The network model is shown below. The gains on the arc entering
nodes C1, C2, etc. are equal to 1/2. This causes the amount of
flow leaving C1, C2, etc. to be equal to 1 for each unit produced.
The arcs entering the nodes labeled A and B are the production
capacities in each period. Arcs passing from one period to the
next, A1 to A2 for instance, carry inventories. The arcs leaving
C limit the production capacity at C. The arc leaving nodes such
as C1' describe the demand and net profit in each period.
It is necessary to add side constraints so that for every unit
of C produced, one unit of each A and B is required.
Let x(Ai, Ci) be the flow on arc (Ai, Ci) where i is the period
Let x(Bi, Ci) be the flow on arc (Bi, Ci) where i is the period
x(Ai, Ci) = x(Bi, Ci) for i = 1