随机供应中断和退货环境下库存的应急控制

随机供应中断和退货环境下库存变化, 失去传统上的单调性, 呈现复杂的随机波动状态, 从而, 极大地增加了控制难度. 为解决系统库存的短缺和超储问题, 本文提出一个应急控制(包括应急采购和应急处理)策略. 在库存水平的动态变化表示为Lévy过程条件下, 利用连续时间Markov链、更新过程和鞅理论, 构建了系统期望折扣总利润模型, 并设计了交叉熵法确定最优控制策略. 仿真结果表明, 中断强度和类型及退货批次和批量, 对最优应急处理水平和应急采购量均有较大影响. 而退货类型仅影响最优应急处理水平, 对最优应急采购量影响较小.     

随机中断环境下的库存控制研究

考虑一需求为复合Poisson分布、提前期为指数分布和短缺损失的连续检查库存系统. 在假设供应商和零售商工作和中断的持续时间服从独立指数分布条件下, 利用水平穿越法, 确定零售商库存水平的平稳分布函数, 在此基础上, 构建长程平均费用率模型, 并利用交叉熵法得到最优库存控制策略. 最后, 通过仿真实验, a分析了中断强度和系统参数对最优库存策略和平均费用率的影响.     

基于购买行为的随机生命周期易逝品库存策略

研究需求和商品生命周期均为随机的零售商库存管理问题,提出按照购买行为特征对需求进行分类,在不同类型的客户之间进行库存分配并允许缺货的库存策略.通过构建动态规划模型,求解出零售商最优库存策略,包括补货策略和库存分配策略.与先到先服务策略相比,该策略能显著提升零售商的利润,减少商品损坏的损失.     

Inference for Weibull distribution under generalized order statistics

Based on generalized order statistics from Weibull distribution the approach of Bayesian and non-Bayesian estimation are discussed. We present a simple and efficient simulational algorithm for generating a generalized order statistics sample from any continuous distribution. Specializations to Bayesian and non-Bayesian estimators, some lifetime parameters and confidence intervals of progressive II censoring and record values are obtained and compared with the existing results. Two examples are given to illustrate the proposed estimators and the simulation algorithm.     

Behavior monitoring under uncertainty using Bayesian surprise and optimal action selection

The increasing trend towards delegating tasks to autonomous artificial agents in safety–critical socio-technical systems makes monitoring an action selection policy of paramount importance. Agent behavior monitoring may profit from a stochastic specification of an optimal policy under uncertainty. A probabilistic monitoring approach is proposed to assess if an agent behavior (or policy) respects its specification. The desired policy is modeled by a prior distribution for state transitions in an optimally-controlled stochastic process. Bayesian surprise is defined as the Kullback–Leibler divergence between the state transition distribution for the observed behavior and the distribution for optimal action selection. To provide a sensitive on-line estimation of Bayesian surprise with small samples twin Gaussian processes are used. Timely detection of a deviant behavior or anomaly in an artificial pancreas highlights the sensitivity of Bayesian surprise to a meaningful discrepancy regarding the stochastic optimal policy when there exist excessive glycemic variability, sensor errors, controller ill-tuning and infusion pump malfunctioning. To reject outliers and leave out redundant information, on-line sparsification of data streams is proposed.     

需求随机依赖库存环境下的订货仿真优化模型

需求的随机性和依赖库存性是库存问题的特点之一,在需求以泊松分布的形式随机依赖库存的条件下讨论了（Q,T）型库存控制问题。为了评估库存控制策略的平均盈利水平,建立了该库存问题的离散事件系统仿真模型,设计了一种基于仿真的种群重叠、遗传操作非重叠的进化算法,用以优化库存控制策略,类似设计了基于仿真的模拟退火和粒子群优化算法进行比较。通过实例分析了不同参数的变化对模型最优解的影响,灵敏度分析表明需求依赖库存效应越明显时,利润水平越高,最优订货策略越倾向于高库存、短周期和现货销售。仿真实例说明了基于仿真的优化算法的可行性、有效性。     

Integrated inventory and transportation decision for ubiquitous supply chain management

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.     

On jointly optimising the changes of seasonable goods and inventory replenishment

Retailers often need to replace soon-to-be-unseasonable products with new seasonable goods when the season changes. The trade-off for such activities involves choosing between the salvage loss of the unseasonable product and the profit of selling the seasonable product early. This article develops a periodic-review inventory model for planning the changes of seasonable goods with state-dependent demand and cost parameters. We show that the single-period optimal policy for product changes is a threshold policy based on the initial inventory of the unseasonable goods. The corresponding optimal inventory policy follows a Purchase-Keep-Dispose policy if the incumbent product is kept or a base-stock policy if the incumbent product is replaced. Numerically, we find that the structure of the multi-period optimal policy resembles that of the single-period model. We propose a heuristic to solve the multi-period model and demonstrate its effectiveness. Our research provides insights into dynamically managing seasonable goods.     

Analysis of Admission and Inventory Control Policies for Production Networks

Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.     

零售电商和回收政策对闭环供应链的影响研究

构建第三方回收下的双渠道闭环供应链模型,考虑了三种不同的决策情形来探讨零售电商参与和处理基金政策对供应链中决策、利润、需求和消费者剩余的影响。结果表明：零售电商参与使得传统零售商的产品价格和利润水平降低,制造商可以通过调整对零售电商的批发价格来提高其利润;第三方回收商的回收决策和最优利润不受到零售电商参与的影响,处理基金政策可以有效地提高产品回收数量,但也会使得正向供应链中企业的定价提高;零售电商会蚕食制造商原有的市场份额,但产品总需求量不发生变化。当进一步考虑处理基金政策时,市场总需求量出现下降的趋势;此外,零售电商参与和处理基金政策都会造成供应链中消费者总剩余的减少。     

Optimal Lot Sizing Policies For Sequential Online Auctions

This study proposes methods for determining the optimal lot sizes for sequential auctions that are conducted to sell sizable quantities of an item. These auctions are fairly common in business to consumer (B2C) auctions. In these auctions, the tradeoff for the auctioneer is between the alacrity with which funds are received, and the amount of funds collected by the faster clearing of inventory using larger lot sizes. Observed bids in these auctions impact the auctioneer's decision on lot sizes in future auctions. We first present a goal programming approach for estimating the bid distribution for the bidder population from the observed bids, readily available in these auctions. We then develop models to compute optimal lot sizes for both stationary and non-stationary bid distributions. For stationary bid distribution, we present closed form solutions and structural results. Our findings show that the optimal lot size increases with inventory holding costs and number of bidders. Our model for non-stationary bid distribution captures the inter-auction dynamics such as the number of bidders, their bids, past winning bids, and lot size. We use simulated data to test the robustness of our model.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

A heuristic method for the inventory routing and pricing problem in a supply chain

The inventory routing problem (IRP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers and inventory policy for retailers. In the past, the pricing and demand decisions seem ignored and assumed known in most IRP researches. Since the pricing decision affects the demand decision and then both inventory and routing decisions, it should be considered in the IRP simultaneously to achieve the objective of maximal profit in the supply chain. In this paper, a mathematical model for the inventory routing and pricing problem (IRPP) is proposed. Since the solution for this model is an NP (non-polynomial) problem, a heuristic method, tabu search adopting different neighborhood search approaches, is used to obtain the optimal solution. The proposed heuristic method was compared with two other methods considering the IRPP separately. The experimental results indicate that the proposed method is better than the two other methods in terms of average profit.     

动态定价策略下的精确库存成本建模与优化

提出一种更接近实际的需求率公式,在式中同时考虑了价格和出厂时间对客户需求率的影响.基于新的需求率公式,建立了动态定价策略下的精确库存持有成本模型和库存商品的利润函数.注意到利润函数的复杂性,使用遗传算法分析了利润函数的性质,得出最优定价时间、定价价格和最大利润的关系,并分析了库存持有成本变化和消费者购买欲望变化对各定价参数的影响.     

Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.     

Optimal pricing policies for services with consideration of facility maintenance costs

For survival and success, pricing is an essential issue for service firms. This article deals with the pricing strategies for services with substantial facility maintenance costs. For this purpose, a mathematical framework that incorporates service demand and facility deterioration is proposed to address the problem. The facility and customers constitute a service system driven by Poisson arrivals and exponential service times. A service demand with increasing price elasticity and a facility lifetime with strictly increasing failure rate are also adopted in modelling. By examining the bidirectional relationship between customer demand and facility deterioration in the profit model, the pricing policies of the service are investigated. Then analytical conditions of customer demand and facility lifetime are derived to achieve a unique optimal pricing policy. The comparative statics properties of the optimal policy are also explored. Finally, numerical examples are presented to illustrate the effects of parameter variations on the optimal pricing policy.     

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

This paper¹ considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all. This work was supported by Science Foundation Ireland under Grant No. 03/CE3/I405 as part of the Centre for Telecommunications Value-Chain-Driven Research (CTVR) and Grant No. 00/PI.1/C075. ¹This paper is an extended version of [19].     

Multi-period optimization with loss-averse customer behavior: Joint pricing and inventory decisions with stochastic demand

To maximize a firm's profit over a finite planning horizon, we develop a dynamic optimization model by considering loss aversion when making pricing and inventory decisions. We estimate customer demand through a choice model, which incorporates reference price, utility function and customer loss aversion. Our model forms the core of the expert system for decision support. Through a sequence of Bellman equations, we find that the firm's profit is a concave function of price and inventory, and we solve the model optimally. The profit is positively correlated with the reference price, and the price and inventory decisions are non-monotonic functions of loss aversion intensity. Our results shed new light on pricing and inventory management with customer behavior in a multi-period system. Through various theorem developments, we are able to identify the optimal inventory level and the corresponding price. Numerical examples are provided to illustrate and validate the model and to derive managerial insights. To show the potential significance, we demonstrate how a dynamic programming model yields good results with customer loss aversion under realistic customer behavior assumptions. Our system can improve the efficiency of decision making and provide better customer service.     

Joint pricing and replenishment policies for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint

This study develops an inventory model for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint. The model assumes price sensitive demand when the product has no deterioration and price and time dependent demand when the product has deterioration. Under these considerations, the study attempts to offer best policy for selling price and replenishment cycle for the retailer that aims at maximizing the total profit per unit time. Making use of nearest interval approximation and interval arithmetic, the single objective problem is transformed to multi objective problem. Employing Weighted Sum Method, an analytical approach along with simple algorithm is developed to identify Pareto optimal solution. Finally, the behavior of the model with varied parameters is illustrated in numerical examples.     

Non-stationary fuzzy Markov chain

This paper deals with a recent statistical model based on fuzzy Markov random chains for image segmentation, in the context of stationary and non-stationary data. On one hand, fuzzy scheme takes into account discrete and continuous classes through the modeling of hidden data imprecision and on the other hand, Markovian Bayesian scheme models the uncertainty on the observed data. A non-stationary fuzzy Markov chain model is proposed in an unsupervised way, based on a recent Markov triplet approach. The method is compared with the stationary fuzzy Markovian chain model. Both stationary and non-stationary methods are enriched with a parameterized joint density, which governs the attractiveness of the neighbored states. Segmentation task is processed with Bayesian tools, such as the well known MPM (Mode of Posterior Marginals) criterion. To validate both models, we perform and compare the segmentation on synthetic images and raw optical patterns which present diffuse structures.