OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

Optimal preventive maintenance,protection, and replacement of a revenue-earning asset

The problem of determining the optimal pattern of expenditure on preventive maintenance or protection for a revenue-earning asset subject to catastrophic breakdown or destruction is discussed. It is assumed that the probability of breakdown at any time depends on the age of the asset and on the current rate of prevention expenditure. The objective considered is the maximization of the expected present value of revenues earned net of prevention and replacement costs. Three distinct cases are discussed: (a) when revenue is earned only until breakdown; (b) when there is automatic replacement following a breakdown; and (c) when there is the option of periodic replacement. Use of the Pontryagin maximum principle enables the determination of the optimal prevention schedules in all cases. In addition, when periodic replacement is possible the optimal replacement interval can be determined. Numerical methods are required to obtain solutions.     

Ordered Site Access and Optimal Forest Rotation

The ordered-site-access model of forest harvesting formulated for once-and-for-all forests in [7] is extended to the case of ongoing forests. The economic content of the corresponding optimal harvest schedule is delineated. For an infinite harvest sequence, the optimal schedule is shown to include the classical Faustmann rotation as a special case, and the effect of net revenue functions changing with harvest is studied. For the practically more important case of planning for a finite sequence of [INLINEEQUATION] harvests, the optimal harvest schedule is determined for a Faustmann environment with limited, and unlimited harvesting capacity, and its rapid convergence to the Faustmann rotation is shown for the case of unlimited harvesting capacity. The case of harvest cost functions varying with harvest rate is discussed. The existence of a steady-state optimal harvesting schedule (involving a pathwise uniform age distribution) for the more realistic Heaps-Neher environment and its relation to the Faustmann rotation are analyzed. The evolution of the optimal harvest schedule for a finite harvest sequence in a Heaps-Neher environment toward this steady-state (Faustmann type) rotation is demonstrated.     

A fuzzy multi-objective programming for optimization of fire station locations through genetic algorithms

Location of fire stations is an important factor in its fire protection capability. This paper aims to determine the optimal location of fire station facilities. The proposed method is the combination of a fuzzy multi-objective programming and a genetic algorithm. The original fuzzy multiple objectives are appropriately converted to a single unified ‘min–max’ goal, which makes it easy to apply a genetic algorithm for the problem solving. Compared with the existing methods of fire station location our approach has three distinguish features: (1) considering fuzzy nature of a decision maker (DM) in the location optimization model; (2) fully considering the demands for the facilities from the areas with various fire risk categories; (3) being more understandable and practical to DM. The case study was based on the data collected from the Derbyshire fire and rescue service and used to illustrate the application of the method for the optimization of fire station locations.     

Human resources scheduling to improve the product quality according to exhaustion limit

The role of human resources in manufacturing systems is very significant, and without efficient human resources we encounter high-price products with low quality. To improve the efficiency of human resources, we need to provide an optimal working schedule for each worker in production period. In this paper, we proposed a mixed-integer nonlinear model to find the best working schedule based on product quality cost and workers reliability. In this model, if the worker’s exhaustion level reaches a specific limit, the worker can rest to increase his reliability level and an accommodator should work instead of him. Since the proposed model is NP-hard, we used an artificial immune system to provide the best working schedule. The results indicate that this model can provide efficient and effective human resources schedule in manufacturing systems.     

A stochastic approach to optimize Maritime pine (Pinus pinaster Ait.) stand management scheduling under fire risk. An application in Portugal

The paper discusses research aiming at the development of a management scheduling model for even-aged stands that may take into consideration fuel treatments to address the risk of wildfires. A Stochastic dynamic programming (SDP) approach is proposed to determine the policy (e.g. the fuel treatment and thinning schedules and the rotation age) that produces the maximum expected discounted net revenue. Fuel treatment activities encompass shrub cleanings. Emphasis was on combining a deterministic stand-level growth and yield model with wildfire occurrence and damage models to design a SDP network. SDP stages are defined by age and state variables include both the stand basal area and the number of years since the last fuel treatment. Fire occurrence and damage scenarios are addressed at each stage. Results from an application to Maritime pine (Pinus pinaster Ait.) stand management scheduling in Leiria National Forest, Portugal, are presented. Results suggest that the modeling strategy may help assess the impact of wildfire risk on the optimal stand management schedule. They confirm that the maximum expected discounted net revenues decreases. Further, albeit some timber may be salvaged after the wildfire, rotation age also decreases when the risk of fire is considered. Finally, they provide interesting insights about the role of thinning and fuel treatment policies in mitigating risk.     

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.     

Cost optimal periodic train scheduling

For real world railroad networks, we consider minimizing operational cost of train schedules which depend on choosing different train types of diverse speed and cost. We develop a mixed integer linear programming model for this train scheduling problem. For practical problem sizes, it seems to be impossible to directly solve the model within a reasonable amount of time. However, suitable decomposition leads to much better performance. In the first part of the decomposition, only the train type related constraints stay active. In the second part, using an optimal solution of this relaxation, we select and fix train types and try to generate a train schedule satisfying the remaining constraints. This decomposition idea provides the cornerstone for an algorithm integrating cutting planes and branch-and-bound. We present computational results for railroad networks from Germany and the Netherlands.     

An optimal replenishment policy for deteriorating items with effective investment in preservation technology

In this paper, considering the amount invested in preservation technology and the replenishment schedule as decision variables, we formulate an inventory model with a time-varying rate of deterioration and partial backlogging. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, under given replenishment schedule, we show that the total profit per unit time is a concave function of preservation technology cost. We then provide a simple algorithm to figure out the optimal preservation technology cost and replenishment schedule for the proposed model. We use numerical examples to illustrate the model.     

考虑政府补贴的原料回收与有机肥生产供应链博弈分析

保护环境是政府的重要工作职责。为了减少养殖带来的环境污染,本文考虑了由养殖户、制造商、市场组成的原料回收-有机肥生产供应链和政府补贴政策,建立了养殖户-制造商博弈决策模型,以及供应链-政府决策博弈模型,给出了最优解的表达式,并分析了养殖户收益、制造商收益、政府支出的影响因素。结果表明,实施补贴政策情形下,养殖户和制造商收益都得到提升,政府在环境方面的支出可以减少;进一步分析表明,政府直接补贴制造商的效果更好。本文给出了考虑环保需求和存在政府补贴的供应链运作与博弈优化策略,研究结论对于相关企业提高收益和政府部门制定补贴政策具有一定的指导意义。     

Optimal production and abatement policies of a firm

A pollution control problem from the employment and environmental policy point of view for a profit maximizing firm is studied. Two versions of the model are considered: model A with emission certificates and model B with environmental standards. The nature of the optimal solution for both a static and a dynamic model is analyzed and an economic interpretation is given. Using the theory of optimal control it can be shown that along the optimal path the increasing expenditure in pollution control is accompanied by an increasing stock of employees. The saddle point property of the equilibrium is established and the relation between the level of pollution in the stationary state and the charge per unit of effluents is derived. A sensitivity analysis of equilibrium values with respect to the changes in the parameters of the model is presented.     

A Cutting Stock and Scheduling Problem in the Copper Industry

This case study was carried out for Thomas Bolton Ltd, a copper component manufacturer. The focus was on the first major production operation that is carried out in the foundry. This operation consists of three processes — melting scrap metal, casting it as ‘logs’ and cutting logs into ‘billets’. The timely production of the billets is essential as these feed a bottleneck process. The objective of the study was to investigate alternative methods of generating a production plan for the foundry that minimized costs whilst meeting the demand for billets at the bottleneck. The production plan was required to include a daily production schedule and a list of the cutting patterns to use when cutting the logs into billets. Thus, both the scheduling and cutting stock problems were addressed. A two-stage solution procedure was proposed. Alternative heuristic methods were investigated at the first stage and an optimal solution using Integer Programming (IP) was proposed for the second stage. It is shown that current performance could be improved using all of the heuristics considered at the first stage, but that using an IP-based heuristic method gives the best results.     

A MIP formulation for the minmax regret total completion time in scheduling with unrelated parallel machines

The paper proposes a Mixed Integer Programming (MIP) formulation of the scheduling problem with total flow criterion on a set of parallel unrelated machines under an uncertainty context about the processing times. To model the problem we assume that lower and upper bounds are known for each processing time. In this context we consider an optimal minmax regret schedule as a suitable approximation to the optimal schedule under an arbitrary choice of the possible processing times.     

A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.     

Robust cutting parameters optimization for production time via computer experiment

This study intends to determine the optimal cutting parameters required to minimize the cutting time while maintaining an acceptable quality level. Usually, the equation for predicting cutting time is unknown during the early stages of cutting operations. This equation can be determined by studying the output cutting times vs. input cutting parameters through CATIA software, with assistance from the statistical method, response surface methodology (RSM). Then, the equation is formulated as an objective function in the form of mathematical programming (MP) to determine the optimal cutting parameters so that the cutting time is minimized. The formulation in MP also includes the constraints of feasible ranges for process capability consideration and surface roughness for quality concerns. The important ranking obtained from the statistical method in cooperation with the optimal solutions found from MP can also be used as references for the possibility of robust design improvements.     

Supply chain scheduling: Just-in-time environment

We study the benefits of coordinated decision making in a supply chain consisting of a manufacturer, a distributor, and several retailers. The distributor bundles finished goods produced by the manufacturer and delivers them to the retailers to meet their demands. The distributor is responsible for managing finished goods inventory. An optimal production schedule of the manufacturer, if imposed on the distributor, may result in an increased inventory holding cost for the distributor. On the other hand, an optimal distribution schedule of the distributor, if imposed on the manufacturer, may result in an increased production cost for the manufacturer. In this paper we develop mathematical models for individual optimization goals of the two partners and compare the results of these models with the results obtained for a joint optimization model at the system level. We investigate the computational complexities of these scheduling problems. The experimental results indicate that substantial cost savings can be achieved at the system level by joint optimization. We also study conflict and cooperation issues in the supply chain. The cost of conflict of a supply chain partner is a measure of the amount by which the unconstrained optimal cost increases when a decision is to be made under the scheduling constraint imposed by the other partner. We quantify these conflicts and show that the cost of conflicts are significant. We also show that a cooperative decision will generate a positive surplus in the system which can be shared by the two partners to make cooperation and coordination strategy more attractive.     

Retailer’s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging

Pricing is a major strategy for a retailer to obtain its maximum profit. Therefore, in this paper, we establish an economic order quantity model for a retailer to determine its optimal selling price, replenishment number and replenishment schedule with partial backlogging. We first prove that the optimal replenishment schedule not only exists but also is unique, for any given selling price. Next, we show that the total profit is a concave function of p when the replenishment number and schedule are given. We then provide a simple algorithm to find the optimal selling price, replenishment number and replenishment timing for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm.     

最佳灰色回归组合模型及其在中国火灾预测中的应用

火灾每年给国家和人民生命财产造成巨大损失.火灾现象具有随机性、模糊性,是个复杂的灰色系统行为.研究火灾发生规律及发展趋势,具有实用价值.为此,首先给出最小二乘估计(LSE)意义下的最佳组合预测模型的定义,并求得组合模型的权的公式和证明权的唯一性.其次,用回归分析方法建立多个回归模型,并按以下三条标准:①回归指数(或相关系数)r大、②系统误差s小、③模型精度p高,选定最佳非线性回归模型;用灰色理论建立多个灰色模型,并按以下三条标准:①后验差比值c小、②小误差概率P大、③预测关联度ξ大,选定最佳灰色模型;再用最小二乘法将最佳回归模型与最佳灰色模型有机地结合起来建立的中国火灾最佳灰色回归组合预测模型.最佳灰色回归组合预测模型综合利用前两者提供的不同的有用信息,改善了单一模型的局限性,提高了模型的预测精度,减少了预测误差,使预测效果更佳.组合模型预测中国年火灾起数处于动态增长过程.     

Modelling impact of advertising and optimizing advertising policy: an application in recreation

This paper deals with the problem of the desirable level of advertising expenditure, the optimal distribution of this expenditure in time and the allocation over the media: TV, radio and newspaper for a recreation park in the Netherlands.Although the model id developed for the specific situation of this park, in principle it can be applied in all situations where the interest is in short-term (day-by-day) effects of promotional activities on sales. Examples are: other situations in the recreation and leisure business, cultural events (theatre, cinema) and sales promotions (e.g. weekend offerings) for products in supermarkets.First a model was specified and estimated that relates number of visitors to advertising effort. It also takes into account non-advertising variables that effect the number of visitors.Then this model was used in a heuristic advertising planning procedure, which by means of incremental analysis, for a given budget level searches for the optimal allocation of the advertising budget over media and time.With this procedure, ways to readjust the advertising policy were found: by allocating the budget differently over media and time and by changing the overall budget level.Several recommendations were made to the management of the park, a number of which have already been implemented.