Optimizing Stand Level Forest Harvesting Using a Trade off Objective Function

—We have developed a tabu search method to optimize the stand level harvest decision over intermediate time frames (10-30 years) within the context of a longer term hierarchical plan. In this paper, we focus on the objective function for our model. We are interested in the trade off between two main issues, one the cost of building roads to access the resource and the other the loss of forest productivity when stands are harvested too early or too late. We develop a biological productivity loss function and show how to examine the trade offs between the cost of roads and the productivity losses. INTRODUCTION In this paper, we address the problem of optimizing the stand harvest schedule for medium-range tactical planning, while meeting volume requirements in each period as specified by a previously executed strategic planning process. We assume that accessing stands in the forested area will require some road building, and that, consequently, a network of potential road links has been designed to cover the area. Although many tactical level objectives are worth considering, we will concentrate on the minimization of two costs. The first is the negative impact on longterm forest productivity caused by harvesting stands either too early or too late. The second is the cost of building roads to access the stands to be harvested. These cost factors are in opposition, since improving the timing of harvests can only be done by increasing the investment in road building. We do not assume, however, that the decision-maker has fixed a road building budget or a tolerance level for lost productivity. Instead, we produce a spectrum of solutions to the scheduling problem which range from those with very little road building to those where a high investment in road construction is required. By then recording the non-dominated solutions, we produce an efficient frontier or trade off curve which clearly presents the trade off effect over the range of road budget decisions which are available. Our model is constrained to meet maximum opening size and adjacency delay constraints. We do not assume that the adjacency delay period is equal to one planning period. The spatial decision unit is the stand, avoiding preblocking of stands. We use a Tabu Search metaheuristic to solve the model. This paper is organized as follows. In section 1 we describe the planning problem and the model. In section 2 we describe the basic solution philosophy and technical issues in dealing with adjacency constraints and the road network. In section 3 we present some results, which were obtained from a forest coverage of a region of Cumberland County, Nova Scotia. Section 4 concludes with some conclusions and discussion. THE PLANNING PROBLEM This problem is to optimize decisions made at the tactical level of forest planning. The tactical planning problem is considered in the context of a hierarchical forest planning system [Weintraub and Davis 1996, Weintraub and Cholaky 1991, Gunn and Rai 1987], where the strategic planning process has been previously executed. The strategic planning exercise has used a long planning horizon and, amongst other goals, has enforced the requirement that production levels be consistent with sustained yield. One result of this process is the 1Eldon A. Gunn and Evelyn W. Richards, Technical University of Nova Scotia, Department of Industrial Engineering PO Box 1000, Halifax, N.S., Canada B3J 2X4