Optimal production lot size with process deterioration under an extended inspection policy

A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.

Effects of Imperfect Quality and Defective Items on Economic Production Lot Size

The classical EPQ model has been used for a long ti me and is widely accepted and implemented. Nevertheless, the analysis for finding an economic lot size has based on a number of unrealistic assumptions. A common unrealistic assumption in using EPQ is that all units produced are of good quali ty. The classical EPQ model shows that the optimal lot size will generate minimum ma nufacturing cost, thus producing minimum setup cost and inventory cost. However, this is only true if all products manufactured in the process are assumed to be of good quality (i.e. all products are within the specification limits). In rea lity this is not the case, therefore, it is necessary to consider the cost of im perfect quality items, because this cost can influence the economic lot size. Ma ny studies and recent papers have indicated that there is a significant relation ship between economic production lot size and process/product quality. However, their models included either the imperfect quality items (not necessarily de fective) which are to be sold at a discounted price or defective items which can be reworked or rejected. The aim of this paper is to provide a framework to integrate three different sit uations (discounted pricing/rework/reject) into a single model. 100% inspection is performed in order to distinguish the amount of good quality items, imper fect quality items and defective items in each lot. In this paper, a mathematica l model is developed, and a numerical example is presented to illustrate the sol ution procedures. It is found that the economic production lot size tends to inc rease as the average percentage of imperfect quality items and defectives (rejec ted items) increases.

A RELATIVE BENEFIT ALGORITHM FOR BASIC ECONOMIC LOT SIZE PROBLEM

The paper develops an algorithm that solves economic lot size problem in O(n~2) time in the Wagner-Whitin case. The algorithm is based on the standard dynamic programming approach which requires the computation of the maximal relative benefit for some possible subplans of the production plan. In this algorithm the authors have studied the forward property and decomposition properties which can make computation easy. The proposed algorithm appears to perform quite reasonably for practical application.

基于动态步长梯度下降的EKF-SLAM改进算法

现代重型货物运输所处环境日益复杂,要求AGV-SLAM算法具备更高的鲁棒性和准确性以实现高精确装卸作业.因此,本文提出基于动态步长梯度下降的改进EKF-SLAM算法.首先对AGV行进过程建模分析,分别建立AGV的运动学模型和观测模型.考虑到EKF-SLAM算法在状态估计时可能引入的截断误差问题,本文针对AGV自身位姿和环境特征位置预测估计精确度较低的问题,提出了一种改进算法.该算法引入梯度下降算法,并结合动态步长策略,步长的取值与AGV系统的前进速度、采样时间正相关.仿真结果表明,该改进算法相较于标准EKF-SLAM算法,在停车场数据集下能够快速生成更优的估计路标和路径,从而在一定程度上提高了传统算法的鲁棒性和准确性,具有行业应用的参考价值.

生产能力约束下易逝品动态批量决策研究

针对易逝品在生产能力有限的情况下的决策问题,首先通过构建包含生产成本和库存持有成本在内的成本最小化模型,分析了生产成本和库存持有成本为一般化的单调递增凹函数的最优动态批量决策和相互影响。然后通过求解模型得出了最优解的结构特性,并设计出前向动态规划算法以及分析了无投机性成本结构的特殊情形。研究发现:在生产计划中,不同周期生产的产品库存应按照先进先出的原则满足各周期需求;若任意周期的需求都不大于生产能力,则著名的零库存性质在时间依赖的库存损失率及库存持有成本和生产能力双重约束下仍然成立。

CAPACITATED LOT SIZING AND SCHEDULING PROBLEMS USING HYBRID GA/TS APPROACHES

The capacitated lot sizing and scheduling problem that involves indetermining the production amounts and release dates for several items over a given planning horizonare given to meet dynamic order demand without incurring backloggings. The problem consideringovertime capacity is studied. The mathematical model is presented, and a genetic algorithm (GA)approach is developed to solve the problem. The initial solutions are generated after usingheuristic method. Capacity balancing procedure is employed to stipulate the feasibility of thesolutions. In addition, a technique based on Tabu search (TS) is inserted into the genetic algorithmdeal with the scheduled overtime and help the convergence of algorithm. Computational simulation isconducted to test the efficiency of the proposed hybrid approach, which turns out to improve boththe solution quality and execution speed.

Collaborative supply chain planning under dynamic lot sizing costs with capacity decision

Studies show that supply chain cooperation improves supply chain performance. However, it remains a challenge to develop and implement the realistic supply chain cooperation scheme. We investigate a two-echelon supply chain planning problem with capacity acquisition decision under asymmetric cost and demand information. A simple negotiation-based coordination mechanism is developed to synchronize production/order strategies of a supplier and a buyer. The coordination scheme shows how the supplier and the buyer modify their production and order policy in order to find a joint economic lot sizing plan, which saves the overall supply chain cost. The allocation of the cooperation benefit is determined by negotiation. Due to the complexity of the multiple periods, multiple level supply chain lot sizing with capacity decision, a heuristic algorithm is developed to find coordination solutions. Finally, the results of the numerical study indicate the performance of supply chain coordination scheme.

A Note on an Economic Lot-sizing Problem with Perishable Inventory and Economies of Scale Costs:Approximation Solutions and Worst Case Analysis

This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.

Dynamic programming algorithm for economic lot-sizing problem with bounded inventory and out-sourcing

This paper addresses a single item dynamic lot-sizing model with inventory capacity and out-sourcing. The goal is to minimize the total costs of production, setup, inventory holding and out-sourcing. Two versions of an out-sourcing model with time-varying costs are considered: stock out case and conservation case. Zero Inventory Order property has been found and some new properties are obtained in an optimal solution. Dynamic programming algorithms are developed to solve the problem in strongly polynomial time respectively. Furthermore, some numerical results demonstrate that the approach proposed is efficient and applicable.

Parallel ant colony algorithm and its application in the capacitated lot sizing problem for an agile supply chain

In order to study the capacitated lot sizing problem for a supply chain of corporate multi-location factories to minimize the total costs of production, inventory and transportation under the system capacity restriction and product due date, while at the same time considering the menu distributed balance, the mathematical programming models are decomposed and reduced from the 3 levels into 2 levels according to the idea of just-in-time production. In order to overcome the premature convergence of ACA (ant colony algorithms), the idea of mute operation is adopted in genetic algorithms and a PACA (parallel ant colony algorithms) is proposed for supply chain optimization. Finally, an illustrative example is given, and a comparison is made with standard BAB (Branch and Bound) and PACA approach. The result shows that the latter is more effective and promising.

MIP Formulations and Metaheuristics for Multi-Item Capacitated Lot-Sizing Problem with Non-Customer Specific Production Time Windows and Setup Times

Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. This problem is NP-hard in the strong sense. Moreover, it is very difficult to solve with an exact method;it is for that reason we have made use of the approximate methods. We improved the variable neighborhood search (VNS) algorithm, which is efficient for solving hard combinatorial optimization problems. This problem can be viewed as an optimization problem with mixed variables (binary variables and real variables). The new VNS algorithm was tested against 540 benchmark problems. The performance of most of our approaches was satisfactory and performed better than the algorithms already proposed in the literature.

Computationally Efficient Problem Reformulations for Capacitated Lot Sizing Problem

In this article, we propose novel reformulations for capacitated lot sizing problem. These reformulations are the result of reducing the number of variables (by eliminating the backorder variable) or increasing the number of constraints (time capacity constraints) in the standard problem formulation. These reformulations are expected to reduce the computational time complexity of the problem. Their computational efficiency is evaluated later in this article through numerical analysis on randomly generated problems.

Reducing a Lot Sizing Problem with Set up, Production, Shortage and Inventory Costs to Lot Sizing Problem with Set up, Production and Inventory Costs

We reduce lot sizing problem with (a) Set Up, Production, Shortage and Inventory Costs to lot sizing problem with (b) Set Up, Production, and Inventory Costs. For lot sizing problem (as in (b)), Pochet and Wolsey [1] have given already integral polyhedral with polynomial separation where a linear program yield “integer” solutions. Thus problem (b) which we have created can be more easily solved by methods available in literature. Also with the removal of shortage variables is an additional computational advantage.

Hybrid Formulation of the Multi-Item Capacitated Dynamic Lot Sizing Problem

It is shown that when backorders, setup times and dynamic demand are included in capacitated lot sizing problem, the resulting classical formulation and one of the transportation formulations of the problem (referred to as CLSP_BS) are equivalent. And it is shown that both the formulations are “weak” formulations (as opposed to “strong” formulation). The other transportation version is a strong formulation of CLSP_BS. Extensive computational studies are presented for medium and large sized problems. In case of medium-sized problems, strong formulation produces better LP bounds, and takes lesser number of branch-and-bound (B&B) nodes and less CPU time to solve the problem optimally. However for large-sized problems strong formulation takes more time to solve the problem optimally, defeating the benefit of strength of bounds. This essentially is because of excessive increase in the number of constraints for the large sized problems. Hybrid formulations are proposed where only few most promising strong constraints are added to the weak formulation. Hybrid formulation emerges as the best performer against the strong and weak formulations. This concept of hybrid formulation can efficiently solve a variety of complex real life large-sized problems.

Lot Sizing in Production Scheduling at a Personal Protection Equipment Company

This work presents an optimization model to support decisions during production planning and control in the personal protective equipment (PPE) industry (in particular, gloves). A case study was carried out at a Brazilian company with the aim of increasing productivity and improving customer service with respect to meeting deadlines. In this case study, the mixed integer linear programming model of Luche (2009) was revisited. A new model for single-stage lot sizing was applied to the production scheduling of gloves. Optimizing this scheduling was not a simple task because of the scale of the equipment setup time, the diversity of the products and the deadlines for the orders. The model was implemented in GAMS IDE and solved by CPLEX 12. The model and the associated heuristic produce better solutions than those currently used by the company.

Modeling and Solving Lot-Splitting Scheduling Problem Based on Process

In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, the choice of machine also affects the optimal lot-size. In addition, different choices of lot-size between the constrained processes will impact the manufacture efficiency. Considering that each process has its own appropriate lot-size, we put forward the concept of scheduling with lot-splitting based on process and set up the scheduling model of lot-splitting to critical path process as the core. The model could update the set of batch process and machine selection strategy dynamically to determine processing route and arrange proper lot-size for different processes, to achieve the purpose of optimizing the makespan and reducing the processing batches effectively. The experiment results show that, comparing with lot-splitting scheduling scheme based on workpiece, this model optimizes the makespan and improves the utilization efficiency of the machine. It also greatly decreases the machined batches （42%） and reduces the complexity of shop scheduling production management.

含批量加工设备的木门流水车间排产方案

针对包含批量加工工序的两阶段实木复合流水车间排产问题,建立了该问题的混合整数规划模型。根据拉式生产方式和木门加工工艺特点,将原问题拆分为独立的两阶段子问题;针对第2阶段子问题基于Dantzig-Wolfe分解转化为集合划分模型,采用分支定价算法获得其最优整数解;根据第2阶段整数解求解第1阶段子问题,得到该车间这两阶段的排产方案。通过算例分析验证了所提算法可求解大规模木制家具批量生产问题,并能在牺牲少量最优值的情况下,高效快速地得到排产方案。

供应链管理与经济订货量模型

供应链管理的一个关键环节是库存管理,而库存管理中最早提出、最基本的数学模型是经济订货量模型.本文介绍该模型的起源与发展,以及该模型提出的历史背景和提出者的人生经历,从中可以体会到提出原创模型需要天时、地利等外部环境,更需要好奇心和发现与解决问题的意识等内在动力.

木材树种批量检验抽样方案的研究

批量木材检验既要保证合理的精度,又要考虑检验人员的工作强度,因此研究批量木材检验的抽样方案具有重要意义。为制定按批量百分比分配的随机抽样方案,根据木材分类方法,整合历史抽样数据,使用MATLAB拟合并建立回归方程。在随机抽样方案的基础上研究复杂抽样的设计效应(design effect,deff),并增加了放宽和加严的规则。采用分层抽样模式,根据不同分类方法设定检验批次,制定了单一树种类或多树种类分组的随机抽样、多树种类未分组的随机抽样和现场无法判断样本信息的随机抽样三种方案。所有研究方案与现行抽样方案的对比和实际验证,在参数区间和执行方面均具有可行性,加快了批量木材抽样中样本量的计算。本研究对于木材现场检验具有更好的适用性,可以提高木材检验工作的效率。

功率器件可靠性试验样本数量确定理论及影响

在功率器件的可靠性试验、评估和验证中,样本数量的大小决定着试验结果的准确性。然而,在不同的标准中,对于相同试验,样本数量的选择却不尽相同,给实际应用带来了困难。通过研究各类标准中的试验内容,将样本数量的选择分为探究型试验和验收型试验两类,分析、解释了选择不同样本数量的理由。对样本数量计算公式进行了分析,并将公式中的变量与标准规定指标联系起来。结果表明,批允许不合格率(LTPD)和置信度会影响样本数量。因此,在满足标准规定指标的前提下,可以根据实际需求适当调整试验样本数量,为器件可靠性试验评估提供有效的手段。