE LetV1be the set of the CDCs;V2the set of the RDCs;V3the set of the macro- customers;fi, i ∈ V1, the fixed cost of theith potential CDC (inclusive of all the fixed expenses connected to the site and to the expected value of the stock); gj, j ∈ V2, the fixed cost of thejth potential RDC (inclusive of all the fixed expenses connected to the site and to the expected value of the stock);tij k, i ∈ V1,j ∈ V2, k∈V3, the unit transportation cost from the production plant to the demand pointk through theith CDC and thejth RDC;dk,k ∈ V3, the demand of macro-customer k;cij k = dktij k, i ∈ V1,j ∈ V2,k ∈ V3, the transportation cost whether macro- customerkis serviced through theith CDC and thejth RDC. Moreover, letzi, i∈V1, be a binary decision variable equal to 1 if theith CDC is selected, and 0 otherwise;
yij, i ∈ V1,j ∈V2, a binary decision variable equal to 1 if thejth RDC is opened and supplied by theith potential CDC, and 0 otherwise;xij k, i∈V1,j ∈V2,k∈V3, a variable representing the fraction of the total demand of the customerk served through theith CDC and thejth RDC.
The problem was formulated as follows.
Minimize
i∈V1
fizi +
j∈V2
gj
i∈V1
yij+
i∈V1
j∈V2
k∈V3
cij kxij k (8.1) subject to
i∈V1
j∈V2
xij k =1, k∈V3, (8.2)
yij ⩽zi, i∈V1, j ∈V2, (8.3)
i∈V1
yij ⩽1, j ∈V2, (8.4)
xij k ⩽yij, i∈V1, j ∈V2, k∈V3, (8.5)
zi ∈ {0,1}, i∈V1, (8.6)
yij ∈ {0,1}, i∈V1, j∈V2, (8.7) xij k ∈ {0,1}, i∈V1, j∈V2, k∈V3, (8.8) where constraints (8.2) establish that each customerk∈V3must be served by one and only one CDC–RDC pair, constraints (8.3) impose that a CDC must be opened if an RDC is assigned to it; constraints (8.4) require that each RDC is assigned to a single CDC; constraints (8.5) impose that the transportation service between a CDC–RDC pair is activated if it is used by at least one macro-customer.
Because no capacity constraint is imposed, problem (8.1)–(8.8) satisfies thesingle assignmentproperty (see Section 3.3.1). In order to satisfy the service level constraint, the LTL services j–k between RDC–customer pairs distant by more than a pre- established thresholdLare discarded by setting the associatedxij k variables equal to 0.
LINKING THEORY TO PRACTICE 317
Cost
Distance
300 370 430 500 560 620 680 750 1250
23 500 23 300 23 100 22 900 22 700 22 500 22 300
Figure 8.11 Total cost (in thousands of euros)-service level curve at DowBrands.
The solution of problem (8.1)–(8.8) was evaluated through a general-purpose MIP solver for various values ofLbetween 300 and 1200 km (see Figure 8.11). It is worth noting that, asLdecreases, at first the cost increases slowly, then it increases sharply.
Also, whenLbecomes very large, there is no need for RDCs. On the basis of these evaluations, the company’s management set Lequal to 430 km. By implementing this solution the company achieved a saving of about 1.5 million dollars per year compared to the previous configuration.