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Some ideas of neuro-dynamic programming (NDP) are illustrated by considering the problem of optimally managing a forest stand under uncertainty. Because reasonable growth models require state information such as height (or age), basal area, and stand diameter, as well as an indicator variable for treatments that have been performed on the stand, they can easily lead to very large state spaces that include continuous variables. Realistic stand management policies include silvicultural options such as pre-commercial and commercial thinning as well as post-harvest treatments. We are interested in problems that are stochastic in their basic growth dynamics, in market prices, and in disturbances, ranging from insects to fire to hurricanes. NDP algorithms are appropriate for problems with large dimensions that may lack a simple model of dynamics and stochastic processes. This paper looks at applying these ideas in the context of a multispecies model. Results show that policies obtained using NDP are optimal within a 95% confidence interval or better. The set of states and controls incorporated into our NDP model allows us to develop optimal policies with a level of detail not typically seen in the forestry literature.

Rule curves are monthly reservoir-operation guidelines for meeting the minimum of water shortage over the long run. This paper proposes a dynamic programming (DP) approach for finding the optimal rule curves of single- and multi-reservoir systems. The proposed DP approach uses a traditional DP technique conditionally and applies the principle of progressive optimality (PPO) to search its optimal solutions. The proposed DP–PPO approach is suitable because of the multi-stage, nonlinear, and continuous-type characteristics of the rule curve search. Its dimensionality is relatively small, as compared with that of the traditional one. Results of an illustrative application to a multi-reservoir system under two different initial feasible solutions (i.e., new or existing reservoirs) have demonstrated that the DP–PPO approach is generally fast and robust. Its convergence varies only slightly, according to the initial conditions.Key words: rule curves, principle of progressive optimality, dynamic programming (DP), monthly reservoir operation.

Forest managers are faced with complicated road construction and deactivation decisions. When construction, upgrading, and deactivation strategies must be determined simultaneously over broad spatial and temporal scales, the problem becomes very complex and decision support systems are needed. In this paper, we report the development and application of an optimal road class and deactivation model using dynamic programming. We tested our model on projected road networks on Hardwicke Island, British Columbia. Sensitivity of inputs such as construction costs, upgrade costs, hauling and maintenance costs, deactivation costs, length of time horizon, discount rate, and haul volume were tested within and between two road networks. Comparison of road networks revealed that haul volume concentration, average haul distance, and total road length are the most important variables that affect road class decisions and total network costs. Within our case study, the road network with the lowest average hauling distance resulted in the lowest total cost (CAN$0.24/m3 less), because hauling costs are the largest component (46%) of total transportation costs. The dynamic programming model can be used to assess numerous road construction and maintenance assumptions under various silviculture and harvest systems.

Bridges and pavements represent the major investment in a highway network. In addition, they are in constant need of maintenance, rehabilitation, and replacement. One of the problems related to highway infrastructure is that the cost of maintaining a network of bridges with an acceptable level-of-service is more than the budgeted funds. For large bridge networks, traditional management practices have become inadequate for dealing with this serious problem. Bridge management systems are a relatively new approach developed to solve the latter problem, following the successful application of similar system concepts to pavement management. Priority setting schemes used in bridge management systems range from subjective basis using engineering judgement to very complex optimization models. However, currently used priority setting schemes do not have the ability to optimize the system benefits in order to get optimal solutions. This paper presents a network optimization model which allocates a limited budget to bridge projects. The objective of the model is to determine the best timing for carrying out these projects and the spending level for each year of the analysis period in order to minimize the losses of the system benefits. A combined dynamic programming and neural network approach was utilized to formulate the model. The bridge problem has two dimensions: the time dimension and the bridge network dimension. The dynamic programming sets its stages in the time dimension, while the neural network handles the network dimension. Key words: bridge management, dynamic programming, neural networks, budget allocation.

In the last decade, a number of methods based on the theories of linear and dynamic programming were developed for the scheduling of linear projects. However, these methods are only capable of handling sequential or serial activities. In this paper, a dynamic programming formulation for the scheduling of nonsequential or nonserial activities is presented. The objective of the current formulation is to determine the project time–cost profile, which determines possible project durations and their minimum project total costs. The formulation considers the effects of crew formations, interruptions, and lags for production activities in determining the minimum project total cost, minimum project direct cost, and minimum project duration. In addition, the approach presented is capable of handling activity durations and interruptions described by continuous and discrete functions. The formulation is also capable of handling both serial and nonserial linear projects. An example project is provided to illustrate the computational steps, validate the calculation algorithm, and show the capabilities of the proposed method. Key words: time-cost trade-off, linear projects, planning and scheduling, project control, project management, nonserial linear projects.

Dynamic programming has been utilized to optimize scheduling of repetitive projects. The optimization criterion of existing techniques, however, is limited to minimizing the project duration and does not account for the impact of such optimization on the project cost. While the minimization of the project duration may reduce the project indirect costs, it does not guarantee a minimum total cost for the project. In practice, minimizing the overall cost of a project is frequently regarded to be more important than minimizing its duration. The objective of this paper is to present a flexible model that incorporates cost in the optimization process. In addition, the model is capable of considering the weather impact and the learning curve effect in the optimization process, simulating two important factors affecting productivity on this class of projects. The model utilizes dynamic programming and performs the solution in two stages: first, a forward path to identify local minimum conditions; and then a backward path to ensure a global minimum state. A numerical example from the literature is analyzed in order to demonstrate the use of the model, test its validity, and illustrate the significance of incorporating cost, weather impact, and the learning curve effect in the optimization process. Key words: planning and scheduling, repetitive projects, linear scheduling, cost optimization, dynamic programming, learning curve effect, weather impact.

The aim of this paper is to describe a methodology that has been used to assist in formulating sound production and marketing plans for a forest enterprise by relating information on stem frequency, size, and defect collected in routine inventories of forest resources to the projected demand for various log types. Emphasis is given to efficient bucking on landings of resources that are to be felled within a planning period as a whole, rather than efficient prescriptions for either each stand or each individual stem. The central model is a Dantzig–Wolfe decomposition procedure with a linear programming master and dynamic programming subproblems. The dynamic programming algorithm is used to maximize return from bucking a sequence of logs from single stems. From a set of alternative bucking patterns for different stem classes, the linear program selects those that maximize overall financial return, subject to satisfying constraints on resource availability and for a mix of log types from which end-use product demands can be met. Informational requirements for and applications of the model are presented with reference to a plantation resource of Caribbean pine belonging to the Fiji Pine Commission.

A four state-descriptor dynamic programming model was used to seek economically optimal thinning regimes for high and low thinning in loblolly pine (Pinustaeda L.). Given the assumptions of the study, low thinning generated higher present values than high thinning. Growth equations were estimated from data generated by a stochastic growth simulator. Reasons for the occurrence of slightly suboptimal solutions are discussed. The paper reviews situations in which the principle of optimality might be violated when thinning problems are being solved with forward recursion dynamic programming.