A periodic review inventory model with loss-averse retailer,random supply capacity and demand

This paper studies a periodic review inventory model with random supply capacity and demand, where the retailer is loss-averse. For the single-period problem, it is shown that the retailer will not order unless the initial inventory level is less than a critical value, and the order-up-to level is generally not a constant. Moreover, the critical value and optimal order quantity are only dependent on the random demand and independent on the random capacity. We also investigate the impacts of loss aversion, price and cost on the optimal order quantity and maximum expected utility. Then a dynamic programming approach is used to analyse the retailer’s ordering policy in the multi-period case. In each period, if the initial inventory level is above a given value, an order will not be placed. Otherwise, the upper bound on the optimal order quantity is given. The numerical experiments are conducted to illustrate the optimal ordering policies.     

A comprehensive analysis of the Newsvendor model with unreliable supply

A single-period, uncertain demand inventory model is analyzed under the assumption that the quantity ordered (produced) is a random variable. We first conduct a comprehensive analysis of the well known single period production/inventory model with random yield. Then, we extend some of the results existing in literature: our main contribution is to show that earlier results are only valid for a certain range of system parameters. Under the hypothesis that demand and the error in the quantity received from supplier are uniformly distributed, closed-form analytical solutions are obtained for all values of parameters. An analysis under normally distributed demand and error is also provided. The paper ends with an analysis of the benefit achieved by eliminating errors.     

经济生产批量与CUSUM控制图最优化联合设计

针对传统经济生产批量一般以完美生产过程为对象,质量成本通常也仅以符合规格为判断的标准等问题,提出了一种考虑田口损失函数的将经济生产批量与累积和控制图联合设计的模型。对于生产过程,提出了一种更符合实际情况的三阶段的制造过程,建立了考虑均值随机偏移的三阶段损失模型,并以此为基础,建立了综合考虑包括质量损失及与批量相关的储存成本、订货成本等在内的总期望成本,目的是获得最优化的经济生产批量和累积以及控制图参数设计联合模型,并使生产过程的总期望成本最小。采用行径搜索法对模型进行求解,并举出数值例子进行比较和参数敏感度分析加以说明模型的应用情况。     

Determining the optimal lot size for the finite production model with random defective rate,the rework process,and backlogging

This paper considers the effects of the reworking of defective items on the economic production quantity (EPQ) model with backlogging allowed. The classic EPQ model assumes that manufacturing facility functions perfectly during a production run. However, due to process deterioration or other factors, the production process may shift and produce imperfect quality items. In this study, a random defective rate is considered, and when regular production ends, the reworking of defective items starts immediately. Not all of the defective items are reworked, a portion of them are scrap and are discarded. Repairing and holding cost per reworked item and disposal cost per scrap item are included in the proposed mathematical modelling and analysis. The renewal reward theorem is utilized to deal with the variable cycle length, and the optimal lot size that minimizes the overall costs for the imperfect quality EPQ model is derived where backorders are permitted.     

Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption

A two-echelon supply chain involving one manufacturer and one retailer for a single product is considered in this paper. The end customers’ demand is assumed to be random. The production of the manufacturer is subject to random yield, and there is a possibility of supply disruption in which case no item from her can reach the retailer. The retailer has a backup supplier who is costlier but perfectly reliable, and is having a limit up to which he may deliver. In addition to placing an order to the manufacturer, the retailer is allowed to reserve a quantity from the backup supplier in the ordering period; he may buy up to the reserved quantity after realising actual market demand in the trading period. Aiming at studying the effects of the various uncertainties involved in the chain on the optimal decisions, we develop and analyse centralised and decentralised models. We also propose a contract mechanism to coordinate the chain and find threshold conditions for which the coordinated model would collapse. Numerical examples are provided to illustrate the developed model.     

A stochastic inventory model for an immediate liquidation and price-promotion decision under price-dependent demand

We consider a periodic review stochastic inventory system where the current on-hand inventory exceeds the maximum supply needs in the future. Consequently, one must make an immediate inventory liquidation decision on the liquidation quantity and promotional price with the goal of maximising the overall profit where the demand during the liquidation period (DDLP) is a random variable whose distribution depends on the promotional price. We develop a price-dependent DDLP model and an inventory model for optimising the liquidation quantity and unit promotional price. The model is applicable for general distributions of the DDLP and regular demand (i.e. demand during the future periods following the promotion period). We also investigate four special cases where the DDLP and regular demand are assumed to be either exponential or uniform random variables. The two models that assume the exponential distribution for regular demand can be examined analytically and simplified using the mathematical properties we derive. The additional two models that assume the uniform distribution for regular demand do not have closed-form expressions but can be solved numerically. Some numerical examples are presented for further elaboration of the models and to demonstrate their practical use.     

Cohesive bonding interface model for the effective properties of randomly structured composites

The present paper aims at quantifying the effective behaviour of random composites at the microstructure scale using different combinations of intrinsic phase and interface properties. The composite microstructure is generated using Monte Carlo simulation. The methodology allows random spatial distribution of phases. It aims also at providing different evolutions of the interface quantity as function of phase ratio. Microstructures are then converted into finite element model. The FE model handles the interface effect using a cohesive zone model. This model represents the interface separation and traction using three parameters derived from a surface potential function. The sensitivity of the effective elastic properties to both interface and phase properties is then quantified. The predicted results show a strong non-linear dependence of the effective properties on the interface effect.     

A renewal reward approximation for the variance of electric power production costs

The cost of producing electric power over a specified study horizon is a random quantity influenced by random failures and repair times for the generating units and variations in demand over time. Previous approaches for determining the variance of the production cost have required implicit or explicit enumeration of a large set of availability or capacity states for the generation system. In this paper, a simplifying assumption makes possible' a renewal reward model for the production cost. Formulas are provided to estimate the asymptotic variance for intermediate to long study horizons and their results are illustrated with a numerical example.     

A generalized economic model for joint determination of production run,inspection schedule and control chart design

This paper presents a generalized model for a continuous production process for simultaneous determination of production quantity, inspection schedule and control chart design, with a non-zero inspection time for false alarms. Traditionally, the quality control problem and the inventory control problem have been viewed as two separate problems. Rahim (1994) developed an economic model for joint determination of production quantity, inspection schedule, and control chart design for a typical production process which is subject to a non-Markovian random shock. The model consists of the following cost components: (1) the production setup cost, (2) the inventory holding cost, and (3) the cost of maintaining the quality of the product under the surveillance of an x-chart. The optimal production quanity, the optimal inspection schedules, and the economic design parameters of the control charts were determined by striking a balance among these costs. For mathematical simplicity, it was assumed that production ceases only if the process was found to be out-of-control. However, in reality, this assumption may be inapplicable in many industrial situations. In many production processes the machine must be shut down when a search for the assignable cause is being carried out, even though occasionally the alarm turns out to be false. The purpose of this paper is to generalize the above model to cases where production ceases not only for a true alarm but also for a fixed amount of time whenever there is a false alarm. Examples of Weibull shock models are used to illustrate the proposed generalized model.     

Optimal production run length and inspection schedules in a deteriorating production process

This paper presents an economic manufacturing quantity model which determines an optimal production run length and inspection schedules simultaneously in a deteriorating production process. It is assumed that a production process is subject to a random deterioration from the in-control state to the out-of-control state and, thus, produces some proportion of defective items. An optimal production run length and an optimal number of inspections are derived, and unique properties of the proposed model are discussed. A numerical experiment is carried out to examine the behavior of the proposed model and compare the proposed model to an existing model.     

地区市场分割对创新数量、创新质量的影响机制研究

从创新数量与创新质量角度分析市场分割的影响机制、影响大小、影响规律具有重要意义。本文基于中国高技术产业统计年鉴数据,综合采用面板数据模型、面板门槛回归模型、贝叶斯向量自回归模型全面分析了市场分割与创新数量、创新质量之间的关系。研究结果表明:市场分割总体上与创新数量、创新质量无关,市场分割对创新的正向影响与负向影响产生的效应相当;市场分割越严重,对创新数量的正向影响越大,对创新质量的间接负向效应也越大;但市场分割也有积极的一面,表现为市场分割有利于低水平创新数量和创新质量地区创新;此外创新数量与创新质量具有一定的负向互动机制。     

Supply chain coordination with trade credit under the CVaR criterion

Trade credit is a popular payment method in the supply chain. However, it may transfer the market risk facing by the retailer to the manufacturer in the form of default risk. To reduce the default loss, we set up a modified newsvendor model incorporating random default probability. Under the goal of loss minimisation, the manufacturer’s optimal production quantity is derived with the criterion of conditional value at risk, and compared with the retailer’s optimal order quantity. It is found that, compared with traditional newsvendor setting, the setting of default possibility in trade credit can increase the order quantity but decrease the production quantity. If the risk aversion level and gross profit of product are low, the manufacturer may deliver below the quantity ordered. Although the default loss can be reduced by cutting order, the profits of both agents decrease, thereby leading to a deviation from the supply chain coordination. Trade credit coordinating the supply chain requires an extremely long credit period, which is not feasible. Moreover, quantity discount contract is able to improve the retailer’s order quantity, but insufficient to achieve coordination, which also depends on the manufacturer’s risk aversion level.     

Economic production quantity model for deteriorating inventory with random machine unavailability and shortage

Both random machine unavailability and shortage are common occurrences in manufacturing industries. In this paper, machine unavailability is considered in deriving an economic production quantity (EPQ) model for deteriorating items. We develop four EPQ models for deteriorating inventory with random machine unavailability and shortage. The study considers lost sales, backorder and two kinds of machine unavailability distributions. Numerical examples are provided to illustrate the theory. Key parameter changes that affect costs are shown in the sensitivity analysis. From the results of the sensitivity analysis, it is shown that the random machine unavailability parameter and holding cost have significant effects on the optimal total cost and production down-time.     

A bidding decision model in multiagent supply chain planning

The multiagent environment for supply chain planning application is based on a framework unifying the internal behaviour of agents and coordination among agents. This system presents a formal view of coordination using Contract Net Protocol (CNP) that relies on the basic loop of agent behaviours: order receiving, order announcement, bid calculation, and order scheduling followed by order execution. Among these, bid calculation is most difficult. It needs to determine the quantity, cost and time in which a new order can be implemented. Fuzzy programming has made progress in mathematics since Bellman and Zadeh (1970) first studied decision-making in a fuzzy mathematics programming. Currently there are many valuable works in this field (Zimmermann 1983, 1985, Tanaka and Asai 1984) and fuzzy programming has become an effective tool to deal with the decision-making problems in fuzzy systems. Similarly, stochastic programming is a useful tool to treat decision-making problems in a stochastic system (Kolbin 1977, Kall and Wallace 1994). However, in many practical systems, fuzzy factors and random factors arise concurrently, and this problem has not received the attention it deserves. Therefore, there is a need to develop a new kind of optimization technique to make decisions in a fuzzy random system. In this paper, we build the Bid Calculation model, including a random parameter set, the set of product quantity that will be stored to inventory, a fuzzy parameter set, the Maximum Sales Rates (MSR) set, and we discuss an approach to solve the model, as well as present an implementation procedure with the GA method.     

A program for identifying the form of the distribution law of random quantities and their modeling

A program for identifying the form of the distribution law of a random quantity is described. The dependence of the optimum number of intervals when constructing histograms from a volume of the sample (10–100,000) and of the kurtosis (in the limits 2–9.65) is determined by computer modeling. Using 50 different functions, the program can also model random quantities with unimodal and bimodal distribution laws. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 9–14, May, 2007.     

价格随机条件下的应急双向期权数量弹性契约

旨在用期权应对批发价格波动的风险,用数量弹性契约来应对市场价格和市场需求随机波动带来的风险,探索双向期权数量弹性契约协调供应链的内在规律。将双向期权契约与数量弹性契约相融合,协调批发价、市场价格和市场需求均随机波动的供应链,寻找最优的供应链决策,并进行了算例仿真。研究结果表明：在批发价格波动时,采用双向期权弹性契约比采用基准数量弹性契约效果更好。双向期权弹性契约可以协调批发价格和市场价格均随机的供应链。     

The value of updated information on future price behaviour

This paper studies the value of information on future price behaviour. We consider a one-period inventory modelling framework with random period length and two order opportunities. The selling price is determined dynamically and the demand is price-sensitive. The second ordering-pricing decision reflects the updated information on future price behaviour on supply chain flexibility. We consider three models with different levels of flexibility: the static model, the quantity flexible model and the combined quantity and timing (fully) flexible model. We compare between the values of three different features in the supply chain: updated information on price behaviour, dynamic pricing and supply flexibility. And we demonstrate the effect of holding cost and demand uncertainty on these three values. We also consider a specific condition with fixed selling prices. We give explicit analysis on the optimal order decisions, and analytically show the impact of information and quantity flexibility on the optimal order decisions.     

Economic ordering model for deteriorating items with random demand and deterioration

In modern marketplaces, competitive products frequently face volatile demand. In particular, the majority of deteriorating items are frequently subject to dual uncertainty, simultaneously suffering from demand and deterioration. Accordingly, this study attempts to develop an economic ordering model for a newsboy-style deteriorating item with lognormal demand and Poisson-type deterioration. Finally, an effective and practical economic ordering model involving deteriorating inventory is developed for optimising the order quantity of a given deteriorating item during an upcoming selling period to maximise expected profits of retailers. Numerical examples demonstrate that, as expected, the proposed economic ordering model can obtain an optimal solution for the inventory problem involving deteriorating items under uncertain and random demand and deterioration.     

Economic lot sizing for an imperfect production system subject to random breakdowns

This article considers an economic manufacturing quantity model for an imperfect production process that is subject to random machine breakdowns. The product is manufactured intermittently in batches to meet a constant demand. During a production run, the system is assumed to deteriorate over time. As a result, a fixed proportion of items produced are defective. The system is also subject to random breakdowns. A no-resumption inventory control policy is adopted. Under this policy, the production run is aborted when a breakdown occurs. Production will be resumed only when all on-hand inventories are depleted. Corrective maintenance is carried out immediately after a breakdown. The time-to-shift and the time-to-breakdown are two random variables following different exponential distributions. The objective is to find an optimal production lot size that minimizes the expected (long-run) total cost per unit time. Several models are investigated and a numerical approach is developed to obtain an optimal production lot size.     

质子交换膜中质子输送过程的模拟

模拟了质子在质子交换膜(PEMs)中的输送过程。根据Nafion等磺化类PEMs的可能结构。借助无规行走模型研究了PEMs中不同组分间质子跃迁距离等参数对质子输送扩散系数的影响。并把从两维体系得到的结果和三维体系的结果进行比较。通过改变不同组分间的跃迁距离分析PEMs体系的变化。结果表明两者模拟结果无大的差别。已有文献表明质子在PEMs中输送是链段运动输送和质子跃迁输送双重作用的结果。二者的贡献大小取决于具体质子导电体系的种类。利用格子重排和无规行走模型研究了这两种机理对质子导电性能的贡献。