考虑货架存放期的经济批量排产问题的改良算法

经济批量排产问题是关于在单一设备上协调地、周期性地生产多种产品的问题.其解要求在生产准备与库存总成本最小的条件下,决定 I 种产品的生产序列.本文研究的经济批量排产问题考虑了产品货架存放期因素.指出了Dobson算法的不足,并提出了求解该问题的新算法(改进的装箱算法),新算法不仅以生产次数最大的产品为基础进行装箱,而且进一步以生产次数略低的产品为基础进行装箱.排产时,先按生产次数降序进行装箱,再按单次生产时间与生产准备时间之和降序装箱.计算结果显示,本算法结果更优.     

考虑货架存放期的经济批量排产问题的求解

在化工、造纸、制药、钢铁等工业生产中，一台设备或一条生产线可以生产多种产品的情况很常见。在生产中，如何安排各类产品的生产顺序以及生产数量显得十分重要。这类问题通常称作经济批量排产问题，这类问题是生产库存中的经典问题。本文研究的经济批量排产问题考虑了产品货架存放期因素，针对以往研究的不足，本文提出用批量变动方法求解该类问题，由计算结果显示，按照这种排产方法花费的成本要低于其他两种经济批量排产问题常用的方法。     

经济批量问题的数学模型与算法新进展

经济批量问题一般是讨论稳定的外部需求和有限的生产能力条件下实际生产过程的优化计划排产，具有重要应用价值。本文在综合大量国内外有关文献的基础上，对经济批量问题的数学模型和算法新进展作了比较系统，全面的介绍。     

满足多断点折扣费用函数的经济批量问题的多项式时间算法

在进货费用为全单位数量折扣函数的基础上,建立了一类有限时期内的经济批量问题.通过分析最优解的性质,设计了一个计算复杂性为O(T3+mT2)的动态规划算法,其中m为全单位数量折扣费用中的断点数,T为时期数.最后的算例进一步说明了该算法的有效性.     

考虑机器调整次数和产品质量的卷烟批量计划和柔性流水车间调度集成问题

针对卷烟企业生产中的批量计划和柔性流水车间调度集成问题,构建了整数规划模型,目标函数由卷烟生产时间、生产线调整次数、卷烟质量、库存成本四部分组成。鉴于该问题的NP-hard性,设计遗传算法进行求解,通过合理设计遗传算子,避免不可行解出现。应用某卷烟企业数据得到优化排产结果,与该企业之前依照经验排产方案进行对比,发现优化排程结果在减少品牌转换次数,提高生产的连续性方面具有明显优势。该算法已作为某卷烟企业排产人员的排产参考,应用于排产决策中,取得了良好的效果,对卷烟企业制定排产计划具有一定的实际指导意义。     

多供应商多零售商下经济批量问题的多项式时间算法研究

基于多供应商和多零售商构成的经济批量问题,通过构建优化模型,分析了订购费用为全部单位数量折扣和增加数量折扣两种情形模型最优解的相关性质。将这些性质应用到动态规划算法设计中,对订购费用为全部单位数量折扣时的一种特殊情形及增加数量折扣的一般情形分别设计了求解问题最优解的多项式时间算法,并用算例说明了算法的执行过程和有效性。     

二供应商经济批量问题的多项式时间算法

为了从采购费用结构不同的供应商中找到最佳补货策略,考虑一个零售商从两个供应商补货的二供应商经济批量问题.零售商在两个供应商处的采购费用结构分别为复合安装费用和全单位数量折扣费用结构.通过对问题结构性质的分析论证,将问题的可行解转化为一个有向网络,降低问题求解的计算复杂性.综合动态规划和Dijkstra最短路算法证明了该问题是多项式时间可解的.     

基于遗传算法的生产批量优化问题

本文针对生产费用、生产准备费用和库存费用综合指标最小的最优的能力约束生产批量问题,建立基于遗传算法的数学模型,通过模拟试验及实际问题的计算验证了算法的可行性。     

基于多个供应商和多个零售商组成的经济批量问题研究

本文考虑了由两个供应商和两个零售商组成的经济批量问题,当在每个供应商处的进货费用函数为数量折扣费用函数时,我们分析了该问题最优解的性质,并设计了一个计算复杂性为的动态规划算法,进而说明该问题是多项式可解的.     

CIMS下基于成组单元的无能力约束的生产批量计划的新方法

CIMS中基于成组单元的生产批量计划问题是确定属于M个族的N种不同的项目在给定的计划范围T内的每一个时间段上的批量，使得在T内项目总的调整费用（族调整费用和项目调整费用之和）和库存保管费用以及生产费用之和最小（GTLS）本文基于GTLS问题的性质，从一个新的角度即从调整变量出发，运用遗传算法（GA）随机搜索进行求解．对GTLS构造了两阶段启发式算法（Heuristic），通过仿真实验，测试6个问题表明，GTLS／GA比GTLS／Heuristic平均改善5％以内．     

A profit-maximizing economic lot scheduling problem with price optimization

The economic lot scheduling problem (ELSP) is a well known problem that focuses on scheduling the production of multiple items on a single machine such that inventory and setup costs are minimized. In this paper, we extend the ELSP to include price optimization with the objective to maximize profits. A solution approach based on column generation is provided and shown to produce very close to optimal results with short solution times on a set of test problems. The results are discussed and recommendations for further research are provided.     

多种变质性物品的经济批量问题

本文考虑了多种变质性物品在同一台设备上生产的最优基本生产周期问题。本文采用了基本周期法,给出了问题的数学模型,分析了模型最优解的存在性,并给出了求解该模型的算法和算例,从算例的结果说明基本周期法比公共周期法解决经济批量问题更优。     

The Economic Lot Scheduling Problem without Capacity Constraints

This study presents a comprehensive analysis on the Economic Lot Scheduling Problem (ELSP) without capacity constraints. We explore the optimality structure of the ELSP without capacity constraints and discover that the curve for the optimal objective values is piecewise convex with repsect to B, i.e., the values of basic period. The theoretical properties of the junction points on the piecewise convex curve not only provides us the information on “which product i” to modify, but also on “where on the B-axis” to change the set of optimal multpliers in the search process. By making use of the junction points, we propose an effective search algorithm to secure a global optimal solution for the ELSP without capacity constraints. Also, we use random experiments to verify that the proposed algorithm is efficient. The results in this paper lay important foundation for deriving an efficient heuristic to solve the conventional ELSP with capacity constraints.     

The use of genetic algorithms to solve the economic lot size scheduling problem

The purpose of this paper is to investigate the use genetic algorithms (GAs) for solving the Economic Lot Size Scheduling Problem (ELSP). The ELSP is formulated using the Basic Period (BP) approach which results in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced. This formulation is ideally suited for using GAs. The GA is tested on Bomberger's classical problem. The resulting solutions were better than those obtained using an iterative dynamic programming (DP) approach. The total cost of GA solutions to the problem with utilization up to 65% were within 3.4% of the lower bound. The GA also performed well for higher utilization yielding solutions within 13.87% of the lower bound for utilization up to 86%. The GA was tested on a 30-item problem and good solutions were obtained. The results of the GA under different binary representations, crossover methods, and initialization methods are compared to identify the best settings. The results indicate that for this particular problem, binary representation works better than Gray coding, 2-point crossover is best, and an infeasible starting population is better than feasible.     

Economic lot scheduling problem with imperfect production processes

In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.     

A search heuristic for the sequence-dependent economic lot scheduling problem

Almost all of the research on the economic lot scheduling problem (ELSP) has assumed that setup times are sequence-independent even though sequence-dependent problems are common in practice. Furthermore, most of the solution approaches that have been developed solve for a single optimal schedule when in practice it is more important to provide managers with a range of schedules of different length and complexity. In this paper, we develop a heuristic procedure to solve the ELSP problem with sequence-dependent setups. The heuristic provides a range of solutions from which a manager can choose, which should prove useful in an actual stochastic production environment. We show that our heuristic can outperform Dobson's heuristic when the utilization is high and the sequence-dependent setup times and costs are significant.     

考虑外包的单产品再制造批量决策

在已有动态批量决策问题的基础上,考虑了再制造与外包这两个因素建立了单产品的再制造批量决策模型。对考虑外包的单产品再制造批量决策问题最优解的性质进行了讨论,在此基础上利用动态规划的思想给出了时间复杂性为O(T4)的算法,并用C++实现了本算法,实验表明本算法是有效的。     

The single item uncapacitated lot-sizing problem with time-dependent batch sizes: NP-hard and polynomial cases

This paper considers the uncapacitated lot sizing problem with batch delivery, focusing on the general case of time-dependent batch sizes. We study the complexity of the problem, depending on the other cost parameters, namely the setup cost, the fixed cost per batch, the unit procurement cost and the unit holding cost. We establish that if any one of the cost parameters is allowed to be time-dependent, the problem is NP-hard. On the contrary, if all the cost parameters are stationary, and assuming no unit holding cost, we show that the problem is polynomially solvable in time O(T³), where T denotes the number of periods of the horizon. We also show that, in the case of divisible batch sizes, the problem with time varying setup costs, a stationary fixed cost per batch and no unit procurement nor holding cost can be solved in time O(T³ logT).