Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
-Which constraint represents transshipment through the distribution center?
A) 2X13 + 3X23 = 900
B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0
C) X13 + X23 - X34 - X35 - X36 = 0
D) X13 + X23 - X34 - X35 - X36 ≥ 0

Question

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
-Which constraint represents transshipment through the distribution center?
A) 2X13 + 3X23 = 900 
B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0 
C) X13 + X23 - X34 - X35 - X36 = 0 
D) X13 + X23 - X34 - X35 - X36 ≥ 0

Quizplus · Accepted Answer

The constraint that represents transshipment through the distribution center is the one that balances the incoming shipments with the outgoing shipments at the distribution center. This constraint is: X13 + X23 - X34 - X35 - X36 = 0. This is because the distribution center is not a source or a destination for any of the shipments, but serves only as a transshipment point where shipments are transferred from one incoming arc to one or more outgoing arcs.

Consider the Following Network Representation of Shipment Routes Between Plants