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)

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.