A linear programming model combining land levelling and transportation problems

The levelling process of a vast area of land, for irrigation or any other development plan, is usually done in two stages. The first stage starts by determining the levels of the terrain, while the second stage solves the earthwork allocation for the predetermined levels. The most recent attempt, reported in the literature, to find global optimality for this problem was a trial-and-error approach which solves a linear transportation problem for every possible terrain’s level and selects the level that results in the lowest transportation cost. This approach, however, being an iterative procedure, can only come closer to the optimum solution depending on how small the iteration steps are, but does not guarantee global optimality. The paper presented here offers a linear programming model that combines the levelling of terrains and the associated transportation in a single linear programming problem, thus guaranteeing global optimality.