Supply chain model with variable lead time under credit policy

The success of the Japanese in the employment of just-in-time (JIT) production has received a great deal of attention in the past two decades. The underlying goal of JIT is to eliminate wastes, which can be achieved through various efforts such as shortening lead time and improving quality. The objective of this study is to extend the model of Huang et al. (Eur J Oper Res 202:473–478, 2010) by allowing deterministic variable lead time and quality improvement investment on an integrated inventory model. That is, this article develops an integrated inventory model which jointly determines the optimal order quantity, process quality, lead time, and the frequency of deliveries simultaneously. Furthermore, a solution procedure is suggested for solving the proposed model, and numerical examples are given to illustrate the benefit of coordination between vendor and buyer.     

Single setup multiple delivery model of JIT system

The delivery strategy of JIT system is an important factor influencing JIT performance. In order to implement delivery strategy in different JIT environments, the single-setup-multiple-delivery (SSMD) model is studied. The number of deliveries, the focus of the SSMD model, is discussed emphatically. In the proposed SSMD model, the lead time of raw material supplier is considered and the production of the manufacturer is affected by the lead time. The cost functions of the supply chain, consisting of the raw material supplier, the manufacturer and the buyer, are built respectively. By minimizing the cost of the supply chain, the optimal number of deliveries is obtained in non-cooperation policy and cooperation policy separately. The interval of the number of deliveries, which can reduce the cost, compared to the single-setup-single-delivery model, is also analyzed in non-cooperation policy and cooperation policy. A numerical example is setup to confirm advantages of the proposed SSMD model.     

Optimal pricing and replenishment policies of an EOQ model for non-instantaneous deteriorating items with shortages

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained.     

A replenishment policy for perishable products with non-linear holding cost under stochastic supply lead time

The development and application of inventory models for deteriorating items is one of the main concerns of subject matter experts. The inventory models developed in this field have focused mainly on supply chains under the assumption of constant lead time. In this study, we develop an inventory model for a main class of deteriorating items, namely perishable products, under stochastic lead time assumption. The inventory system is modeled as a continuous review system (r, Q). Demand rate per unit time is assumed to be constant over an infinite planning horizon and the shortages could be backordered completely. For modeling the deterioration process, a non-linear holding cost is considered. Taking into account the stochastic lead time as well as a non-linear holding cost makes the mathematical model more complicated. We customize the proposed model for a uniform distribution function that could be tractable to solve optimally by means of an exact approach. We then solve an example taken from the literature to demonstrate the applicability and effectiveness of the proposed model. Finally, by doing several sensitivity analyses for the key parameters of the model, some managerial insights are proposed.     

Solving a multi-product distribution planning problem in cross docking networks: An imperialist competitive algorithm

Cross docking is a distribution strategy to efficiently control the physical flow of inventory. In this approach, the concept of warehouse shifts from a place for holding the inventory to a site for receiving, classifying, and shipping to the product destination in a very short time. Shipments are typically kept for less than 24 h in the cross dock. The major advantage of this strategy is to reduce the cycle time and inventory level while fulfilling customer’s demands. In general, relevant studies are based on one-product type delivery and pickup assumption whereas in reality, customers are likely to order different types of products in various amounts. This paper focuses on considering the scheduling problem of cross docking multi-product type deliveries and pickups, so that the objective, minimizing the summation of transportation cost and holding cost, can be satisfied. The efficiency and capability of the mathematical model is evaluated by presenting a case study and sensitivity analysis of the parameters influencing the problem. In order to solve the model, as the problem is NP-hard, an efficient heuristic procedure to provide effective initial solution within reasonable computational times is applied and then improved by an imperialist competitive algorithm. Computational results which consist of comparing the proposed heuristic and meta-heuristic with optimal solution obtained by Generalized Algebraic Modeling System show that the suitability of the proposed solving approach is quite sensible for solving such complicated problems.     

Optimal production run length and maintenance schedule for a deteriorating production system

This study considers manufacturing cost, inventory holding cost, system setup and maintenance costs, restoration cost, and warranty cost to a deteriorating production system whose state can be classified into in-control or out-of-control state at any time. This study develops a framework of simultaneous determination of optimal production run length and maintenance schedule and shows that there exists a unique optimal production run length and scheduled maintenance policy that minimize the expected total cost per item. The mathematical conditions to the optimal production run length and scheduled maintenance policy for a production cycle are deduced.     

劣化系统的最佳检测与维修周期分析

提出了一类基于半马氏决策过程的劣化失效系统检测与维修优化模型.将位相型(PH)分布引入模型后,决策过程的状态空间发生变化,为了获得适用于原有模型假设的检测与维修优化策略,提出了一种改进的值迭代算法.运用该算法,求得了使系统长期运行平均费用率最低的预防性维修阈值与检测间隔分布.最后,通过具体算例验证了模型与迭代算法的可行性.     

考虑运输成本的JIT采购模型及算法

以供应商和采购商组成的供应链为研究对象，建立了考虑运输成本的JIT采购批量分割决策模型。针对运输成本是运输重量不规则函数的事实，应用费率模拟函数估算运输成本，分别导出了面向整车运输和零担运输的决策模型；基于两个模型解的最优订货批量相等，且整车运输模型解交付次数低、库存成本高，而零担运输模型解交付次数高、运输成本高，提出JIT-Lot-Sp-Opt算法，搜索得到最优交付次数，对JIT采购进行优化决策。实验结果证明，模型和算法在不损失精确性和优化性的前提下求解简单，具有实用性。     

Economical delivery strategies of products in a JIT system under a global supply chain

This study supplies an optimal total cost model, including approach I and approach II, to manufacturers with several assemblers in the same area to decide the most economical product delivery strategy in the global just-in-time (JIT) system. In approach II, manufacturers deliver products to downstream assemblers via a JIT system with third party logistics (3PL) support. There is a distinction between approach I and approach II according to whether or not the delivery quantity is limited to economical delivery lot size. A case study analysis is used to illustrate the proposed models, in which the following conclusions can be obtained. Firstly, the JIT product delivery strategy according to economical delivery lot size can be obtained to achieve a cost-effective global supply chain. Second, upstream manufacturers can apply a JIT system under a global supply chain to downstream manufacturers with lower cost through support from 3PL with economical delivery lot size.     

通货膨胀环境下需求依赖库存的经济订货批量模型

为考虑通货膨胀和货币时间价值对库存的影响,研究了通货膨胀的条件下需求受库存水平影响且允许短缺发生的经济订货批量问题,其中通货膨胀率由内部通货膨胀率与外部通货膨胀率两部分组成。以系统成本最小化为目标,建立了四个不同补货策略下的仿真模型,并提供了寻求模型整体最优解的简单方法。最后,通过实例对这四个模型进行了比较,同时分析了参数变化对模型最优解的影响。     

A heuristic technique for inventory replenishment policy with increasing demand pattern and shortage allowance

In the growth stage of a product life cycle, the demand rate is usually unstable and follows an increasing pattern. The traditional inventory policies, which have been developed for stationary demand pattern, are not appropriate to this situation. Although there exist some researches in the past dealing with inventory policy for the case of increasing demand pattern, most of them focused on the inventory systems in which shortages are not allowed. In reality, the presence of shortages is sometimes economically preferable when holding cost is significant as compared with shortage cost. The aim of the research presented in this paper is, therefore, to develop a replenishment policy for inventory systems with nonlinear increasing demand pattern and shortage allowance in such a way that the total demand during a predefined planning horizon can be exactly met. A heuristic technique to help determine the operational parameters for the inventory policy is then developed. In the proposed heuristic technique, the consecutive improvement method developed by Wang (Comput Oper Res, 29:1819–1825, 2002) will first be used to help determine replenishment times. And then, a new concept of reduction cost, which is defined as the difference between the holding cost when shortage is allowed and the incurred shortage cost, is introduced and applied to help find the optimal shortage starting point in each replenishment cycle. Numerical experiments are also conducted to illustrate the applicability of the proposed technique.     

The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm

This paper addresses an economic lot scheduling problem (ELSP) for manufacturing environments regarding slack costs and deteriorating items using the extended basic period approach under Power-of-Two (PoT) policy. The purpose of this research is to determine an optimal batch size for a product and minimizing total related costs to such a problem. The cost function consists of three components, namely, setup cost, holding cost includes deteriorating factor, and slack cost. The ELSP is concerned with the scheduling decision of n items and lot sizing. Avoiding schedule interference is the main problem in ELSP. The used PoT policy ensures that the replenishment cycle of each item to be integer and this task reduces potential schedule interferences. Since the ELSP is shown as an NP-hard problem, an imperialist competitive algorithm is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.     

A service level model for the control wafers safety inventory problem

This paper considers the control wafers safety inventory problem (CWSIP) in the wafer fabrication photolithography area. The objective is to minimize the total cost of control wafers, where the cost includes new wafers cost, re-entrant cost and holding cost while maintaining the same level of production throughput. For the problem under pulling control production environment, a nonlinear programming model is presented to set safety inventory levels so as to minimize total cost of control wafers. A numerical example is given to illustrate the practicality of the model. The results demonstrate that the proposed model is an effective tool for determining the service level of safety inventory of control wafers for each grade.     

A service level model for the control wafers safety inventory problem

This paper considers the control wafers safety inventory problem (CWSIP) in the wafer fabrication photolithography area. The objective is to minimize the total cost of control wafers, where the cost includes new wafers cost, re-entrant cost and holding cost while maintaining the same level of production throughput. For the problem under pulling control production environment, a nonlinear programming model is presented to set safety inventory levels so as to minimize total cost of control wafers. A numerical example is given to illustrate the practicality of the model. The results demonstrate that the proposed model is an effective tool for determining the service level of safety inventory of control wafers for each grade.     

Design of a just-in-time periodic material supply system for the assembly lines and an application in electronics industry

The purpose of the paper is the development of a mathematical model and a heuristic approach where the routes are constructed and the service period is determined for the design of an internal milk-run material supply system. The material supply by this system occurs on a just-in-time basis from a central warehouse to several stations of an assembly line. The objective of the proposed mathematical model is the minimization of the total material handling and inventory holding cost. Besides, the proposed heuristic approach intends to construct routes based on an initial service period value and attempts to improve the solution by considering different period values. The most suitable solution is decided on the basis of the least total material handling and WIP/inventory holding cost. The application of the proposed heuristic in a TV assembly plant demonstrates the utility of it to the real practice.     

Optimal nonperiodic inspection scheme for a multicomponent repairable system with failure interaction using A * search algorithm

This paper proposes an approach for finding optimal nonperiodic inspection scheme for a multicomponent repairable system with failure interaction. Failure of one component of the system is hard, i.e., as soon as it occurs, the system stops operating. Failures of the other components are soft, namely, they do not cause the system stop, but increase the system operating costs. Soft failures are detected only if inspection is performed. Thus, the components with soft failure are all inspected at the scheduled inspection instances and are minimally repaired if found failed. When the component with hard failure fails, it is also repaired. However, its failure increases the failure rate of the other components. The system’s expected total cost associated to a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between real occurrence of the soft failures and their detection at inspections. The objective is to determine the optimal inspection scheme that yields minimum expected total cost. In the proposed approach, the expected total cost is formulated in terms of inspection scheme. Then, A ^* search algorithm, with a proposed heuristic cost function, for calculating lower bounds, is employed to search through alternative inspection schemes to determine the optimal one. The proposed approach is illustrated through a simplified numerical example.     

An integrated vendor–buyer inventory model with imperfect items and planned back orders

In this paper, we develop a mathematical model to determine an integrated vendor–buyer inventory policy, where the vendor’s production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor prepares for the repeating flow of orders of size $ {Q_{\mathrm{P}}}=nQ $ from the buyer by producing items in batches of size Q _P and planning to have each batch delivered to the buyers in n deliveries, each with a lot of Q units. Once the buyer receives the items, a 100 % screening process is conducted. We assume the screening process and demand take place simultaneously. We also assume that shortages are allowed and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected annual integrated total cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer. The results also show that even though there is a cost associated with each back order, it is profitable for the company to have planned back orders if customers are willing to wait for the next delivery when a shortage occurs.     

基于半马尔科夫决策过程的风力机状态维修优化

恶劣的工作环境、昂贵的维修成本和停机损失对风力机及其部件的维修提出挑战。以齿轮箱、叶片等风力机核心机械部件为对象,将部件退化过程离散成有限的退化状态;以长期折扣成本最低为目标,考虑风速、备件物流、停机损失等因素的影响,建立基于半马尔科夫决策过程的状态维修优化模型。分析各退化状态下的维修策略、检测间隔时间以及不同退化状态间的转移概率,并采用策略迭代算法求解模型。以某风力机齿轮箱为例,通过对等周期、非等周期检测条件下检测间隔时间和维修成本的分析,得到优化的维修决策。研究结果表明,该模型能有效描述风力机核心部件的退化过程,实现风力机维修优化。     

一种多周期随机需求生产/库存模型

为使存贮、生产和缺货等费用的总和最小，建立了一种多周期随机需求生产／库存模型，该模型采用（S，Q）策略对生产和库存进行控制，即当成品库存降至8时准备生产，生产量为Q。通过对该模型费用函数特性的分析，设计了一种迭代学习算法，根据该算法可以得出系统的最优生产准备点及最优生产量。将所提出的迭代学习算法与遗传算法进行了比较，结果显示，两者所得到的控制量是吻合的，且迭代学习算法的求解速度更快，从而证实所建立的模型和提出的迭代学习算法是正确有效的。     

A degradation-based model for joint optimization of burn-in, quality inspection, and maintenance: a light display device application

This paper presents a degradation-based model to jointly determine the optimal burn-in, inspection, and maintenance decisions, based on degradation analysis and an integrated quality and reliability cost model. Degradation modeling plays an important role in reliability prediction and analysis for many highly reliable components and equipment, when the failures can rarely be observed. Unlike traditional applications, quality and reliability must be considered simultaneously for devices subject to degradation, because quality inspection decisions often impact anticipated reliability and failure-time distributions. This paper presents an integrated model to jointly optimize quality and reliability for devices subject to degradation, with a focus on burn-in, quality inspection, and maintenance policies. Based on the degradation modeling and analysis, the reliability function and the time-to-failure distribution are derived under the condition that the quality inspection is applied following the burn-in period. The optimal burn-in, quality inspection, and preventive maintenance policies are determined by minimizing the expected total cost per usage lifetime. The proposed model is illustrated using the application of light display devices, in which the degradation path follows a negative shifted lognormal distribution with a random failure threshold. A numerical example is provided to illustrate the application of our model to the light display devices.