The Declarative Framework Approach to Decision Support for Constrained Search Problems - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 177

A mathematical model of optimization for multi-stage transportation problem has been
formulated as a linear programming problem of minimizing the objective function which
represents the total cost of transport and production under constraints (1) to (5). Constraint
(1) ensures that every requirement is met, that is, that each distribution center receives
delivery from the factory due to the production capacity. The fulfillment of the delivery for
delivery point enforces constraint (2). Balancing the distribution centers, i.e. the supply and
shipping ensures constraint (3). Constraints (4), (5) are the standard constraints for the
problem of integer linear programming.
Objective Function - minimize transportation and production costs:

NE EM N E

   

AX  GY  C X

* * ( * )

is , is , s j , s j , i i s ,

i  11 s sj  11 i  1 s  1

Subject to:

E



XW  for i = 1..N (1)

is , i

s  1

E



YZ  for j = 1..M (2)

s j , j

s  1

N M

  for s = 1..E

X  Y (3)

is , s j ,

i  1 j  1

i X  for i = 1..N ,s = 1..E, integer

0 (4)

,

s Y  for s = 1..E, j = 1..M, integer

0 (5)

,

Fig. 7. The part of ERD (simplified Martin's notation) diagram for questions parameters
tables