Paper and wood products companies need to define cutting

schedules that will maximize the total wood yield of their forests over some planning

period. Suppose that a company with control of p forest units wants to identify the

best cutting schedule over a planning horizon of k years. Forest unit i has a total acreage

of aj units, and studies that the company has undertaken predict that this unit will have

wij tons of woods available for harvesting in the jth year. Based on its prediction of

economic conditions, the company believes that it should harvest at least Ij tons of

wood in year j. Due to the availability of equipment and personnel, the company can

harvest at most Uj tons of wood in year j. Formulate the problem of determining a

schedule with maximum wood yield as a network flow problem.

a) describe a reduction of this problem to network flow

b) Draw a diagram of such a ow network for p = 2 and k = 3.