Optimal spare ordering policy under a rebate warranty

This paper develops, from the customer’s perspective, the optimal spare ordering policy for a non-repairable product with a limited-duration lifetime and under a rebate warranty. The spare unit for replacement is available only by order and the lead time for delivery follows a specified probability distribution. Through evaluation of gains due to the rebate and the costs due to ordering, shortage, and holding, we derive the expected cost per unit time and cost effectiveness in the long run and examine the optimal ordering time by minimizing or maximizing these cost expressions. We show that there exists a unique optimum solution under mild assumptions. We provide a numerical example and illustrate sensitivity analysis.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

EOQ holds under stochastic demand,a technical note

We consider a variant of the economic order quantity (EOQ) model. Mainly, we assume that demand occurs at random, one unit at a time, and is characterized by independent and identically distributed times between two demand epochs. We also assume that the ordering policy is characterized by ordering the same amount whenever the inventory level drops to zero, and a demand occurs. Surprisingly, we show that the optimal order quantity that minimizes the expected inventory cost follows the familiar EOQ formula.     

Continuous-review,lost-sales inventory models with Poisson demand,a fixed lead time and no fixed order cost

This paper considers continuous-review lost-sales inventory models with no fixed order cost and a Poisson demand process. There is a holding cost per unit per unit time and a lost sales cost per unit. The objective is to minimise the long run total cost. Base stock policies are, in general, sub-optimal under lost sales. The optimal policy would have to take full account of the remaining lead times on all the orders currently outstanding and such a policy would be too complex to analyse, let alone implement. This paper considers policies which make use of the observation that, for lost sales models, base stock policies can be improved by imposing a delay between the placement of successive orders. The performance of these policies is compared with that of the corresponding base stock policy and also with the policy of ordering at fixed and regular intervals of time.     

Optimum ordering polices with the effect of weather condition,random lead times and salvage cost

In this paper we deal with an optimum ordering policy for a one-unit system with a general lifetime, where the failed unit is scrapped without repair. A spare can only be provided after a lead time. Two kinds of orders (regular and emergency) are possible, each having a different, generally distributed lead time. Weather conditions are subject to a Markov process with two states-normal and abnormal which has a constant rate λ from normal to abnormal weather condition and μ from abnormal to normal respectively. The operational status of the unit is affected by the abnormal weather condition. The costs include downtimes, salvage, penalty, ordering costs. The optimal policy discussed is the one which maximizes the cost effectiveness, and is illustrated with a numerical example     

Optimal spare ordering policy for preventive replacement under cost effectiveness criterion

This paper presents a spare ordering policy for preventive replacement with age-dependent minimal repair and salvage value consideration. The spare unit for replacement is available only by order and the lead-time for delivering the spare due to regular or expedited ordering follows general distributions. To analyze the ordering policy, the failure process is modelled by a non-homogeneous Poisson process. By introducing the costs due to ordering, repairs, replacements and downtime, as well as the salvage value of an un-failed system, the expected cost effectiveness in the long run are derived as a criterion of optimality. It is shown, under certain conditions, there exists a finite and unique optimum ordering time which maximizes the expected cost effectiveness. Finally, numerical examples are given for illustration.     

A generalized discrete-time order replacement model

In this article, we consider a discrete-time order replacementproblem. More precisely, we treat a generalized model with morecomplex cost structure than Kaio & Osaki (1979, IEEE Trans.Reliab., R-29, 405–406) and with two decision variables:allowable inventory time and ordering time. Based on the discreteprobabilistic argument, we derive the optimal ordering policyto deliver a spare unit preventively by a regular order, soas to minimize the expected cost per unit time in the steadystate. Numerical examples are devoted to carrying out the sensitivityanalysis of model parameters on the optimal ordering policyand its associated expected cost value.     

An inventory model for slow moving items subject to obsolescence

In this paper, we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance. The inventory system is controlled according to a one-for-one replenishment policy with a fixed lead time. Adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks. We show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs. We propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period. We find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs.     

Models for 1-out-of Q systems with stochastic lead times and expedited ordering options for spares inventory

The purpose of this article is to develop two kinds of continuous-time cyclic inventory models with stochastic lead times and expedited ordering options. The order form under consideration is similar to that arising in the spare part inventory management. Especially, the control problem to determine the timing for the regular order is considered, and the optimal policy which minimizes the long-run average cost is analytically characterized. Finally, numerical examples are presented to evaluate the uncertainty of stochastic lead times, and the optimal inventory policy, which is composed of both the ordering time and the order quantity, is numerically calculated.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction

This study deals with the lead time and ordering cost reduction problem in the single-vendor single-buyer integrated inventory model. We consider that buyer lead time can be shortened at an extra crashing cost which depends on the lead time length to be reduced and the ordering lot size. Additionally, buyer ordering cost can be reduced through further investment. Two models are presented in this study. The first model assumes that the ordering cost reduction has no relation to lead time crashing. The second model assumes that the lead time and ordering cost reduction are interacted. An iterative procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.     

Integrating inventory control and a price change in the presence of reference price effects: a two-period model

Demand and procurement planning for consumer electronics products must cope with short life cycles, limited replenishment opportunities and a willingness to pay that is influenced by past prices and decreases over time. We therefore propose the use of an integrated pricing and inventory control model with a two-period linear demand model, in which demand also depends on the difference between a price-history-based reference price and the current price. For this model we prove that the optimal joint pricing/inventory policy for the replenishment opportunity after the first period is a base-stock list-price policy. That is, stock is either replenished up to a base-stock level and a list-price is charged, or it is not replenished and a discount is given that increases with the stock-level. Furthermore, we use real-world cell phone data to study the differences between an integrated policy and traditional sequential optimization, where prices are initially optimized based on the expected demand and ordering cost, and the resulting demand distribution is used to determine an optimal inventory policy. Finally, we discuss possible extensions of the model.     

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.     

考虑不完美检测的两阶段点检与备件订购策略联合优化

针对设备维修与备件管理相互影响与制约的问题, 在基于延迟时间理论的基础上, 提出了两阶段点检与备件订购策略联合优化。点检是不完美的, 当点检识别设备的缺陷状态时, 进行预防更新; 设备故障时, 进行故障更新。结合设备更新时备件的状态, 采用更新报酬理论建立了以第一阶段点检时间、第二阶段点检周期和备件订购时间为决策变量, 以最小化单位时间期望成本为目标的模型。最后, 通过人工蜂群算法对模型求解, 并在数值分析中将两阶段点检策略与定期点检策略进行比较, 结果表明:两阶段点检策略始终优于定期点检策略, 验证了所建模型的有效性。     

Analysis of a two-echelon inventory system with two supply modes

In this paper, we consider a serial two-echelon periodic review inventory system with two supply modes at the most upstream stock point. As control policy for this system, we propose a natural extension of the dual-index policy, which has three base-stock levels. We consider the minimization of long run average inventory holding, backlogging, and both per unit and fixed emergency ordering costs. We provide nested newsboy characterizations for two of the three base-stock levels involved and show a separability result for the difference with the remaining base-stock level. We extend results for the single-echelon system to efficiently approximate the distributions of random variables involved in the newsboy equations and find an asymptotically correct approximation for both the per unit and fixed emergency ordering costs. Based on these results, we provide an algorithm for setting base-stock levels in a computationally efficient manner. In a numerical study, we investigate the value of dual-sourcing in supply chains and illustrate that dual-sourcing can lead to significant cost savings in cases with high demand uncertainty, high backlogging cost or long lead times.     

两类供应风险下装配商的最优订购策略

针对两类供应风险(不确定产能与随机产出率)下装配制造商的零部件订购决策这一难题,运用随机非线性规划方法,以装配商期望利润最大化为目标,建立零部件订购决策的多维优化模型,刻画了确定需求下的最优订购量,并对其进行了灵敏性分析。最后,通过数值算例验证了模型结论并进一步探讨不同类供应风险的影响,为装配商的零部件订购决策和风险管理提供有益的管理启示。     

Economic optimization of off-line inspection with inspection errors

In this paper, we find the optimal inspection policy for the production process of a finite batch of items with inspection errors. We study the effects of inspection errors on the optimal solution and determine which unit should be inspected to minimize the expected total costs. We also find the expected number of inspections for a given batch size. Comparisons of total costs are investigated numerically among the cost minimizing policy, the policy of perfect information, and the policy of zero-defects.     

Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions

In this paper, we assume that the demands of different customers are not identical in the lead time. Thus, we investigate a continuous review inventory model involving controllable lead time and a random number of defective goods in buyer’s arriving order lot with partial lost sales for the mixtures of distributions of the lead time demand to accommodate more practical features of the real inventory systems. Moreover, we analyze the effects of increasing investment to reduce the lost sales rate when the order quantity, reorder point, lost sales rate and lead time are treated as decision variables. In our studies, we first assume that the lead time demand follows the mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. By analyzing the total expected cost function, we develop an algorithm to obtain the optimal ordering policy and the optimal investment strategy for each case. Finally, we provide numerical examples to illustrate the results.     

Determining optimal order splitting and reorder level for N-supplier inventory systems

This paper considers multiple-supplier single-item inventory systems, where the item acquisition lead times of suppliers and demand arrival are random, and backorder is allowed. The acquisition takes place when the inventory level depletes to a reorder level, and the order is split among multiple suppliers. The acquisition lead times may have different distributions, the unit purchasing prices from suppliers may be different, and thus the order quantities for different suppliers may be different. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per unit time, consisting of the fixed ordering cost, procurement cost, inventory holding cost and shortage cost, is minimized. We develop a mathematical model describing the system in detail. We also conduct extensive numerical experiments to analyze the advantages and distinct characteristics of multiple-supplier systems.