A dynamical model of water recycling in a mine-processing enterprise

We consider a mine-processing enterprise, which runs a number of production plants. Each plant uses a considerable amount of water which is polluted during the production process. The aim is to determine the optimal amounts of water to be taken from a river or to be pumped back from a waste water reservoir. The problem is decomposed in two tasks. Task 1 is formulated as a time-discrete optimal control model and determines the amounts of water pumped in each period. The solution method used is dynamic programming. While Task 1 has an ecological objective (minimize environmental damage), in Task 2 the aim is to determine, by which pump configurations the desired quantities of water are most efficiently brought to reservoir (with least cost). Because of the special structure of this linear programming problem it can be solved simply by sorting with respect to unit costs.     

Optimal project portfolio selection with carryover constraint

In a typical capital rationing problem, a project portfolio is selected to maximize expected return on investment while adhering to the capital budget constraint. Sometimes projects may be delayed and they have to be funded beyond their planned completion time. This type of ‘unplanned carryovers’ represents a financial obligation to the company. If future years' capital budgets cannot be expanded to cover such obligations, future projects may be cancelled or postponed to fund the unplanned carryover. In this paper, we develop a methodology based on multi-attribute utility theory and chance-constrained programming to optimize portfolio selection subject to the constraints that the selected portfolio does not exceed the available budget and that the carryover of the unspent funds to the next fiscal year does not exceed predetermined limits. We use this technique to select an optimal project portfolio for Lockheed Martin Space Systems' infrastructure investments.     

多层气藏中气体流动问题的新模型及其应用

本文针对气井产量与井筒集是变数时,建立了多层气藏内真实气体渗流问题的新模型,求出了三种典型外边界条件下各储层压力分布精确解,作为特例,又得到了均质气藏内压力分布的精确解并给出了在气田开发中的应用.     

The Development of a Mathematical Model of the Operations of a National Glass Manufacturer

In this paper, a mathematical model of the entire operations of a national glass manufacturer is developed. This includes the float glass manufacture, distribution, storage operations and the technical considerations dictated by the plant as well as the operating procedures. The model is initially for a planning year, and is generated from a ‘monthly model’. This monthly model interconnects with other monthly models primarily via stock flows. The mathematical model is formulated in a unique way that allows certain production aspects to be modelled using a ‘pseudo-continuous’ time frame, rather than a discrete one. The generation of the overall model (as a mixed integer linear programming problem) and its solution is also discussed.     

油藏渗流问题的新模型及其精确解

本文在考虑到井筒储集和表皮效应情况下,利用双重介质渗流方程组建立了油藏渗流问题的新模型,并通过各种极限形式得到了外边界为无限大,有界封闭,有界定压三种情况下二类常见油藏(裂缝性油藏,均质油藏)内压力分布的精确解析表达式.     

Laplace方程有孔椭圆区域边值问题的解析解

本文利用相似流动替换方法 ,解决了中心有圆孔的椭园形区域上 Laplace方程第一类边值问题 ;采用分区域解法 ,给出了中心有椭园孔的椭园形区域上 Laplace方程第一类边值问题的解析通解 .这一结果在许多工程领域有重要应用 ,本文给出了油藏工程实例     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Carryover sequence-dependent group scheduling with the integration of internal and external setup times

This paper addresses a group scheduling problem in a two-machine flow shop with a bicriteria objective and carryover sequence-dependent setup times. This special type of group scheduling problem typically arises in the assembly of printed circuit boards (PCBs). The objective is to sequence all board types in a board group as well as board groups themselves in a way that the objective function is minimized. We introduce the carryover sequence-dependent setup on machines, and call it internal setup. As an opportunity for manufacturers to decrease the costs, the focus is to completely eliminate the role of the kitting staff. Thus, we introduce the external setup (kitting) time for the next board group and require it to be performed by the machine operator during the time he is idle. Consequently, the internal and external setup times are integrated in this research, and to the best of our knowledge it is for the first time a research on PCB group scheduling is performed by integrating both setups. In order to solve this problem, first a mathematical model is developed. Then a heuristic together with two other meta-heuristic algorithms (one based on tabu search and the other based on genetic algorithm) are proposed and their efficiency and effectiveness on several problems are tested. Also a statistical experimental design is performed in order to evaluate the impact of different factors on the performance of the algorithms.     

Reservoir storage with skew inflows

The storage problem for infinite reservoirs where annual inflows are distributed as independent gamma variables is treated in this paper. After having determined the distribution of the water content in the reservoir under consideration for a given period, an attempt was made to derive the expressions for the first four moments of the surplus and deficit, and then to approximate their distributions by the Type I curve using the Pearson criterion. The expected value of the range was also derived, and its variance was approximated by a linear equation of the reservoir life. Finally, the distribution of the range was approximated by the Type III curve.     

仓库容量有限条件下的随机存贮管理2

讨论了仓库容量有限条件下的随机存贮管理优化问题,认为时间是连续分布的.对于存贮一种商品的问题,根据订货点和自己仓库容量的关系分两种情况讨论,得到平均损失费与订货点、到货时间之间的关系式,利用实测数据拟合出到货时间的概率密度,建立了以平均损失费用的数学期望为目标函数的最优化模型,并使用MATLAB数学软件进行求解,得到三种商品的最优订货点分别为41,37和36.经过分析得知仓库容量与销售速率的比例、单位商品的损失费均对确定订货点都有重要影响.对于存贮多种商品的问题,根据到货时间的取值范围与两个时间临界点(销售完租借仓库中某种商品的时间和销售完所有该种商品的时间)之间的位置关系,将每种商品分为六种情况,m种商品组合起来,就有6()种不同情况,在此基础上,以m种商品的总体平均损失费用的数学期望作为目标函数,建立问题的最优化模型.针对题目中给出的三种商品的情形进行求解,得到最优订货点L*=4.807.最后,对销售速率随机的情形建立模型并进行了讨论.     

Fleet routing position-based model for inventory pickup under production shutdown

This paper addresses the problem of collecting inventory of production at various plants having limited storage capacity, violation of which forces plant shutdowns. The production at plants is continuous (with known rates) and a fleet of vehicles need to be scheduled to transport the commodity from plants to a central storage or depot, possibly making multiple pickups at a given plant to avoid shutdown. One operational objective is to achieve the highest possible rate of product retrieval at the depot, relative to the total travel time of the fleet. This problem is a variant (and generalization) of the inventory routing problem. The motivating application for this paper is barge scheduling for oil pickup from off-shore oil-producing platforms with limited holding capacity, where shutdowns are prohibitively expensive. We develop a new model that is fundamentally different from standard node-arc or path formulations in the literature. The proposed model is based on assigning a unique position to each vehicle visit at a node in a chronological sequence of vehicle-nodal visits. This approach leads to substantial flexibility in modeling multiple visits to a node using multiple vehicles, while controlling the number of binary decision variables. Consequently, our position-based model solves larger model instances significantly more efficiently than the node-arc counterpart. Computational experience of the proposed model with the off-shore barge scheduling application is reported.     

双重介质分形油藏渗流问题

将油井有效半径引入双重介质分形油藏渗流问题的内边界之中,从而建立了双重介质分形油藏的一种渗流模型,并在考虑了井筒储集和表皮效应的情况求得了外边界为无限大、有界封闭和有界定压三种情况下双重介质分形油藏压力分布的精确解析表达式,利用拉氏数值反演Stehfest方法分析了双重介质分形油藏压力动态特征,讨论了各种参数对压力动态的影响。     

On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects

We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing the classical model of Nerlove and Arrow (Economica 29:129–142, 1962). In particular, we allow the dynamics of the product goodwill to depend on its past values, as well as previous advertising levels. Building on previous work (Gozzi and Marinelli in Lect. Notes Pure Appl. Math., vol. 245, pp. 133–148, 2006), the optimal advertising model is formulated as an infinite-dimensional stochastic control problem. We obtain (partial) regularity as well as approximation results for the corresponding value function. Under specific structural assumptions, we study the effects of delays on the value function and optimal strategy. In the absence of carryover effects, since the value function and the optimal advertising policy can be characterized in terms of the solution of the associated HJB equation, we obtain sharper characterizations of the optimal policy.     

Optimization of power production and costs in microgrids

This paper proposes a mathematical formulation for energy management in a connected microgrid. The aim is determining the optimal operating strategy for energy storage, to fulfil a time-varying energy demand and operational constraints while achieving a tradeoff between microgrid running costs and energy storage system life. The microgrid is composed by various renewable power production plants, storage devices and controllable loads, and has the ability to increase energy efficiency and reduce costs for energy purchasing from the main grid. The problem is formulated as a mixed-integer linear optimization problem. The optimization is aimed at minimizing the overall cost function of the system while satisfying the customer demand and safety of the electrical network. A case study of an existing microgrid is investigated: the microgrid consists of a photovoltaic and a hydroelectric power plant, a battery storage, an office building and an industrial facility. The optimization problem is solved in an efficient way by using commercial software. Simulation results show the feasibility and the effectiveness of the proposed approach to satisfy the load and reduce total costs.     

Optimal Loading Sequences for Fresh-Apple Storage Facilities

This paper reports on the use of a dynamic programming model to sequence the loading of storage facilities at an apple-packing plant operating in the state of New York, USA. The post-harvest quality of perishable agricultural products is significantly affected by delays in getting the product under storage conditions. This model minimizes this delay by identifying the optimal order in which storage facilities should be loaded. An optimal sequence is identified which is insensitive to changes in the relative importance of storage facilities, but which is influenced by differences in the deterioration rate among apple varieties.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

New approach for describing transient pressure response generated by horizontal wells of arbitrary geometry

This paper is aimed at developing a methodology for studying the transient pressure behavior of horizontal wells with any curvilinear trajectory in an isotropic/anisotropic arbitrarily shaped reservoir. This methodology employs generalized functions to represent the tortuous horizontal well. A particular way of removing the singularities involved in the partial differential equation is based on reducing the original problem to the conventional solution of the homogeneous diffusivity equation under any given initial and boundary conditions. The Green function method and any standard numerical technique are combined in a single computational strategy to obtain the transient pressure response generated by a curved and twisted horizontal well in reservoirs with irregular boundaries. Analytical methods can be also used, whenever possible, to solve the reduced problem. This proposal can be easily broadened to analyze the performance of the pressure transient of any kind of reservoir sources or sinks that can be modeled using generalized functions. Some models are presented.     

A Three-Dimensional Optimization Problem in Water-Resources Engineering

The problem under consideration is related to a system consisting of two storage facilities in series. Part of the water reaching the upstream reservoir may be diverted for storage in the downstream facility. However, there is a certain lag between the time when water is released from the upper reservoir and the time when it is available for utilization in the lower one. Thus the vector describing the state of the system at any one time consists of three elements:

1. a)
   amount of water stored in the upstream reservoir;
    
2. b)
   amount of water stored in the downstream reservoir;
    
3. c)
   amount of water in transit.
    

An optimum operating policy for the system had to be derived.The method of dynamic programming was applied in the analysis of this problem. The algorithm obtained was programmed for solution on an IBM 7090 digital computer. Optimal policies were obtained for each admissible state of the system.     

Stochastic modelling of reservoir operations

The nature of hydrologic parameters in reservoir management models is uncertain. In mathematical programming models the uncertainties are dealt with either indirectly (sensitivity analysis of a deterministic model) or directly by applying a chance-constrained type of formulation or some of the stochastic programming techniques (LP and DP based models). Various approaches are reviewed in the paper. Moran's theory of storage is an alternative stochastic modelling approach to mathematical programming techniques. The basis of the approach and its application is presented. Reliability programming is a stochastic technique based on the chance-constrained approach, where the reliabilities of the chance constraints are considered as extra decision variables in the model. The problem of random event treatment in the reservoir management model formulation using reliability programming is addressed in this paper.