A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

A supply chain model for imperfect production system with stochastic lead time demand

This study deals an integrated manufacturer-buyer supply chain system for imperfect production under stochastic lead time demand.Here,defective rate has been followed as a function of production rate.Also,the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand rate.Buyer purchases the products from the manufacturer.Also,we assume that shortage during the lead time is permitted and demand during the shortage period is fully backordered.The objective is to derive the optimal production rate,ordering quantity and to maximize joint total profit.Basically,two different models for different probability distribution functions of stochastic lead time demand have been developed.Some numerical examples are provided to show the applicability of the proposed models comparing the optimum average profits.Finally,sensitive analysis,conclusion and future researches are presented.

Multi-Item EOQ Model with Both Demand-Dependent Unit Cost and Varying Leading Time via Geometric Programming

The objective of this paper is to derive the analytical solution of the EOQ model of multiple items with both demand-dependent unit cost and leading time using geometric programming approach. The varying purchase and leading time crashing costs are considered to be continuous functions of demand rate and leading time, respectively. The researchers deduce the optimal order quantity, the demand rate and the leading time as decision variables then the optimal total cost is obtained.

Combined heuristics for determining order quantity under time-varying demands

The time-varying demands for a certain period are often assumed to be less than the basic economic order quantity （EOQ） so that total replenishment quantity rather than economic order quantity is normally considered by most of the heuristics. This acticle focuses on a combined heuristics method for determining order quantity under generalized time-varying demands. The independent policy （IP）, abnormal independent policy （AIP） and dependent policies are studied and compared. Using the concepts of normal/abnormal periods and the properties of dependent policies, a dependent policy-based heuristics （DPH） is proposed for solving the order quantity problems with a kind of time-varying demands pattern under which the first period is normal. By merging the Silver-Meal （S-M） heuristics and the dependent policy-based heuristics （DPH）, a combined heuristics （DPH/S-M） is developed for solving order quantity problems with generalized time-varying demands. The experimentation shows that （1） for the problem with one normal period, no matter which position the normal period stands, the DPH/S-M could not guarantee better than the S-M heuristics, however it is superior to the S-M heuristics in the case that the demands in the abnormal periods are in descending order, and （2） The DPH/S-M is superior to the S-M heuristics for problems with more than one normal period, and the more the number of normal periods, the greater the improvements.

An Inventory Model for Deteriorating Items with Exponential Declining Demand and Time-Varying Holding Cost

In the present paper, a total optimal cost of an inventory model with exponential declining demand and constant deterioration is considered. The time-varying holding cost is a linear function of time. Shortages are not allowed. The items (like food grains, fashion apparels and electronic equipments) have fixed shelf-life which decreases with time during the end of the season. A numerical example is presented to demonstrate the model and the sensitivity analysis of various parameters is carried out.

An Ordering Policy for Deteriorating Items with Time-Dependent Quadratic Demand and Salvage Value under Permissible Delay in Payment

The article deals with an economic order quantity (EOQ) inventory model for deteriorating items in which the supplier provides the purchaser a permissible delay in payment. This is so when deterioration of units in the inventory is subject to constant deterioration rate, demand rate is quadratic function of time and salvage value is associated with the deteriorated units. Shortages in the system are not allowed to occur. A mathematical formulation is developed when the supplier offers a permissible delay period to the customers under two circumstances: 1) when delay period is less than the cycle of time;and 2) when delay period is greater than the cycle of time. The method is suitable for the items like state-of-the-art aircrafts, super computers, laptops, android mobiles, seasonal items and machines and their spare parts. A solution procedure algorithm is given for finding the optimal order quantity which minimizes the total cost of an inventory system. The article includes numerical examples to support the effectiveness of the developed model. Finally, sensitivity analysis on some parameters on optimal solution is provided.

Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.

A Time Dependent Inventory Model for Exponential Demand Rate with Constant Production Where Shelf-Life of the Product Is Finite

In this paper a time dependent inventory model is developed on the basis of constant production rate and market demands which are exponentially decreasing. It advances in quest of total average optimum cost considering those products which have finite shelf-life. The model also considers the small amount of decay. Without having any sort of backlogs, production starts. Reaching at the desired level of inventories, it stops production. After that due to demands along with the deterioration of the items it initiates its depletion and after certain periods the inventory gets zero. The decay of the products is level dependent. The objective of this paper is to find out the optimum inventory cost and optimum time cycle. The model has also been justified with proving the convex property and by giving a numerical example.

An Inventory Model for Perishable Items with Time Varying Stock Dependent Demand and Trade Credit under Inflation

In the classical inventory models, it is assumed that the retailer pays to the supplier as soon as he received the items and in such cases the supplier offers a cash discount or credit period (permis-sible delay) to the retailer. In this paper we presented an inventory model for perishable items with time varying stock dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer and the length of credit period is dependent on the order quantity. The purpose of our study is to minimize the present value of retailer’s total cost. Numerical examples are also given to demonstrate the presented mode.

考虑随机需求的高铁快递运输计划优化方法

为了充分利用高速铁路非高峰期的列车运输能力,提升高速铁路运营的经济效益,研究载客动车组客货共运模式下的高铁快递运输计划优化问题。首先,考虑高铁快递运输需求的时效性与随机性,以最大化高铁快递运营企业期望总利润为优化目标,同时满足列车运输能力、车站装卸效率、标准箱到发量守恒等约束,构建高速铁路快递运输计划优化的2阶段随机规划模型。在第1阶段,以最大化高铁快运期望总利润为目标,确定各列车的运输能力分配计划;在第2阶段,根据第1阶段获得的列车运输能力分配计划,确定随机需求场景下的高铁快递实际装运方案,使该场景下的运营收益达到最大。其次,基于蒙特卡洛模拟随机生成需求场景,采用反向消减算法(BRA)将2阶段随机规划模型转化为包含有限场景数的确定性整数线性规划模型,从而调用商业求解器GUROBI进行求解。最后,以宁杭高速铁路为背景进行算例分析,验证模型和算法的有效性。结果表明,相较于基于确定性需求得到的运输计划,利用随机规划方法得到的方案更能适应需求的随机性,从而达到更好的盈利效果,同时可以兼顾服务水平与企业收益,适用于实际运营中高铁快递运输计划的设计与优化。

支撑新能源电力系统灵活性需求的用户侧资源应用与关键技术

伴随着传统电力系统向以新能源为主体的新型电力系统转型升级,高比例新能源的接入和传统机组占比下降导致电力系统灵活性产生缺额。电动汽车、数据中心、P2X(power-to-X)等需求侧资源可以在多时间尺度为电力系统提供灵活性,是新型电力系统灵活性的重要组成部分。该文首先描述高比例新能源背景下输电网和配电网在不同时间尺度的灵活性需求,然后对比总结了典型需求侧资源的调节特性与应用实践,研究了需求侧资源在支撑高比例新能源输电网和配电网中运行、规划2个层面多时间尺度灵活性需求的应用场景。最后针对未来需求侧资源的研究重点,从聚合技术、电碳协同优化调控策略、可信调节能力量化和通信与信息交换标准等角度,对支撑新型电力系统需求侧资源应用的关键技术进行了总结与展望。

基于需求模式自适应匹配的间歇性需求预测方法

大型制造企业售后配件的需求分布稀疏、波动性大,需求频率和需求数量不确定性较高,序列呈现出典型的间歇性特点。在实际运维中,配件需求在频率和数量方面存在较大波动,从而产生变化多样的需求模式,而现有间歇性需求预测主要采用单一或静态组合的固定预测模型,难以充分挖掘不同需求模式下需求序列的演化规律,预测精度和稳定性均难以保证。为解决上述问题,提出一种基于需求模式自适应匹配的间歇性需求预测方法,通过动态识别和匹配需求模式提升间歇性序列预测效果。该方法包括两个阶段:在模型训练阶段,首先,根据配件历史需求数据的间歇性特征,将它划分为需求量序列和间隔量序列,并对两类序列分别进行聚类,以捕获每类序列对应的不同需求和间隔模式;其次,建立包含统计学分析模型、浅层机器学习模型及深度学习模型的预测模型库,测试各模型对每种需求模式的预测效果,识别并标记每类需求模式的最优预测模型。在预测阶段,将待预测序列划分为需求量序列和间隔量序列,确定需求模式并匹配最佳预测模型,进而将需求量和间隔量的预测值合并,形成最终预测结果。在美国汽车公司和英国空军的间歇性配件需求数据集上的实验结果表明,所提方法可适用于不同需求模式的配件历史数据,通过自适应匹配需求模式和最优预测模型,有效提升了预测精度。

融合时频空间特征的土石坝地震易损性分析改进MLP模型研究

针对现有地震易损性分析中采用的峰值加速度、峰值速度等地震动指标未能充分反映地震动复杂的时频空间特征,且现有基于对数空间线性函数关系假设的地震需求模型难以揭示地震动指标与地震响应间复杂非线性关系的问题,提出一种融合时频空间特征的土石坝地震易损性改进多层感知机(Multi Layer Perceptron,MLP)模型。该模型利用胶囊网络(Capsule Network,CapsNet)能够充分捕捉和表征目标特征空间位置分布的优势,从地震动小波时频图中提取反映地震动时频空间分布的深层特征,并以特征拼接的方式与既有特征进行融合,构建地震动融合指标;进一步地,采用树形Parzen优化算法(Tree structured Parzen Estimator,TPE)对MLP的神经元数量、学习率等超参数进行优化,提出基于TPE-MLP的土石坝地震需求模型,以反映地震动融合指标与地震响应间的复杂非线性关系,进而实现土石坝地震易损性的可靠分析。案例分析表明,相比于既有地震动指标,基于地震动时频空间特征融合指标的土石坝地震需求模型的MAE降低了40.5%,表明了所提模型的可靠性和优越性。

考虑分时电价下需求响应的用户侧储能优化配置

针对用户侧储能在投资与运行方面经济性不足的问题,提出一种考虑分时电价下需求响应的用户侧储能规划与运行两阶段优化策略.第一阶段通过建立分时电价优化模型,采用粒子群(PSO)和序列二次规划(SQP)混合算法求解得出分时电价策略,第二阶段基于第一阶段得出的分时电价策略建立考虑两个时间尺度的储能双层优化模型,上层模型以最大化全寿命周期净收益为目标优化长时间尺度的储能配置,下层模型以最大化日运行收益为目标优化短时间尺度的储能运行,结合混合整数线性规划方法和KKT条件,调用CPLEX求解器进行求解,通过两阶段的联合优化,实现用户侧储能配置和运行收益综合最优.最后,结合实例进行仿真,结果表明所提方法可以有效提高用户侧储能系统的经济性.

基于张量表示的间歇性序列自适应区间预测

在实际业务中,配件需求发生随机、需求量波动大,配件序列数据呈现明显的间歇性分布,同时由于人工报单失误或特殊事件等因素的影响,实际配件需求易发生异常变化,导致传统的时间序列预测方法难以捕捉配件需求量的演化规律,预测结果不确定性高、可靠性不足。为解决上述问题,提出了一种基于张量表示的间歇性序列自适应区间预测方法。首先,利用层次聚类,基于间歇性序列的平均需求间隔和平方变异系数指标筛选相似序列形成序列簇,用于提取簇内公共需求演化信息,增加可预测性;其次,通过张量分解重构原始需求序列,在最大限度保留序列核心信息的前提下平滑序列中的异常值;最后,构建一种自适应预测区间算法,通过动态更新机制得到配件需求量的预测值和预测区间,以确保结果的可靠性。利用某大型轨道交通制造企业实际售后数据进行验证,与现有典型时间序列预测方法相比,所提方法可有效挖掘不同特点间歇性序列的演化趋势,提高小样本间歇性序列的预测精度。实验结果表明:所提方法在间歇性特有指标均方根标准误差(RMSSE)上,相较于需求预测主流的深度学习方法平均降低了0.32,且当预测结果出现失真时,可提供一个可靠的弹性预测区间,为实际应用中企业智能备件计划决策提供了一种新的解决方案。

考虑负荷不确定性的微电网多时间尺度调度策略

随着分布式能源渗透率增高,微电网内负荷的不确定性及能源响应负荷波动的时间尺度不同为系统灵活调度带来了挑战。电动汽车(EV)因其快速响应能力,合理安排其充放电行为可以有效缓解微电网的供电压力,平滑负荷曲线。在以经济运行最优为目标下,提出一种考虑负荷不确定性及电动汽车资源的微电网多时间尺度调度优化模型。在日前调度阶段,结合需求响应技术以风光消纳最优为目标,优化电动汽车资源的充放电行为,确定各种资源调度安排;在实时调度阶段,负荷预测出现偏差时,将储能电池、电动汽车资源作为灵活性资源,实时滚动,对日前调度计划做出修正。以某一微电网进行仿真验证,结果表明所提模型能实现风光全部消纳,有效减少负荷曲线的峰谷差,提高其应对负荷不确定性的能力。

考虑异方差性的城市电网电动汽车充电负荷预测

随着电动汽车渗透率的上升,充电设施和充电负荷将成为城市电网发展的关键增长点。然而,大量电动汽车集中充电导致负荷波动剧烈,并加剧了负荷序列的异方差性。为此,提出了一种考虑异方差性的电动汽车充电负荷预测模型。首先,通过图形检测法识别评估充电负荷序列的异方差性,综合负荷变化趋势分析可能导致异方差的原因;其次,通过时间序列分解剥离原始序列中的异方差,挖掘负荷分量与气候、温度的关联关系;最后,构建针对异方差性的中长期充电负荷预测框架,融合长序列预测模型,对负荷进行分解与重构。仿真结果表明,所提模型提高了负荷预测的准确性,为城市电网的合理规划与稳定运行提供了重要支持。

考虑需求响应及不确定性的综合能源优化调度

如何在区域综合能源系统中建立有效的需求侧模型,对于需求响应政策的实施至关重要。为提高用户参与需求响应积极性,引入实时定价机制,同时考虑系统的经济低碳性和电气热用户的用能满意度,构建兼顾系统和用户利益的综合需求响应主从博弈模型。针对用户参与需求响应的不确定性,引入贝叶斯方法更新负荷曲线。算例分析表明,所提博弈模型及贝叶斯方法能够有效平衡系统和用户之间的利益,提高了综合需求响应的可靠性。

基于耐震时程法的大跨度钢桁拱桥易损性分析

为克服复杂桥梁结构在地震易损性评估时需要进行大量非线性时程分析的不足,提出一种基于耐震时程法(ETM)的易损性分析方法用于桥梁结构易损性的快速评估。首先,基于ETM合成了若干条耐震时程曲线(ETA),将其与概率地震需求模型相结合。随后,考虑桥梁模型的不确定性,借助OpenSEES建立一座大跨度上承式钢桁拱桥的有限元模型样本库,并分别使用ETM和增量动力分析(IDA)法对其中的桥梁模型进行时程分析并得到典型构件的易损性曲线,将二者结果进行对比以验证ETM的适用性。最后,利用验证后的方法分析该桥各构件纵向地震下的易损性。结果表明:ETM与IDA所得结果的相对误差基本控制在5%以内,说明基于耐震时程的易损性方法可有效兼顾分析效率和计算精度;在纵向地震作用下,上承式钢桁拱桥的引桥墩和交界墩在50%中等损伤概率下的地震动强度指标仅为0.597g和0.972g,远小于其他构件,说明混凝土桥墩为最易损构件;拱肋和立柱在地震作用下发生破坏的概率较小,但拱顶和拱脚相对薄弱;设置固定支座的短立柱在纵向地震作用下易发生损伤,可通过改变拱上立柱的支座布置形式进行优化。

基于时变价格弹性矩阵的深谷电价多目标定价策略

随着碳中和、碳达峰目标的提出,构建高比例新能源的新型电力系统已成为未来能源电力的发展形态,由此导致的高比例新能源渗透使系统净负荷曲线呈现剧烈的波动性和显著的深谷特征,对电力系统安全运行以及供需平衡提出了新挑战。为此,提出了一种基于时变价格弹性矩阵的需求侧深谷电价多目标定价模型。首先,确立基于模糊隶属度的深谷时段划分方法,并利用贝叶斯判别法对时段划分结果进行合理性评估。其次,针对用户需求响应的动态性,建立具有时变特征的价格弹性矩阵模型衡量用户的响应程度。最后,以用户满意度和系统峰谷差作为待优化的两个目标,建立多目标混合整数规划的深谷电价定价模型,并用非支配排序遗传算法求解模型并得到其Pareto最优解。为了检验所提模型的有效性,将其应用于中国华东地区某省的实际场景进行仿真分析。结果表明,上述模型可在高比例新能源渗透情景下降低峰谷差,促进用户用电行为向深谷时段转移,缓解电力系统在深谷时段的运行压力。