Part 5: Special Network Problems: Transportation, Transshipment and
Assignment Problems
Transportation Problems
Transportation problem: allow shipments that go directly from supply points to demand
points.
General form:
- 𝑥)3 : amount product sipped from supply point i to demand point j
- m supply points
- 𝑠𝒊 : maximum units that supply point i can supply
- 𝑛 demand points
- 𝑑3 : units that demand point j must receive
- 𝑐)3 : variable cost for units shipped from supply point i to demand point j
min ∑µ &
)”$ ∑3”$ 𝑐)3 𝑥)3
s.t. ∑&3”$ 𝑥)3 < 𝑠) 𝑖 = 1, … , 𝑚 supply constraint
∑µ)”$ 𝑥)3 > 𝑑3 𝑗 = 1, … , 𝑛 demand constraint
𝑥)3 > 0 𝑖 = 1, … , 𝑚 ; 𝑗 = 1, … , 𝑛 non-negativity constraint
Balanced transportation problem: total supply = total demand
- Total supply > total demand: can balance the problem by adding a dummy demand
point (his assigned cost will be equal to 0)
- Total supply < total demand: problem is infeasible
Production planning problem
Will represent it using a network and showing the flow with nodes and arrows.
Can in this case allow backorders, constraints on the number of periods we can supply, the
number of periods we keep inventory, …
Transshipment Problems
Transshipment problems: problem where we have points (= transshipment points) through
which goods can be transshipped on their journey from a supply point to a demand point.
When modelling transshipment problems, we will have supply and demand constraints for
the supply and demand points but constraints for the transshipment points will be added.
Assignment Problems
Transportation Problems
Transportation problem: allow shipments that go directly from supply points to demand
points.
General form:
- 𝑥)3 : amount product sipped from supply point i to demand point j
- m supply points
- 𝑠𝒊 : maximum units that supply point i can supply
- 𝑛 demand points
- 𝑑3 : units that demand point j must receive
- 𝑐)3 : variable cost for units shipped from supply point i to demand point j
min ∑µ &
)”$ ∑3”$ 𝑐)3 𝑥)3
s.t. ∑&3”$ 𝑥)3 < 𝑠) 𝑖 = 1, … , 𝑚 supply constraint
∑µ)”$ 𝑥)3 > 𝑑3 𝑗 = 1, … , 𝑛 demand constraint
𝑥)3 > 0 𝑖 = 1, … , 𝑚 ; 𝑗 = 1, … , 𝑛 non-negativity constraint
Balanced transportation problem: total supply = total demand
- Total supply > total demand: can balance the problem by adding a dummy demand
point (his assigned cost will be equal to 0)
- Total supply < total demand: problem is infeasible
Production planning problem
Will represent it using a network and showing the flow with nodes and arrows.
Can in this case allow backorders, constraints on the number of periods we can supply, the
number of periods we keep inventory, …
Transshipment Problems
Transshipment problems: problem where we have points (= transshipment points) through
which goods can be transshipped on their journey from a supply point to a demand point.
When modelling transshipment problems, we will have supply and demand constraints for
the supply and demand points but constraints for the transshipment points will be added.
