The Declarative Framework Approach to Decision Support for Constrained Search Problems - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 176

4.2 Multi-stage transportation problem
The standard is determining the delivery of homogenous materials (commodity) from n
suppliers to m purchasers. Multi-stage transportation problem, which in addition to
suppliers and customers, there are still intermediate points such as distribution centers
(Fig.2). Where the set W = {W 1 , W 2 , .. W n } specifies the suppliers/manufacturers/, the set O
= {O 1 , O 2 , .. O m } purchasers (delivery points) and set P = {P 1 , .. P k } intermediaries such as
warehouses, distribution centers, logistic warehouses.

Fig. 6. The network for multi-stage transportation problem

Symbol Description

Indices

j delivery point (j=1..M)

i facility/factory (i=1..N)

s distribution center (s=1..E)

N the number of factories

M the number of delivery points

E the number of distribution centers

Input Parameters

C j production cost for the factory i (i=1..N).

W i production capacity for factory i (i=1..N).

Z j demand for delivery point j (j=1..M)

A is the cost of delivery from factory i to distribution center s (i=1..N) (s=1..E)

the cost of delivery from distribution center s to delivery point j (s=1..E)
(j=1..M)

G sj

Decision Variables
X is the part of the delivery from factory i to distribution center s
Y sj the part of delivery from distribution center s to delivery point j
Table 5. The indices, input parameters and the decision variables for optimization model.