随机补货间隔且需求依赖库存水平的库存控制模型

定期补货库存模型在实践中被广泛使用,尤其是在单一供应商中购买多种不同产品的库存系统中更为常见.然而,大多数定期补货库存模型都假设补货的时间间隔是恒定不变的.但在实践中,补货的时间间隔也可能是一个随机的时间长度.提出了一个随机补货时间间隔和需求依赖于当前展示库存水平的库存控制模型,且补货间隔服从指数分布和均匀分布,同时允许短缺发生并且短缺量部分延期供给,并研究了模型最优解的存在性与唯一性.最后,给出了数值算例来说明模型在实际中的应用.     

需求依赖于展示区库存水平的易腐品订购和转运策略

本文主要研究易腐品零售商的订货和转运策略。零售商的库存分为两部分,即展示区/货架库存和仓库库存。零售商定期向供应商订货,零售商收到订购的商品首先将其中一部分商品存放在展示区中,余下的部分储存在仓库。展示区的空间是有限的,并且需求依赖于展示区商品的库存量。本文首先建立了以平均利润最大化为目标的库存优化模型并对模型最优解的存在性进行了分析,然后得到了求解最优订购量、转运量、转运时间间隔以及再订购点的算法,最后给出了不同参数条件下的算例。     

Integrated inventory problem under trade credit in fuzzy random environment

This paper is concerned with an integrated inventory problem under trade credit where both the demand rate and deteriorating rate are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The objective of this paper is to determine the optimal inventory policy by optimizing simultaneously the replenishment cycle length and trade credit period. At first, three decision criteria are given: (1) expected value criterion, (2) chance-constrained criterion and (3) chance maximization criterion. Then, after building the fuzzy random models based on the above decision criterion, a hybrid intelligent algorithm by integrating fuzzy random simulation and genetic algorithm is employed to deal with these models. At the end, three numerical examples are given to illustrate the benefits of the models and show the effectiveness of the algorithms.     

Joint pricing and inventory replenishment decisions with returns and expediting

We study a single-item periodic-review model for the joint pricing and inventory replenishment problem with returns and expediting. Demand in consecutive periods are independent random variables and their distributions are price sensitive. At the end of each period, after the demand is realized, a buyer can return excess stocks to a supplier. Or, if there are stockouts, the buyer can place an expediting order at the supplier to reduce the amount of shortage. Unfilled demands are fully backlogged. We characterize the optimal dynamic policy that determines the pricing, inventory replenishment, and adjustment decisions in each period so that the total expected discounted profit is maximized. For a very general stochastic demand function, we can show that the optimal replenishment policy is a modified base-stock policy, the optimal pricing policy is a modified base-stock-list-price policy, and the optimal policy for inventory adjustment follows a dual-threshold policy. We further study the operational effect of returns and expediting. Analytical and numerical results demonstrate that returns and expediting lead to a significant profit increase in a number of situations, including limited supply capacity, sufficient flexibility of the expediting order, high demand uncertainty, and a price-sensitive market.     

Integrated inventory and inspection policies for stochastic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier when his inventory level drops to a certain point, due to demand which is stochastic in nature. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. The order quantity, reorder point and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks is set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

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.     

PRODUCTION INVENTORY SYSTEM WITH RANDOM SUPPLY INTERRUPTIONS STATUE AND RANDOM LEAD TIMES

This article analyzes a continuous-review inventory system with random supply interruptions and random lead time which may be interrupted by a random number of supplier’s OFF periods. The inventory with constant demand rate is managed by a (r; q1, q2, ··· , qm) policy and supplies from an unreliable sole supplier. By renewal theory and matrix Geometric method, the long-run average cost function is obtained and some important properties of the function are proved. Furthermore, performance of the inventory is derived.     

Modeling and analysis for determining optimal suppliers under stochastic lead times

The policy of simultaneously splitting replenishment orders among several suppliers has received considerable attention in the last few years and continues to attract the attention of researchers. In this paper, we develop a mathematical model which considers multiple-supplier single-item inventory systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q)$(s\text{,}Q)$ policy has been assumed. When the inventory level depletes to a reorder level, the total order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost, and shortage cost, is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared with the models in the literature. According to our extensive experiments, the model developed in this paper is the best model in the literature which considers order splitting for n-supplier inventory systems since it is the nearest model to the real inventory system.     

A multi-product continuous review inventory system in stochastic environment with budget constraint

Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary and storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal review shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when order arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget constraint for inventory. In this paper with mixture of back orders and lost sales, we assume that mean and variance of lead time demand are known but their probability distributions are unknown. After that, we apply the minimax distribution free procedure to find the minimum expected value of the random objective function with budget constraint. The random budget constraint is transformed to crisp budget constraint by chance-constraint technique. Finally, the model is illustrated by a numerical example.     

Optimal production inventory policy for defective items with fuzzy time period

In this paper, an optimal production inventory model with fuzzy time period and fuzzy inventory costs for defective items is formulated and solved under fuzzy space constraint. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is linearly stock dependent. The defective rate is taken as random, the inventory holding cost and production cost are imprecise. The fuzzy parameters are converted to crisp ones using credibility measure theory. The different items have the different imprecise time periods and the minimization of cost for each item leads to a multi-objective optimization problem. The model is under the single management house and desired inventory level and product cost for each item are prescribed. The multi-objective problem is reduced to a single objective problem using Global Criteria Method (GCM) and solved with the help of Fuzzy Riemann Integral (FRI) method, Kuhn–Tucker condition and Generalised Reduced Gradient (GRG) technique. In optimum results including production functions and corresponding optimum costs for the different models are obtained and then are presented in tabular forms.     

Optimizing delivery lead time/inventory placement in a two-stage production/distribution system

In this paper we study a system composed of a supplier and buyer(s). We assume that the buyer faces random demand with a known distribution function. The supplier faces a known production lead time. The main objective of this study is to determine the optimal delivery lead time and the resulting location of the system inventory. In a system with a single-supplier and a single-buyer it is shown that system inventory should not be split between a buyer and supplier. Based on system parameters of shortage and holding costs, production lead times, and standard deviations of demand distributions, conditions indicating when the supplier or buyer(s) should keep the system inventory are derived. The impact of changes to these parameters on the location of system inventory is examined. For the case with multiple buyers, it is found that the supplier holds inventory for the buyers with the smallest standard deviations, while the buyers with the largest standard deviations hold their own inventory.     

Optimal ordering policies in inventory systems with random demand and random deal offerings

In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an ‘order up to’ policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an ‘order up to’ structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.     

Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times

This paper addresses a multi-period production/inventory problem with two suppliers, where demand sizes and supplier lead time are stochastic and correlated. A discrete time, single item inventory system is considered, where inventory levels are reviewed periodically and managed using a base-stock policy. At the end of each period, a replenishment order is placed, which enters a queue at the buffer stage and is consequently forwarded to the first available supplier. We present a mathematical model of this inventory system and determine optimal safety stock levels for it, in closed form, using matrix analytic techniques and the properties of phase type distributions. To account for the effect of order crossovers, which occur whenever replenishment orders do not arrive in the sequence in which they were placed, the inventory shortfall distribution is analyzed. Finally, a set of numerical experiments with a system with two suppliers is presented, where the proposed model is compared to other existing models.     

(s, S) Inventory systems with lost sales and Markov renewal demands

In the study of stochastic inventory systems it is generally assumed that the demand epochs are renewable in nature. The present paper deals with a single-item (s, S) inventory model with a finite number of different types of demands, in which the demand epochs form a Markov renewal process. The lead times are exponentially distributed and the demands that occur during stockout periods are not backordered. For this model the transient and limiting inventory level distributions are computed. Also the theory of point processes is used to obtain the mean reorder and shortage rates and their limiting values. For the special case of renewal demands, the problem of minimizing the long-run expected cost rate is analysed.     

Ordering Policies of Deteriorating Items under Permissible Delay in Payments

In developing mathematical models in inventory control it is assumed that payment will be made to the supplier for the goods immediately after receiving the consignment. However, in practice, it is found that the supplier allows a certain fixed period to settle the account. During this fixed period no interest is charged by the supplier, but beyond this period interest is charged under the terms and conditions agreed upon and, moreover, interest can be earned on the revenue received during the credit period. In this paper an attempt has been made to obtain the optimum order quantity of deteriorating items under a permissible delay in payments. A numerical example is also given.     

Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period’s demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.     

Inventory control in the presence of an electronic marketplace

This paper studies a periodic review inventory model in the presence of an electronic marketplace (EM). Emergency orders can be placed in the EM for additional cost, and excess inventory can be sold to the EM. When the order leadtime from the supplier is one period, the optimal inventory control policy is developed from a dynamic programming model of the problem. The policy is characterized by three critical inventory levels. When the order leadtime from the supplier is longer than one period, an EM policy is developed to determine the quantities of inventory to purchase from and sell to the EM in each period. Based on this EM policy, three ordering policies are proposed to determine the order quantity from the supplier. Numerical results show that significant cost reductions can be obtained by using the EM to adjust the inventory level in each period. The amount of cost reduction is greatly affected by system parameters, especially the order leadtime from the supplier and the costs for transactions in the EM.     

Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties

This paper considers a manufacturing supply chain with multiple suppliers in the presence of multiple uncertainties such as uncertain material supplies, stochastic production times, and random customer demands. The system is subject to supply and production capacity constraints. We formulate the integrated inventory management policy for raw material procurement and production control using the stochastic dynamic programming approach. We then investigate the supplier base reduction strategies and the supplier differentiation issue under the integrated inventory management policy. The qualitative relationships between the supplier base size, the supplier capabilities and the total expected cost are established. Insights into differentiating the procurement decisions to different suppliers are provided. The model further enables us to quantitatively achieve the trade-off between the supplier base reduction and the supplier capability improvement, and quantify the supplier differentiation in terms of procurement decisions. Numerical examples are given to illustrate the results.     

可滞后的易腐库存模型

本文研究了滞后时间为正的、连续盘点的 (s,S)易腐库存模型 .利用矩阵表示方法求出了平稳分布的递推表达式 ,证明了循环周期的分布服从 PH分布 ,并求得了费用函数 f (s,S.K) .     

考虑合格率的单周期产品供应链决策研究

本文研究由一个供应商和一个经销商组成的关于单周期产品的供应链系统。考虑产品具有随机合格率,并且合格率的分布是供应商的私人信息。在分布函数未知情况下比较研究了供应链三种竞争协调策略:供应商具有合格率私人信息,同时给予经销商价格折扣;供应商告诉经销商合格率分布但是不提供价格折扣;供应商管理经销商库存。比较分析和实例研究说明了三种策略对供应链整体绩效具有明显的优劣和实现帕累托优化的条件。