A Transportation Problem with multiple version LP/MIP/MINLP
This MIRO App is based on the trnsport model from the GAMS Model library.
It finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.
Indices:
i
= plants
j
= markets
Given Data:
a(i)
= supply of commodity of plant i (cases)
b(j)
= demand for commodity at market j (cases)
d(i,j)
= distance between plant i and market j (thousand miles)
c(i,j) = F ⋅ d(i,j)
shipping cost per unit shipment between plant i and market j ($/case/thousand miles)
Distances 





New York 
Chicago 
Topeka 
Supply 
Seattle 
2.5 
1.7 
1.8 
350 
San Diego 
2.5 
1.8 
1.4 
600 
Demand 
325 
300 
275 

f
= $ per thousand miles
Decision Variables:
x(i,j)
= amount of commodity to ship from plant i
to market j
(cases)
where x(i,j) ≥ 0
, for all i,j
Constraints:
Observe supply limit at plant i
: ∑j x(i,j) ≤ a(i)
for all i
(cases)
Satisfy demand at market j
: ∑i x(i,j) ≥ b(j)
for all j
(cases)
Objective Function:
Minimize ∑i∑j c(i,j) ⋅ x(i,j)
($K)
Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.