A SEQUENTIAL APPROACH TO DERIVATION OF STAND TREATMENT AND FOREST-WIDE HARVEST PRESCRIPTION OR SUPPLY

Current methods for optimization of stand treatment and forest-wide harvest scheduling use mathematical programming that presumes perfect information on production, costs, and revenues over long planning periods. These approaches simultaneously optimize harvest for all periods in the planning horizon. In contrast, the method presented here assumes that stand-level planning and harvest scheduling proceed sequentially rather than simultaneously over every period. A backward-recursion dynamic program is used to determine the discounted net value of a wide range of current harvest strategies for each stand class in the forest inventory on the basis of a projected set of optimal treatments for future harvest and regeneration of each stand. The most highly valued strategy is selected if there are no volume constraints. Otherwise, suboptimal harvest alternatives are ranked in order of increasing opportunity cost for increasing or decreasing harvest; constraints met only up to a maximum opportunity cost is also demonstrated.     

MODELING REGENERATION AND PEST CONTROL ALTERNATIVES FOR A FOREST SYSTEM IN THE PRESENCE OF FIRE RISK

This paper addresses a fire and pest protection forest management modeling problem by developing a flexible model which integrates the concepts of: 1) species diversity 2) infestation of susceptible species; 3) natural regeneration and planting; 4) conversion of susceptible to non-susceptible species by planting; 5) pest protection by spraying; 6) age-specific harvesting; 7) intertemporal harvest flow policies; and 8) catastrophic loss due to fire. A linear programming (LP) model economically evaluates alternative regimes for protection spraying of susceptible forest species against insect infestations and alternative harvesting strategies which include conversion of susceptible species to non-susceptible, by planting. These strategies are evaluated subject to catastrophic loss due to fire. An iterative simulation-LP approach tests how well the deterministic model holds in a simulated stochastic environment. This validation procedure involves solving the optimization problem deterministically using average values for the fire and infestation proportions and also at each time period updating the system state by simulating the state transition for the next time period using randomly generated updates and re-solving using the updated state as the new initial condition. An optimal wood supply trajectory in a simulated stochastic environment is therefore constructed. The results from the iterative stochastic solution provide a confidence measure for the deterministic solution.     

Measuring Customer Satisfaction Using a Collective Preference Disaggregation Model

A new model to assess customer satisfaction is developed through this paper. The proposed model is based on the principles of multicriteria analysis, using ordinal regression techniques. The procedure uses survey's data on customer satisfaction criteria and disaggregates simultaneously all the global satisfaction judgments via a linear programming disaggregation formulation. The model provides collective global and partial satisfaction functions as well as average satisfaction indices. These results sufficiently describe customer behavior and they can be used in the strategic planning of an organization. The implementation of the model in three real world applications is used for illustration and for testing the model's reliability. Finally, several extensions and future research in the area of customer satisfaction analysis are discussed.     

An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty

Planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities, where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist. With the purpose of tackling such difficulties, this paper presents the development of an interval-fuzzy nonlinear programming (IFNP) model for water quality management under uncertainty. Methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left- and right-hand sides of the nonlinear constraints. Uncertainties in water quality, pollutant loading, and the system objective were reflected through the developed IFNP model. The method of piecewise linearization was developed for dealing with the nonlinearity of the objective function. A case study for water quality management planning in the Changsha section of the Xiangjiang River was then conducted for demonstrating applicability of the developed IFNP model. The results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels. It was also indicated that the proposed linearization method was effective in dealing with IFNP problems; uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives; the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals. It also suggested that the linearized method should be used under detailed error analysis in tackling IFNP problems.     

AN ITERATIVE MULTILEVEL APPROACH TO NATURAL RESOURCE OPTIMIZATION: A TEST CASE

Forest planners face a dilemma. On the one hand, they desire more detail than they currently have in their planning optimization models, and on the other hand, these models are already extremely large and complex. This sort of problem is common in other natural resource management situations as well. This paper investigates an iterative multilevel approach that would allow districts within the forest to have models approaching the size and complexity of current forest models, but still approximate a forest-level optimum. A specific procedure based on equating shadow prices across districts is developed and tested with a case example where a global optimum is determinable as a standard of comparison. The procedure shows promise, but difficulties in recognizing optimality are indicated.     

Management of the risk of wind damage in forestry: a graph-based Markov decision process approach

This study deals with the problem of including the risk of wind damage in long-term forestry management. A model based on Graph-Based Markov Decision Processes (GMDP) is suggested for development of silvicultural management policies. The model can both take stochastic wind events into account and be applied to forest estates containing a large number of stands. The model is demonstrated for a forest estate in southern Sweden. Treatment of the stands according to the management policy specified by the GMDP model increased the expected net present value (NPV) of the whole forest only slightly, less than 2%, under different wind-risk assumptions. Most of the stands were managed in the same manner as when the risk of wind damage was not considered. For the stands that were treated differently, however, the expected NPV increased by 3% to 8%.     

SUSTAINABLE FOREST MANAGEMENT FOR OPTIMIZING MULTISPECIES WILDLIFE HABITAT: A COASTAL DOUGLAS-FIR EXAMPLE

Wildlife species viability optimization models are developed to convert a given set of initial forest conditions, through a combination of natural growth and management treatments, to a forest system which addresses the joint habitat needs of multispecies populations over time. A linear model of forest cover and wildlife populations is used to form a system of forest management control variables for wildlife habitat modification. The paper examines two objective functions coupled to this system for optimizing sustainable joint species viability. The first maximizes the product of periodic joint viabilities over all time periods, focusing management resources on long-term equilibria, with less emphasis on conversion strategy. The second iteratively maximizes the minimum periodic joint viability over all time periods. This focuses management resources on the most limiting time periods, typically the conversion phase periods. Both objective functions resulted in either point or cyclic equilibria, with cycle lengths equal to minimum forest treatment ages. A third objective, based on maximizing the minimum individual species periodic viability is used to examine single species emphasis. Examples are developed through a case study of 92 vertebrate species found in coastal Douglas-fir stands of northwestern California.     

Introducing cost-plus-loss analysis into a hierarchical forestry planning environment

Cost-plus-loss analysis of data for forestry planning has often been carried out for highly simplified planning situations. In this study, we suggest an advance in the cost-plus-loss methodology that aims to capture the hierarchical structure and iterative nature of planning by the large forest owner. The simulation system that is developed to simulate the planning process of the forest owner includes the tactical and operational levels of a continuous planning process. The system is characterized by annual re-planning of the tactical plan with a planning horizon of ten year and with the option to reassess data for selected stands before operational planning. Operational planning is done with a planning horizon of two years and the first year of the plan is considered to have been executed before moving the planning process one year forward. The annual cycle is repeated 10 times, simulating decisions made over a ten-year time horizon. The optimizing planning models of the system consider wood flow requirements, available harvest resources, seasonal variation of ground conditions and spatiality. The data used are evaluated according to standard procedures in cost-plus-loss analysis. Results from a test case indicate high decision losses when planning at both levels is based on the type of data prevalent in the stand databases of Swedish companies. The losses can be reduced substantially if higher-quality data are introduced before operational planning. In summary, the results indicate that the method makes it possible to analyze where in the planning process one needs better data and their value.     

Solving multi-criteria scheduling flow shop problem through compromise programming and satisfaction functions

The multi-criteria scheduling problem is one of the main research subjects in the field of multiple objectives programming. Several procedures have been developed to deal with this type of problem where some conflicting criteria have to be optimized simultaneously. The aim of our paper is to propose an aggregation procedure that integrates three different criteria to find the best sequence in a flow shop production environment. The compromise programming model and the concept of satisfaction functions will be utilized to integrate explicitly the manager’s preferences according to the deviations between the achievement and the aspiration levels of the following criteria: Makespan, total flow time and total tardiness.     

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Modeling target volume flows in forest harvest scheduling subject to maximum area restrictions

In forest harvest scheduling problems, one must decide which stands to harvest in each period during a planning horizon. A typical requirement in these problems is a steady flow of harvested timber, mainly to ensure that the industry is able to continue operating with similar levels of machine and labor utilizations. The integer programming approaches described use the so-called volume constraints to impose such a steady yield. These constraints do not directly impose a limit on the global deviation of the volume harvested over the planning horizon or use pre-defined target harvest levels. Addressing volume constraints generally increases the difficulty of solving the integer programming formulations, in particular those proposed for the area restriction model approach. In this paper, we present a new type of volume constraint as well as a multi-objective programming approach to achieve an even flow of timber. We compare the main basic approaches from a computational perspective. The new volume constraints seem to more explicitly control the global deviation of the harvested volume, while the multi-objective approach tends to provide the best profits for a given dispersion of the timber flow. Neither approach substantially changed the computational times involved.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

基于可信性理论的生产计划期望值模型

基于可信性理论,提出一类新的模糊生产计划期望值模型.然后,讨论这个模糊生产计划模型的基本性质.最后,利用这个模糊模型的基本性质我们可以把模糊生产计划期望值模型转化为一个线性规划模型并且设计相应的算法求解模糊生产计划问题的一个数值例子.     

An EPQ model with setup cost and process quality as functions of capital expenditure

This paper considers an economic production quantity (EPQ) model with imperfect production processes, in which the setup cost and process quality are functions of capital expenditure. The mathematical model is derived to investigate the effects of an imperfect production process on the optimal production cycle time when capital investment strategies in setup reduction and process quality improvement are adopted. An efficient procedure is developed to find the optimal production run length, setup cost and process quality. Finally, a numerical example is provided to illustrate the theoretical results. Some managerial implications are also included.     

A planning and scheduling model for onsertion in printed circuit board assembly

A planning and scheduling model is developed for the onsertion-phase in printed circuit board (PCB) assembly. PCBs are manufactured by machines that mount components, such as chips, on a PCB. On an onsertor machine, a certain number of component types can be stored. These components are subsequently used for the production of a certain PCB batch type. This research develops a production planning and scheduling formulation to determine the component–machine allocations, as well as a PCB sequence. Two strategies are proposed; one focusing on minimal number of changeovers (C-strategy), and the other on minimal process time (P-strategy). Both strategies were validated in a pilot study with real company data, with encouraging results for potential implementation.     

Discrete allocation of a linear resource according to a sum-of-products objective

The allocation of a linear resource according to the sum of the returns from independent activities is considered. The return from each activity is given by a product of concave and nondecreasing functions of a single allocation variable. The model can be used, for instance, to describe probabilities of success of several serial tasks, into which an activity is subdivided. An incremental algorithm is defined and conditions are given for the algorithm to generate an optimal solution; otherwise, the problem is solved by a two-step procedure involving the incremental maximization of the return corresponding to a single activity and the combination of the activities by dynamic programming. Examples are given of problems solvable and not solvable by the incremental algorithm.     

A system for the design of short term harvesting strategy

Short term harvesting requires decisions on which stands to harvest, what timber volume to cut, what bucking patterns (how to cut up the logs) to apply to logs in order to obtain products that satisfy demand and which harvesting machinery to use. This is an important problem in forest management and difficult to solve well in satisfying demand, while maximizing net profits. Traditionally, foresters have used manual approaches to find adequate solutions, which has shortcomings both in time spent by analysts and the quality of solutions. Since demand for timber products is defined by length, diameter and quality of each piece, this leads to a complex combinatorial problem in matching supply (standing trees) and demand. We developed one of the few reported approaches for solving the short term harvesting problem based on a computerized system, using a linear programming approach. Determining adequate bucking patterns is not trivial. We develop a column generation approach to generate such patterns. The subproblem is a specially designed branch and bound scheme. The generation of bucking patterns implemented within the LP formulation led to a significant improvement of solutions. We believe this is the first system implemented with this level of detail. This system has been advantageously implemented in several forest companies. The results obtained show improvements obtained by the firms of 5–8% in net revenues over traditional manual approaches.     

大数据背景下水厂自动投矾模型研究

根据某市自来水有限责任公司第二水厂的历史矾耗数据，建立矾耗流量关于原水浊度、温度等的动态矾耗模型. 通过对数据进行处理得到10900个合格且净水效果高效的数据，将筛选出的数据分为训练样本集和测试样本集. 在回归拟合中，通过拟合R2的大小将原水浊度划分为“低浊”“中浊”“高浊”3个区间，利用泰勒展开公式的非线性变量代换分别对3个区间建立不同的多项式回归模型，得到预测正确率约为72%，总的矾耗流量值约减少了9.6%的结果；在随机森林模型中，使用10900个合格数据，利用训练样本集，以“原水浊度”“pH值”“原水流量”和“水温”为输入变量，建立包含2000棵决策树的随机森林模型，得到预测正确率约为44. 21%，总的矾耗流量值增加了0.04%的结果. 从模型对合格数据的拟合优度看，随机森林模型比非线性回归模型效果更好；在平均绝对误差、平均绝对偏差百分比等评价指标上，前者均优于后者；但从历史数据检验的结果，模型的可解读性，模型的操作难度和推广角度看，分段二元非线性回归模型的优势更为突出.     

具有惩罚因子的模糊集约生产计划

研究基于模糊环境下的集约生产计划问题,并设计了带有惩罚因子的模糊优化模型,以实现生产费用和惩罚费用之和最小.通过模糊变量和模糊等式定义的描述,简化了模型,并给出机会约束规划方法进行模型求解的整体步骤.通过仿真结果和灵敏度分析,表明模型和方法的有效性,并为决策者在模糊环境下的决策提供支持.