A Heuristic for Multiple Lot Sizing For an Order Under Variable Yield

Consider a job shop which must completely fill a large make-to-order demand of a product where production yield is highly variable. After a production lot is completed, if the total output of satisfactory units is inadequate to satisfy the demand, then a new run (with associated setup cost) is made. When the output of good units exceeds the demand, then the excess units are scrapped (with possible salvage value). The optimal lot size minimizes the total of production, setup, holding, shortage, and scrap costs. A heuristic is developed based on the incremental cost of increasing the lot size by one unit. The computational ease and excellent cost performance of the heuristic favor its use in place of the mathematically optimal solution obtained by dynamic programming. Real world manufacturing applications and additional properties of the model are also discussed.     

A Dynamic Lot Sizing Algorithm with Capacity Constraints

A new algorithm has been developed to calculate economic lot sizes for manufactured products. The algorithm allows for fluctuating and uncertain demand patterns which limit the effectiveness of the classical Wilson EOQ formula. In an environment of uncertain future demand, its performance is on a par with the Wagner-Whitin technique. Yet, the computations required are considerably less. For a single product the algorithm would produce results identical to the Part/Period formula of IBM. However, a new derivation is provided which parallels the derivation of the Silver and Meal formula. A new dimension is added when the algorithm is extended to the situation where there are limits on the combined production rate of all products. The algorithm prevents production from exceeding the limit. It therefore allows lot sizing to be implemented gradually, and it continues to protect the production line against sudden increases in demand after implementation. Finally, the dynamic lot sizing algorithm with capacity constraints is compatible with techniques which may be required to provide additional production smoothing.     

延期支付条件下基于EOQ模型的零售商补货策略

以由供应商、零售商和顾客组成的三阶段供应链为研究对象,在供应商给零售商全部延期支付期限,而零售商只给顾客部分延期支付期限的基础上,考虑了变质产品的情形,建立了相应的零售商库存决策模型。通过模型的分析求解,可以得出零售商在上述情况下的最优补货周期的简单判定方法。通过算例说明了模型的有效性。     

An Evaluation and Proposed Modification of the Sepehri-Silver-New Heuristic for Multiple Lot Sizing Under Variable Yield

The scrap or reject allowance heuristic developed by Sepehri, Silver, and New and reported in IIE Transactions is evaluated over a wide variety of combinations of desired batch size, fixed cost, and yield. Although the procedure works, in general, better than previously developed heuristics, there are conditions — large lot size, low fixed cost, and low yield — under which it performs quite poorly.     

Optimal Lot Sizing in Acyclic Multiperiod Production Systems

This paper addresses the problem of lot sizing within an acyclic hierarchical multiperiod production system. Cost conditions are established for the existence of optimal schedules satisfying the Wagner-Whit in property and a generalized nested schedules property. The method of proof is constructive and based on a network model. Imbedded in the proof are algorithms for adjusting any solution so that it satisfies the properties; thus the algorithms can be used to obtain a locally optimum solution from any trial schedule.     

Lot Sizing with Several Groups of Single-Cycling Retailers and One Warehouse

In this paper I describe a consecutiveness rule for grouping N retailers into m groups with independent single-cycle policies for each group which enables the creation of groups using a shortest-path approach. I also suggest a very efficient algorithm to compute the lot sizes for any single-cycle policy which can easily be incorporated into the shortest-path model for the creation of m single-cycle groups.     

A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand

Numerous production-inventory systems experience significant demand variations from period to period. In many cases, actual demand is random as well. Due to the computational complexity and sensitivity of the optimal solution to the problem of selecting batch sizes, heuristic approaches are often employed. In this paper we propose a method for selecting batch sizes when demand is probabilistic with an unstructured dynamic mean. The procedure is a least period cost approach where the optimal order up to point is found for the desired cycle length.     

Simultaneous Lot Sizing and Sequencing for Multistage Production Systems

Inventory and scheduling theory have, in general, been developed independently. This paper presents a model which integrates these two traditionally different aspects of production planning in a multi-stage environment by transforming a lot-sizing problem to an equivalent job-shop scheduling program. The proposed model may improve the effectiveness of existing decision making processes.     

Production and Distribution Lot Sizing in a Two Stage Supply Chain

We develop a two stage model of a manufacturing supply chain. This two stage production transportation model features capacitated production in two stages, and a fixed cost (or concave cost) for transporting the product between the stages. We prove several properties of this model, which we call the Two Stage Production Distribution Problem (2SPDP) model. By placing "non-speculative" assumptions on production and transportation, we show that our model reduces to a related model, with one capacitated production stage with linear production cost, and transportation between two inventory locations with non-linear transportation cost. Finally, we present polynomial algorithms for this model under several different transportation cost structures and capacity assumptions.     

启发式遗传算法的生产能力约束多产品再制造批量决策

建立了生产能力约束条件下的再制造批量决策模型,同时考虑了批量制造、批量再制造和外包,确定性的需求由批量制造、批量再制造和外包来满足.利用启发式遗传算法求解多产品再制造批量模型,研究了种群大小和迭代次数对遗传算法实验的影响,并通过一些算例来证实了算法的有效性.     

随机振动条件下SMT焊点半经验疲劳寿命累积模型

研究了SMT焊点在随机振动条件下引起的振动疲劳情况,给出了SMT焊点半经验随机振动疲劳寿命累积模型,并通过对某SMT电路板进行随机振动疲劳测试,验证了模型的正确性。     

不确定性订货时间下的非平稳EOQ模型

考虑了在订货时间不确定且EOQ不是整数情况下的最优订货量问题.通过平衡不确定性订货时间下库存成本和订货成本的策略,将不确定性订货时间下的最优订货问题转化为求解一般确定性订货时间下的订货问题.并进一步探讨了当EQQ不是整数时,如何通过建立数学规划来得到非平稳最优订货量.在数学规划模型的基础上,提出了一种新的启发式算法,同时给出了和一般求解方法GA算法的数值比较结果,验证了该启发式算法的有效性.     

An EOQ Model for Items with Weibull Distribution Deterioration

An inventory model is considered for deteriorating items with a variable rate of deterioration, where deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. Specifically, the Weibull distribution is used to represent the distribution of the time to deterioration. The EOQ formula is derived under conditions of constant demand, instantaneous delivery and no shortages, and it is shown that the results can be related to previously developed simpler models. A computer program is developed to provide the numerical solution and a numerical example is used to show the solution form and verify that the solution gives minimum total cost per unit time.

An economic lot size model has been developed for situation in which the deterioration follows a Weibull distribution. The theoretical derivation was shown to reduce to the previous model found by Ghare and Schrader when the deterioration was exponential in nature and to a non deteriorating EOQ model when deterioration was made very small. A computer program was developed to provide a numerical solution and its use demonstrated on a numerical example. The computer program is available from the authors.     

A Branch and Bound Algorithm for a Single-Item Multi-Source Dynamic Lot Sizing Problem with Capacity Constraints

In this paper we present a branch and bound algorithm for solving a single-item, multi-source dynamic lot sizing problem with time-varying capacity constraints. We consider a single-item production (and/or procurement) environment where there are multiple sources of supply with different cost structures. Computational results are presented.     

需求、价格和变质系数均为时变的EOQ模型

考虑物品在保管期间出现变质,且变质系数与保管时间正相关,提出了一种需求率随时间指数增长,销售和采购价格均随时间指数下降的变质物品EOQ模型.数值仿真和主要参数灵敏度分析表明,各周期服务水平随时间逐步降低,且随销售价格变动因子和变质系数增长因子变大而下降,随采购价格变动因子变大而上升;计划期内订货次数、各周期服务水平和产品总利润受需求增长因子和短缺量拖后系数变动的影响较小,受销售和采购价格以及变质系数变化的影响较大.     

变质率呈Weibull分布的易变质物品的EOQ模型

基于需求和采购价格均为时变的EOQ模型,进一步考虑呈Weibull分布的变质对易变质物品库存管理的影响,建立了相应的EOQ模型,并对该模型进行仿真计算和主要参数的灵敏度分析。结果表明,该模型存在最优解且各主要参数对最优库存控制有不同程度的影响。     

A Generalized EOQ Model for Items with Weibull Distribution Deterioration

A generalized form of Covert and Philip's EOQ model with Weibull distribution deterioration is developed. Specifically, the 3-parameter Weibull distribution is used to represent the time to deterioration. It is shown that this model can be related to the previously developed simpler models. The solutions to two numerical examples are compared to Covert and Philip's solution.     

供应链中具有供求协调机制的EOQ模型扩展研究

通过对经济批量模型改进研究的分析,指出了提前期的重要性,并将其引入合作条件下的订货模型中,证明了在一个买方和一个卖方的两级供应链中,当市场需求稳定时,买卖双方通过合作协商可以确定一个合理的价格折扣范围,在此折扣范围内,合作能够使供应链上的买卖双方达到共赢.     

Choosing the Optimum Lot Size for a Reordering Policy with Instantaneous Emergency Deliveries

A reordering policy, to maintain the level of stock in an inventory, is given which allows for two types of orders: regular orders which are filled in strict rotation with the time to fill an order exponentially distributed, or an emergency order which, it is supposed, is filled instantaneously (or effectively so). The optimum lot size of an order is that which minimizes the average operating cost per unit time over an infinite time span. The solution is given for the case in which the items in storage are subject to Poisson demand and the costs of maintaining the stock level are linear functions of the lot size of an order.     

刀具生命库存经济订货模型研究

当库存物资呈现寿命递减,并具有自修复能力或变异吸收等生命特征时,基于传统库存模型的相关理论已不能给予客观解释．本文根据刀具生命库存成本模型,以计划期内总成本最小为目标函数,得到模型在理想稳定状态下新刀具最优经济订货批量和最优修复能力的数学模型．结果表明,基于生命特征的库存模型可以更准确表现实际库存的状态;库存修复能力直接影响库存成本的变化,而传统库存模型只是经济生命库存模型中无生命特征的一个特例．