Optimal replenishment policies for deteriorating control wafers inventory

This paper considers a control wafers replenishment problem with inventory deterioration. In the process, control wafers begin to deteriorate after the pre-disposition. The objective of this research is to minimize the total cost of control wafers, where the cost includes ordering cost, holding cost and purchase cost. We first formulate the control wafers inventory problem as a dynamic programming model. We then transform the control wafers’ inventory problem into the mixed 0–1 linear programming model. An illustrative example with four cases is used to illustrate the practicality of these models, and sensitivity analysis is applied to understand the impact of parameters to these models. The results demonstrate that the proposed mixed 0–1 linear programming model is an effective tool for determining the replenishment of control wafers for multi-periods.     

模糊资源约束的联合补充问题

针对不确定环境下的多产品联合补充问题,用三角模糊数表示不确定的资源约束,建立了模糊规划模型,目标函数为最小化订货成本和库存持有成本,决策变量为基本补充周期和每种产品的补充周期.用遗传算法对模型进行求解,以模糊规划模型的目标函数值作为染色体的适应度,阐述了染色体编码、选择、交叉、变异等遗传操作.最后,给出了仿真数值实例,比较了模糊资源约束模型和确定资源约束模型对1 600个随机生成问题的计算结果.     

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 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.     

Bringing order [replenishment process control]

The importance of replenishment management in "make to stock" businesses is often overlooked in demand management studies in favour of forecast management. The real issue in replenishment strategy is addressing the fundamental challenge between holding enough inventory to protect future sales versus reducing inventory to reduce costs and enhance productivity. It is likely that replenishment lead-time will be greater than is desirable, vendors will be unreliable and forecasts will in most cases be wrong. Thus, in this paper, the author urges manufacturers to take control of the replenishment process.     

Inventory replenishment and delivery planning in a two-level supply chain with compound Poisson demands

This paper presents a model for integrating inventory replenishment and delivery planning in a two-level supply chain consisting of a supplier and a retailer. The supplier is authorized to manage the inventory level of the retailer by using the information on demands from final customers and the inventory level of the retailer. The problem considered here is to determine order-up-to levels of the supplier and the retailer simultaneously for the objective of minimizing the expected long-run average cost, which is composed of replenishment cost at the supplier, delivery cost to the retailer, and inventory holding costs at both members. We develop a renewal theoretic optimization model for a case of compound Poisson demands with distribution-free order quantities and present an approximation method for obtaining a solution of the problem. In addition, a closed-form solution is derived for the problem with a special case of compound Poisson demands, in which demand quantities follow an exponential distribution. A series of simulation tests show that the solutions obtained from the approximated cost functions are reasonably good.     

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.     

Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate

An integrated approach is used to clarify the critical issues of scheduling and replenishment planning in an advanced inventory system under stock-dependent selling rate environment. This is because integration removes the barriers between enterprises and improves overall performance. A close collaboration such as just-in-time (JIT) operations also improves product quality of the supply chain. Different from the single-stage inventory model, this study develops an integrated two-stage production-inventory deteriorating model for the buyer and the supplier with stock-dependent selling rate, as well as considering imperfect items and JIT multiple deliveries. Our paper proposes a significant method using a time-weighted-inventory approach to analyze the supplier’s saw-tooth holding cost. We derive the optimal number of inspection, optimal deliveries and the optimal delivery-time interval. A numerical example is also presented to illustrate the theory. The results show that the fixed demand rate, the holding cost and the unit inspection cost are critical in the management of the deteriorating inventory model.     

Model and algorithm for fuzzy joint replenishment and delivery scheduling without explicit membership function

We study a joint replenishment and delivery scheduling (JRD) problem in which a central warehouse serves n-retailers in the presence of vague operational conditions such as ordering cost and inventory holding cost. In the proposed fuzzy set-based approach, an exact membership function is not assumed and instead can be approximated using piecewise linear functions based on alpha level sets because of their easy handling and efficiency. Subsequently, the fuzzy total cost is defuzzified by the widely used signed distance method to ranking fuzzy numbers. However, due to the JRD's difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. To find an optimal solution, an effective and efficient differential evolution (DE) algorithm is designed. After determining the appropriate parameters of the DE by parameter tuning test, the effectiveness of the DE is verified by numerical examples. We compare the DE with the available best approach and results show that DE can solve this non-deterministic polynomial hard problem in a robust way with a high convergence rate and low average error.     

Supplier management for manufacturer – a case study of flexible PCB

The purpose of this study is to provide a guideline for manufacturer with multiple products on suppliers selection. The proposed approach has been constructed based on the total cost, given that each supplier possesses different unit prices, purchasing lead time, and variability. A case study of a Taiwanese company manufacturing flexible printed circuit boards (PCBs) is used to illustrate the proposed model, from which the following can be concluded: supplier selection does affect expected raw material cost, expected relevant inventory cost, setup cost, expected capacity cost, transportation cost, and eventually the total cost. Instead of unit price, total cost should be the criterion for supplier selection. In addition, there exists a relationship of trade-off between expected capacity cost and transportation cost.     

供需链中的结盟企业库存管理

供需链中核心企业与结盟企业在风险分担和库存信息上存在不对称，在提货时存在“局部利益最大化”问题，核心企业仅能通过提货量控制结盟企业库存。结加存管理包括根据外部事件及反馈信息进行结盟企业库存维护和利用提货量来控制结盟企业库存，本文建立了结盟企业库存维护的形式化模型和库存控制的随机模型，并提出了一种层次型混合算法。     

基于时间的供应商管理库存整合补货模式下的牛鞭效应研究

为比较基于时间的供应商管理库存整合补货模式和传统补货模式对零售业供应链中牛鞭效应的影响,概述了供应商管理库存在零售业供应链中的应用情况,构建了两种补货模式的系统动力学模型。通过仿真,定量地比较了两种补货模式中供应商和零售商对泊松流随机需求输入的订单响应率的波动。另外,为了比较基于时间的供应商管理库存整合补货模式下补货周期对牛鞭效应的影响,通过改变参数设置模拟了不同补货周期下供应商和零售商的订单响应率波动。结果显示,与传统模式相比,基于时间的供应商管理库存整合补货对牛鞭效应有明显的改善;供应商管理库存整合补货的补货周期对牛鞭效应存在明显的影响,较长周期下的牛鞭效应相对于较短周期要严重。     

Maintaining the balance [replenishment and inventory]

Demand and replenishment are critically dependent on how effectively information systems are used and how well demand signals, batching rules and effective forecasting, are managed and converted into plans and procurement actions. The supply and inventory relationship are more concerned with what is actually made, where inventory is placed and how it is moved through the supply chain. A better understanding of the issues and strategies can be achieved by examining the many combinations of supply and demand and consider them as different scenarios. In this paper three scenarios are cited.     

多资源概率约束下多品种变质产品库存优化

为降低多产品多资源概率约束下易腐产品库存系统的长期平均成本,首先得出了多品种多资源概率约束下易腐产品库存系统的几个有用的性质和定理;然后基于这些定理,给出了一种搜索多品种多资源概率约束下库存系统最优订货策略的多项式算法,在算法中运用系统动力学仿真方法代替传统算法的复杂过程,并证明了多品种多资源概率约束库存系统优化问题等价于一个单资源多品种概率约束库存系统优化问题;最后给出了一个计算实例,表明多资源约束下概率约束对线性约束的优越性和新算法的可行性.     

Evaluation of supply chain structures using a delayed product differentiation process

In this paper, we consider a two-level supply chain consisting of a retailer and n “non-identical” customers. The retailer orders different perishable products in response to the demands of the customers. The unsatisfied demand at a retailer is partially backlogged with a time-proportional backlogging rate. We formulate models for a postponement system and an independent system to minimize the total average cost function per unit time for ordering and keeping n “non-instantaneous deteriorating items.” An algorithm is given to derive the optimal solutions of the proposed models. The impact of the deterioration rate on the inventory replenishment policies is studied with the help of both theoretical and numerical results.     

Minimizing transportation cost of a joint inventory location model using modified adaptive differential evolution algorithm

Transportation is a key issue in supply chain management and is a major concern for a company. This paper considers a joint-location inventory problem involving a set of suppliers producing different products and a set of retailers where some retailers are treated as distribution centers (DCs). The problem is to determine which retailers to be assigned as DCs, which retailers to receive direct shipments, how much of the retailer’s demand to allocate to the DCs, and how much of the DC’s demand is to be met by different suppliers. The problem is formulated as a mixed integer model and it has been solved through an adaptive differential evolution algorithm known as modified J. Adaptive Differential Evolution. The solutions obtained are compared with that of simple genetic algorithm. This paper also shows that the proposed model is robust in nature and offers near-optimal results for different distributions. The sum of the cost of establishing some retailers as DCs and the total transportation cost incurred in shipping products from the suppliers to the retailers via DCs(for some retailers) or directly (for the other retailers) is also compared with the total transportation cost incurred when all the products are shipped directly from the suppliers to the retailers.     

A genetic algorithm to optimize multiproduct multiconstraint inventory control systems with stochastic replenishment intervals and discount

There are two main assumptions in multiperiodic inventory control problems. The first is the continuous review, where, depending on the inventory level, orders can happen at any time, and the other is the periodic review, where orders can only happen at the beginning of each period. In this paper, these assumptions are relaxed, and the periods between two replenishments are assumed independent and identically distributed random variables. Furthermore, the decision variables are assumed integer-type and that there are two kinds of space and budget constraints. The incremental discounts to purchase products are considered, and a combination of backorder and lost sales are taken into account for the shortages. The model of this problem is shown to be a mixed integer-nonlinear programming type, and in order to solve it, both genetic algorithm and simulated annealing approaches are employed. At the end, two numerical examples are given to demonstrate the applicability of the proposed methodologies in which genetic algorithm method performs better than simulated annealing in terms of objective function values.     

Impact of forecasting methods on variance ratio in order-up-to level policy

This paper considers the impact of forecasting methods on the bullwhip effect for a simple replenishment system in which a first-order autoregressive process describes the customer demand and an order-up-to inventory policy characterizes the replenishment decision. The impact of exponential smoothing and minimum mean squared error forecasting is measured for both the bullwhip effect and inventory variances. Previous similar studies have focused on investigating the impact of forecasting methods on bullwhip effect. However, little research has been carried out to explore the impact of forecasting methods for both bullwhip effect and inventory variances. Through simulation experiments, it has been found that depending on the structure of the demand process, the appropriate selection of forecasting technique can reduce, or even eliminate (i.e., “dewhip”) the bullwhip effect. However, in terms of inventory variances it has been shown that the inventory variances for the exponential smoothing are greater than the minimum mean squared error forecasting method and that gap increases as lead time increases. These findings will help companies to choose the appropriate forecasting technique depending on the nature of demand. These guidelines can help companies to reduce the bullwhip effect and inventory variances across supply chain.     

Joint inventory and transshipment control for perishable products of a two-period lifetime

We analyze the impact of transshipments among retailers on their inventory replenishment decisions when products are perishable. Previous studies have shown that transshipments improve their operational efficiencies through inventory reallocation. However, these studies have not investigated transshipments for perishable products having a limited lifetime. In this paper, we consider a centrally managed firm owning several retail stores, which coordinates their replenishment policies along with the utilization of transshipments for perishable goods of a two-period lifetime. For this, the single-period planning horizon is analyzed, with a general solution approach for the optimal replenishment and transshipment decisions. We further present a designated solution approach for a two-location system as a special case and illustrate numerical examples in order to highlight the potential value of implementing transshipments for perishable products.     

联合生产存储问题的模拟退火算法

对确定性需求的联合补充生产存储控制系统进行分析，得出其关键问题是确定系统的联合生产补充周期和各产品的生产补充周期。建立了相应的模型，提出一个模拟退火算法，通过算例表明该算法可得出较优的可行解，与其他算法比较可以更有效地解决此类问题。