Adjacency constraints in harvest scheduling: an aggregation heuristic

Abstract

An heuristic for adjacency constraint aggregation is proposed. The heuristic is composed of two procedures. Procedure 1 consists of identifying harvesting areas for which it is not necessary to write adjacency constraints. Procedure 2 consists of writing one adjacency constraint for each one of the harvesting areas not identified in procedure 1. Such adjacency constraints consider all the adjacency relations between the harvesting area and its surrounding areas. The heuristic is based on the concept of penalties and the four-color theorem. The aggregated constraints present fewer variables per constraint than the aggregator described by B.J. Meneghin, M.W. Kirby, and J.G. Jones (1988. USDA For. Serv. Rocky Mt. For. Range Exp. Stn. Gen. Tech. Rep. RM-161. pp. 46–53) and can easily be generated mechanically from the adjacency matrix. In addition, the proposed heuristic does not require the tedious task of identifying type 1 and 2 constraints as with Meneghin's algorithm. Hence the combinatorial work to compute the aggregated constraints is reduced significantly. Comparisons showed that the proposed heuristic requires about a third of the constraints required by the conventional adjacency constraint formulation and about the same number of constraints as the procedure suggested by B.J. Meneghin, M.W. Kirby, and J.G. Jones (1988).